/*     ----------------------------------------------------------------
*
*                               sgp4unit.cpp
*
*    this file contains the sgp4 procedures for analytical propagation
*    of a satellite. the code was originally released in the 1980 and 1986
*    spacetrack papers. a detailed discussion of the theory and history
*    may be found in the 2006 aiaa paper by vallado, crawford, hujsak,
*    and kelso.
*
*                            companion code for
*               fundamentals of astrodynamics and applications
*                                    2013
*                              by david vallado
*
*     (w) 719-573-2600, email dvallado@agi.com, davallado@gmail.com
*
*    current :
*              12 mar 20  david vallado
*                           chg satnum to string for alpha 5 or 9-digit
*    changes :
*               7 dec 15  david vallado
*                           fix jd, jdfrac
*               3 nov 14  david vallado
*                           update to msvs2013 c++
*              30 aug 10  david vallado
*                           delete unused variables in initl
*                           replace pow integer 2, 3 with multiplies for speed
*               3 nov 08  david vallado
*                           put returns in for error codes
*              29 sep 08  david vallado
*                           fix atime for faster operation in dspace
*                           add operationmode for afspc (a) or improved (i)
*                           performance mode
*              16 jun 08  david vallado
*                           update small eccentricity check
*              16 nov 07  david vallado
*                           misc fixes for better compliance
*              20 apr 07  david vallado
*                           misc fixes for constants
*              11 aug 06  david vallado
*                           chg lyddane choice back to strn3, constants, misc doc
*              15 dec 05  david vallado
*                           misc fixes
*              26 jul 05  david vallado
*                           fixes for paper
*                           note that each fix is preceded by a
*                           comment with "sgp4fix" and an explanation of
*                           what was changed
*              10 aug 04  david vallado
*                           2nd printing baseline working
*              14 may 01  david vallado
*                           2nd edition baseline
*                     80  norad
*                           original baseline
*       ----------------------------------------------------------------      */

#include "SGP4.h"

#define pi 3.14159265358979323846

// define global variables here, not in .h
// use extern in main
char help = 'n';
FILE *dbgfile;

/* ----------- local functions - only ever used internally by sgp4 ---------- */
static void dpper
(
double e3, double ee2, double peo, double pgho, double pho,
double pinco, double plo, double se2, double se3, double sgh2,
double sgh3, double sgh4, double sh2, double sh3, double si2,
double si3, double sl2, double sl3, double sl4, double t,
double xgh2, double xgh3, double xgh4, double xh2, double xh3,
double xi2, double xi3, double xl2, double xl3, double xl4,
double zmol, double zmos, double inclo,
char init,
double& ep, double& inclp, double& nodep, double& argpp, double& mp,
char opsmode
);

static void dscom
(
double epoch, double ep, double argpp, double tc, double inclp,
double nodep, double np,
double& snodm, double& cnodm, double& sinim, double& cosim, double& sinomm,
double& cosomm, double& day, double& e3, double& ee2, double& em,
double& emsq, double& gam, double& peo, double& pgho, double& pho,
double& pinco, double& plo, double& rtemsq, double& se2, double& se3,
double& sgh2, double& sgh3, double& sgh4, double& sh2, double& sh3,
double& si2, double& si3, double& sl2, double& sl3, double& sl4,
double& s1, double& s2, double& s3, double& s4, double& s5,
double& s6, double& s7, double& ss1, double& ss2, double& ss3,
double& ss4, double& ss5, double& ss6, double& ss7, double& sz1,
double& sz2, double& sz3, double& sz11, double& sz12, double& sz13,
double& sz21, double& sz22, double& sz23, double& sz31, double& sz32,
double& sz33, double& xgh2, double& xgh3, double& xgh4, double& xh2,
double& xh3, double& xi2, double& xi3, double& xl2, double& xl3,
double& xl4, double& nm, double& z1, double& z2, double& z3,
double& z11, double& z12, double& z13, double& z21, double& z22,
double& z23, double& z31, double& z32, double& z33, double& zmol,
double& zmos
);

static void dsinit
(
//sgp4fix no longer needed pass in xke
//gravconsttype whichconst,
double xke,
double cosim, double emsq, double argpo, double s1, double s2,
double s3, double s4, double s5, double sinim, double ss1,
double ss2, double ss3, double ss4, double ss5, double sz1,
double sz3, double sz11, double sz13, double sz21, double sz23,
double sz31, double sz33, double t, double tc, double gsto,
double mo, double mdot, double no, double nodeo, double nodedot,
double xpidot, double z1, double z3, double z11, double z13,
double z21, double z23, double z31, double z33, double ecco,
double eccsq, double& em, double& argpm, double& inclm, double& mm,
double& nm, double& nodem,
int& irez,
double& atime, double& d2201, double& d2211, double& d3210, double& d3222,
double& d4410, double& d4422, double& d5220, double& d5232, double& d5421,
double& d5433, double& dedt, double& didt, double& dmdt, double& dndt,
double& dnodt, double& domdt, double& del1, double& del2, double& del3,
double& xfact, double& xlamo, double& xli, double& xni
);

static void dspace
(
int irez,
double d2201, double d2211, double d3210, double d3222, double d4410,
double d4422, double d5220, double d5232, double d5421, double d5433,
double dedt, double del1, double del2, double del3, double didt,
double dmdt, double dnodt, double domdt, double argpo, double argpdot,
double t, double tc, double gsto, double xfact, double xlamo,
double no,
double& atime, double& em, double& argpm, double& inclm, double& xli,
double& mm, double& xni, double& nodem, double& dndt, double& nm
);

static void initl
(
// not needeed. included in satrec if needed later 
// int satn,      
// sgp4fix assin xke and j2
// gravconsttype whichconst,
double xke, double j2,
double ecco, double epoch, double inclo, double& no,
char& method,
double& ainv, double& ao, double& con41, double& con42, double& cosio,
double& cosio2, double& eccsq, double& omeosq, double& posq,
double& rp, double& rteosq, double& sinio, double& gsto, char opsmode
);

namespace SGP4Funcs
{

	/* -----------------------------------------------------------------------------
	*
	*                           procedure dpper
	*
	*  this procedure provides deep space long period periodic contributions
	*    to the mean elements.  by design, these periodics are zero at epoch.
	*    this used to be dscom which included initialization, but it's really a
	*    recurring function.
	*
	*  author        : david vallado                  719-573-2600   28 jun 2005
	*
	*  inputs        :
	*    e3          -
	*    ee2         -
	*    peo         -
	*    pgho        -
	*    pho         -
	*    pinco       -
	*    plo         -
	*    se2 , se3 , sgh2, sgh3, sgh4, sh2, sh3, si2, si3, sl2, sl3, sl4 -
	*    t           -
	*    xh2, xh3, xi2, xi3, xl2, xl3, xl4 -
	*    zmol        -
	*    zmos        -
	*    ep          - eccentricity                           0.0 - 1.0
	*    inclo       - inclination - needed for lyddane modification
	*    nodep       - right ascension of ascending node
	*    argpp       - argument of perigee
	*    mp          - mean anomaly
	*
	*  outputs       :
	*    ep          - eccentricity                           0.0 - 1.0
	*    inclp       - inclination
	*    nodep        - right ascension of ascending node
	*    argpp       - argument of perigee
	*    mp          - mean anomaly
	*
	*  locals        :
	*    alfdp       -
	*    betdp       -
	*    cosip  , sinip  , cosop  , sinop  ,
	*    dalf        -
	*    dbet        -
	*    dls         -
	*    f2, f3      -
	*    pe          -
	*    pgh         -
	*    ph          -
	*    pinc        -
	*    pl          -
	*    sel   , ses   , sghl  , sghs  , shl   , shs   , sil   , sinzf , sis   ,
	*    sll   , sls
	*    xls         -
	*    xnoh        -
	*    zf          -
	*    zm          -
	*
	*  coupling      :
	*    none.
	*
	*  references    :
	*    hoots, roehrich, norad spacetrack report #3 1980
	*    hoots, norad spacetrack report #6 1986
	*    hoots, schumacher and glover 2004
	*    vallado, crawford, hujsak, kelso  2006
	----------------------------------------------------------------------------*/

	static void dpper
		(
		double e3, double ee2, double peo, double pgho, double pho,
		double pinco, double plo, double se2, double se3, double sgh2,
		double sgh3, double sgh4, double sh2, double sh3, double si2,
		double si3, double sl2, double sl3, double sl4, double t,
		double xgh2, double xgh3, double xgh4, double xh2, double xh3,
		double xi2, double xi3, double xl2, double xl3, double xl4,
		double zmol, double zmos, double inclo,
		char init,
		double& ep, double& inclp, double& nodep, double& argpp, double& mp,
		char opsmode
		)
	{
		/* --------------------- local variables ------------------------ */
		const double twopi = 2.0 * pi;
		double alfdp, betdp, cosip, cosop, dalf, dbet, dls,
			f2, f3, pe, pgh, ph, pinc, pl,
			sel, ses, sghl, sghs, shll, shs, sil,
			sinip, sinop, sinzf, sis, sll, sls, xls,
			xnoh, zf, zm, zel, zes, znl, zns;

		/* ---------------------- constants ----------------------------- */
		zns = 1.19459e-5;
		zes = 0.01675;
		znl = 1.5835218e-4;
		zel = 0.05490;

		/* --------------- calculate time varying periodics ----------- */
		zm = zmos + zns * t;
		// be sure that the initial call has time set to zero
		if (init == 'y')
			zm = zmos;
		zf = zm + 2.0 * zes * sin(zm);
		sinzf = sin(zf);
		f2 = 0.5 * sinzf * sinzf - 0.25;
		f3 = -0.5 * sinzf * cos(zf);
		ses = se2* f2 + se3 * f3;
		sis = si2 * f2 + si3 * f3;
		sls = sl2 * f2 + sl3 * f3 + sl4 * sinzf;
		sghs = sgh2 * f2 + sgh3 * f3 + sgh4 * sinzf;
		shs = sh2 * f2 + sh3 * f3;
		zm = zmol + znl * t;
		if (init == 'y')
			zm = zmol;
		zf = zm + 2.0 * zel * sin(zm);
		sinzf = sin(zf);
		f2 = 0.5 * sinzf * sinzf - 0.25;
		f3 = -0.5 * sinzf * cos(zf);
		sel = ee2 * f2 + e3 * f3;
		sil = xi2 * f2 + xi3 * f3;
		sll = xl2 * f2 + xl3 * f3 + xl4 * sinzf;
		sghl = xgh2 * f2 + xgh3 * f3 + xgh4 * sinzf;
		shll = xh2 * f2 + xh3 * f3;
		pe = ses + sel;
		pinc = sis + sil;
		pl = sls + sll;
		pgh = sghs + sghl;
		ph = shs + shll;

		if (init == 'n')
		{
			pe = pe - peo;
			pinc = pinc - pinco;
			pl = pl - plo;
			pgh = pgh - pgho;
			ph = ph - pho;
			inclp = inclp + pinc;
			ep = ep + pe;
			sinip = sin(inclp);
			cosip = cos(inclp);

			/* ----------------- apply periodics directly ------------ */
			//  sgp4fix for lyddane choice
			//  strn3 used original inclination - this is technically feasible
			//  gsfc used perturbed inclination - also technically feasible
			//  probably best to readjust the 0.2 limit value and limit discontinuity
			//  0.2 rad = 11.45916 deg
			//  use next line for original strn3 approach and original inclination
			//  if (inclo >= 0.2)
			//  use next line for gsfc version and perturbed inclination
			if (inclp >= 0.2)
			{
				ph = ph / sinip;
				pgh = pgh - cosip * ph;
				argpp = argpp + pgh;
				nodep = nodep + ph;
				mp = mp + pl;
			}
			else
			{
				/* ---- apply periodics with lyddane modification ---- */
				sinop = sin(nodep);
				cosop = cos(nodep);
				alfdp = sinip * sinop;
				betdp = sinip * cosop;
				dalf = ph * cosop + pinc * cosip * sinop;
				dbet = -ph * sinop + pinc * cosip * cosop;
				alfdp = alfdp + dalf;
				betdp = betdp + dbet;
				nodep = fmod(nodep, twopi);
				//  sgp4fix for afspc written intrinsic functions
				// nodep used without a trigonometric function ahead
				if ((nodep < 0.0) && (opsmode == 'a'))
					nodep = nodep + twopi;
				xls = mp + argpp + cosip * nodep;
				dls = pl + pgh - pinc * nodep * sinip;
				xls = xls + dls;
				xnoh = nodep;
				nodep = atan2(alfdp, betdp);
				//  sgp4fix for afspc written intrinsic functions
				// nodep used without a trigonometric function ahead
				if ((nodep < 0.0) && (opsmode == 'a'))
					nodep = nodep + twopi;
				if (fabs(xnoh - nodep) > pi)
					if (nodep < xnoh)
						nodep = nodep + twopi;
					else
						nodep = nodep - twopi;
				mp = mp + pl;
				argpp = xls - mp - cosip * nodep;
			}
		}   // if init == 'n'

		//#include "debug1.cpp"
	}  // dpper

	/*-----------------------------------------------------------------------------
	*
	*                           procedure dscom
	*
	*  this procedure provides deep space common items used by both the secular
	*    and periodics subroutines.  input is provided as shown. this routine
	*    used to be called dpper, but the functions inside weren't well organized.
	*
	*  author        : david vallado                  719-573-2600   28 jun 2005
	*
	*  inputs        :
	*    epoch       -
	*    ep          - eccentricity
	*    argpp       - argument of perigee
	*    tc          -
	*    inclp       - inclination
	*    nodep       - right ascension of ascending node
	*    np          - mean motion
	*
	*  outputs       :
	*    sinim  , cosim  , sinomm , cosomm , snodm  , cnodm
	*    day         -
	*    e3          -
	*    ee2         -
	*    em          - eccentricity
	*    emsq        - eccentricity squared
	*    gam         -
	*    peo         -
	*    pgho        -
	*    pho         -
	*    pinco       -
	*    plo         -
	*    rtemsq      -
	*    se2, se3         -
	*    sgh2, sgh3, sgh4        -
	*    sh2, sh3, si2, si3, sl2, sl3, sl4         -
	*    s1, s2, s3, s4, s5, s6, s7          -
	*    ss1, ss2, ss3, ss4, ss5, ss6, ss7, sz1, sz2, sz3         -
	*    sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33        -
	*    xgh2, xgh3, xgh4, xh2, xh3, xi2, xi3, xl2, xl3, xl4         -
	*    nm          - mean motion
	*    z1, z2, z3, z11, z12, z13, z21, z22, z23, z31, z32, z33         -
	*    zmol        -
	*    zmos        -
	*
	*  locals        :
	*    a1, a2, a3, a4, a5, a6, a7, a8, a9, a10         -
	*    betasq      -
	*    cc          -
	*    ctem, stem        -
	*    x1, x2, x3, x4, x5, x6, x7, x8          -
	*    xnodce      -
	*    xnoi        -
	*    zcosg  , zsing  , zcosgl , zsingl , zcosh  , zsinh  , zcoshl , zsinhl ,
	*    zcosi  , zsini  , zcosil , zsinil ,
	*    zx          -
	*    zy          -
	*
	*  coupling      :
	*    none.
	*
	*  references    :
	*    hoots, roehrich, norad spacetrack report #3 1980
	*    hoots, norad spacetrack report #6 1986
	*    hoots, schumacher and glover 2004
	*    vallado, crawford, hujsak, kelso  2006
	----------------------------------------------------------------------------*/

	static void dscom
		(
		double epoch, double ep, double argpp, double tc, double inclp,
		double nodep, double np,
		double& snodm, double& cnodm, double& sinim, double& cosim, double& sinomm,
		double& cosomm, double& day, double& e3, double& ee2, double& em,
		double& emsq, double& gam, double& peo, double& pgho, double& pho,
		double& pinco, double& plo, double& rtemsq, double& se2, double& se3,
		double& sgh2, double& sgh3, double& sgh4, double& sh2, double& sh3,
		double& si2, double& si3, double& sl2, double& sl3, double& sl4,
		double& s1, double& s2, double& s3, double& s4, double& s5,
		double& s6, double& s7, double& ss1, double& ss2, double& ss3,
		double& ss4, double& ss5, double& ss6, double& ss7, double& sz1,
		double& sz2, double& sz3, double& sz11, double& sz12, double& sz13,
		double& sz21, double& sz22, double& sz23, double& sz31, double& sz32,
		double& sz33, double& xgh2, double& xgh3, double& xgh4, double& xh2,
		double& xh3, double& xi2, double& xi3, double& xl2, double& xl3,
		double& xl4, double& nm, double& z1, double& z2, double& z3,
		double& z11, double& z12, double& z13, double& z21, double& z22,
		double& z23, double& z31, double& z32, double& z33, double& zmol,
		double& zmos
		)
	{
		/* -------------------------- constants ------------------------- */
		const double zes = 0.01675;
		const double zel = 0.05490;
		const double c1ss = 2.9864797e-6;
		const double c1l = 4.7968065e-7;
		const double zsinis = 0.39785416;
		const double zcosis = 0.91744867;
		const double zcosgs = 0.1945905;
		const double zsings = -0.98088458;
		const double twopi = 2.0 * pi;

		/* --------------------- local variables ------------------------ */
		int lsflg;
		double a1, a2, a3, a4, a5, a6, a7,
			a8, a9, a10, betasq, cc, ctem, stem,
			x1, x2, x3, x4, x5, x6, x7,
			x8, xnodce, xnoi, zcosg, zcosgl, zcosh, zcoshl,
			zcosi, zcosil, zsing, zsingl, zsinh, zsinhl, zsini,
			zsinil, zx, zy;

		nm = np;
		em = ep;
		snodm = sin(nodep);
		cnodm = cos(nodep);
		sinomm = sin(argpp);
		cosomm = cos(argpp);
		sinim = sin(inclp);
		cosim = cos(inclp);
		emsq = em * em;
		betasq = 1.0 - emsq;
		rtemsq = sqrt(betasq);

		/* ----------------- initialize lunar solar terms --------------- */
		peo = 0.0;
		pinco = 0.0;
		plo = 0.0;
		pgho = 0.0;
		pho = 0.0;
		day = epoch + 18261.5 + tc / 1440.0;
		xnodce = fmod(4.5236020 - 9.2422029e-4 * day, twopi);
		stem = sin(xnodce);
		ctem = cos(xnodce);
		zcosil = 0.91375164 - 0.03568096 * ctem;
		zsinil = sqrt(1.0 - zcosil * zcosil);
		zsinhl = 0.089683511 * stem / zsinil;
		zcoshl = sqrt(1.0 - zsinhl * zsinhl);
		gam = 5.8351514 + 0.0019443680 * day;
		zx = 0.39785416 * stem / zsinil;
		zy = zcoshl * ctem + 0.91744867 * zsinhl * stem;
		zx = atan2(zx, zy);
		zx = gam + zx - xnodce;
		zcosgl = cos(zx);
		zsingl = sin(zx);

		/* ------------------------- do solar terms --------------------- */
		zcosg = zcosgs;
		zsing = zsings;
		zcosi = zcosis;
		zsini = zsinis;
		zcosh = cnodm;
		zsinh = snodm;
		cc = c1ss;
		xnoi = 1.0 / nm;

		for (lsflg = 1; lsflg <= 2; lsflg++)
		{
			a1 = zcosg * zcosh + zsing * zcosi * zsinh;
			a3 = -zsing * zcosh + zcosg * zcosi * zsinh;
			a7 = -zcosg * zsinh + zsing * zcosi * zcosh;
			a8 = zsing * zsini;
			a9 = zsing * zsinh + zcosg * zcosi * zcosh;
			a10 = zcosg * zsini;
			a2 = cosim * a7 + sinim * a8;
			a4 = cosim * a9 + sinim * a10;
			a5 = -sinim * a7 + cosim * a8;
			a6 = -sinim * a9 + cosim * a10;

			x1 = a1 * cosomm + a2 * sinomm;
			x2 = a3 * cosomm + a4 * sinomm;
			x3 = -a1 * sinomm + a2 * cosomm;
			x4 = -a3 * sinomm + a4 * cosomm;
			x5 = a5 * sinomm;
			x6 = a6 * sinomm;
			x7 = a5 * cosomm;
			x8 = a6 * cosomm;

			z31 = 12.0 * x1 * x1 - 3.0 * x3 * x3;
			z32 = 24.0 * x1 * x2 - 6.0 * x3 * x4;
			z33 = 12.0 * x2 * x2 - 3.0 * x4 * x4;
			z1 = 3.0 *  (a1 * a1 + a2 * a2) + z31 * emsq;
			z2 = 6.0 *  (a1 * a3 + a2 * a4) + z32 * emsq;
			z3 = 3.0 *  (a3 * a3 + a4 * a4) + z33 * emsq;
			z11 = -6.0 * a1 * a5 + emsq *  (-24.0 * x1 * x7 - 6.0 * x3 * x5);
			z12 = -6.0 *  (a1 * a6 + a3 * a5) + emsq *
				(-24.0 * (x2 * x7 + x1 * x8) - 6.0 * (x3 * x6 + x4 * x5));
			z13 = -6.0 * a3 * a6 + emsq * (-24.0 * x2 * x8 - 6.0 * x4 * x6);
			z21 = 6.0 * a2 * a5 + emsq * (24.0 * x1 * x5 - 6.0 * x3 * x7);
			z22 = 6.0 *  (a4 * a5 + a2 * a6) + emsq *
				(24.0 * (x2 * x5 + x1 * x6) - 6.0 * (x4 * x7 + x3 * x8));
			z23 = 6.0 * a4 * a6 + emsq * (24.0 * x2 * x6 - 6.0 * x4 * x8);
			z1 = z1 + z1 + betasq * z31;
			z2 = z2 + z2 + betasq * z32;
			z3 = z3 + z3 + betasq * z33;
			s3 = cc * xnoi;
			s2 = -0.5 * s3 / rtemsq;
			s4 = s3 * rtemsq;
			s1 = -15.0 * em * s4;
			s5 = x1 * x3 + x2 * x4;
			s6 = x2 * x3 + x1 * x4;
			s7 = x2 * x4 - x1 * x3;

			/* ----------------------- do lunar terms ------------------- */
			if (lsflg == 1)
			{
				ss1 = s1;
				ss2 = s2;
				ss3 = s3;
				ss4 = s4;
				ss5 = s5;
				ss6 = s6;
				ss7 = s7;
				sz1 = z1;
				sz2 = z2;
				sz3 = z3;
				sz11 = z11;
				sz12 = z12;
				sz13 = z13;
				sz21 = z21;
				sz22 = z22;
				sz23 = z23;
				sz31 = z31;
				sz32 = z32;
				sz33 = z33;
				zcosg = zcosgl;
				zsing = zsingl;
				zcosi = zcosil;
				zsini = zsinil;
				zcosh = zcoshl * cnodm + zsinhl * snodm;
				zsinh = snodm * zcoshl - cnodm * zsinhl;
				cc = c1l;
			}
		}

		zmol = fmod(4.7199672 + 0.22997150  * day - gam, twopi);
		zmos = fmod(6.2565837 + 0.017201977 * day, twopi);

		/* ------------------------ do solar terms ---------------------- */
		se2 = 2.0 * ss1 * ss6;
		se3 = 2.0 * ss1 * ss7;
		si2 = 2.0 * ss2 * sz12;
		si3 = 2.0 * ss2 * (sz13 - sz11);
		sl2 = -2.0 * ss3 * sz2;
		sl3 = -2.0 * ss3 * (sz3 - sz1);
		sl4 = -2.0 * ss3 * (-21.0 - 9.0 * emsq) * zes;
		sgh2 = 2.0 * ss4 * sz32;
		sgh3 = 2.0 * ss4 * (sz33 - sz31);
		sgh4 = -18.0 * ss4 * zes;
		sh2 = -2.0 * ss2 * sz22;
		sh3 = -2.0 * ss2 * (sz23 - sz21);

		/* ------------------------ do lunar terms ---------------------- */
		ee2 = 2.0 * s1 * s6;
		e3 = 2.0 * s1 * s7;
		xi2 = 2.0 * s2 * z12;
		xi3 = 2.0 * s2 * (z13 - z11);
		xl2 = -2.0 * s3 * z2;
		xl3 = -2.0 * s3 * (z3 - z1);
		xl4 = -2.0 * s3 * (-21.0 - 9.0 * emsq) * zel;
		xgh2 = 2.0 * s4 * z32;
		xgh3 = 2.0 * s4 * (z33 - z31);
		xgh4 = -18.0 * s4 * zel;
		xh2 = -2.0 * s2 * z22;
		xh3 = -2.0 * s2 * (z23 - z21);

		//#include "debug2.cpp"
	}  // dscom

	/*-----------------------------------------------------------------------------
	*
	*                           procedure dsinit
	*
	*  this procedure provides deep space contributions to mean motion dot due
	*    to geopotential resonance with half day and one day orbits.
	*
	*  author        : david vallado                  719-573-2600   28 jun 2005
	*
	*  inputs        :
	*    xke         - reciprocal of tumin
	*    cosim, sinim-
	*    emsq        - eccentricity squared
	*    argpo       - argument of perigee
	*    s1, s2, s3, s4, s5      -
	*    ss1, ss2, ss3, ss4, ss5 -
	*    sz1, sz3, sz11, sz13, sz21, sz23, sz31, sz33 -
	*    t           - time
	*    tc          -
	*    gsto        - greenwich sidereal time                   rad
	*    mo          - mean anomaly
	*    mdot        - mean anomaly dot (rate)
	*    no          - mean motion
	*    nodeo       - right ascension of ascending node
	*    nodedot     - right ascension of ascending node dot (rate)
	*    xpidot      -
	*    z1, z3, z11, z13, z21, z23, z31, z33 -
	*    eccm        - eccentricity
	*    argpm       - argument of perigee
	*    inclm       - inclination
	*    mm          - mean anomaly
	*    xn          - mean motion
	*    nodem       - right ascension of ascending node
	*
	*  outputs       :
	*    em          - eccentricity
	*    argpm       - argument of perigee
	*    inclm       - inclination
	*    mm          - mean anomaly
	*    nm          - mean motion
	*    nodem       - right ascension of ascending node
	*    irez        - flag for resonance           0-none, 1-one day, 2-half day
	*    atime       -
	*    d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433    -
	*    dedt        -
	*    didt        -
	*    dmdt        -
	*    dndt        -
	*    dnodt       -
	*    domdt       -
	*    del1, del2, del3        -
	*    ses  , sghl , sghs , sgs  , shl  , shs  , sis  , sls
	*    theta       -
	*    xfact       -
	*    xlamo       -
	*    xli         -
	*    xni
	*
	*  locals        :
	*    ainv2       -
	*    aonv        -
	*    cosisq      -
	*    eoc         -
	*    f220, f221, f311, f321, f322, f330, f441, f442, f522, f523, f542, f543  -
	*    g200, g201, g211, g300, g310, g322, g410, g422, g520, g521, g532, g533  -
	*    sini2       -
	*    temp        -
	*    temp1       -
	*    theta       -
	*    xno2        -
	*
	*  coupling      :
	*    getgravconst- no longer used
	*
	*  references    :
	*    hoots, roehrich, norad spacetrack report #3 1980
	*    hoots, norad spacetrack report #6 1986
	*    hoots, schumacher and glover 2004
	*    vallado, crawford, hujsak, kelso  2006
	----------------------------------------------------------------------------*/

	static void dsinit
		(
		// sgp4fix just send in xke as a constant and eliminate getgravconst call
		// gravconsttype whichconst, 
		double xke,
		double cosim, double emsq, double argpo, double s1, double s2,
		double s3, double s4, double s5, double sinim, double ss1,
		double ss2, double ss3, double ss4, double ss5, double sz1,
		double sz3, double sz11, double sz13, double sz21, double sz23,
		double sz31, double sz33, double t, double tc, double gsto,
		double mo, double mdot, double no, double nodeo, double nodedot,
		double xpidot, double z1, double z3, double z11, double z13,
		double z21, double z23, double z31, double z33, double ecco,
		double eccsq, double& em, double& argpm, double& inclm, double& mm,
		double& nm, double& nodem,
		int& irez,
		double& atime, double& d2201, double& d2211, double& d3210, double& d3222,
		double& d4410, double& d4422, double& d5220, double& d5232, double& d5421,
		double& d5433, double& dedt, double& didt, double& dmdt, double& dndt,
		double& dnodt, double& domdt, double& del1, double& del2, double& del3,
		double& xfact, double& xlamo, double& xli, double& xni
		)
	{
		/* --------------------- local variables ------------------------ */
		const double twopi = 2.0 * pi;

		double ainv2, aonv = 0.0, cosisq, eoc, f220, f221, f311,
			f321, f322, f330, f441, f442, f522, f523,
			f542, f543, g200, g201, g211, g300, g310,
			g322, g410, g422, g520, g521, g532, g533,
			ses, sgs, sghl, sghs, shs, shll, sis,
			sini2, sls, temp, temp1, theta, xno2, q22,
			q31, q33, root22, root44, root54, rptim, root32,
			root52, x2o3, znl, emo, zns, emsqo;

		q22 = 1.7891679e-6;
		q31 = 2.1460748e-6;
		q33 = 2.2123015e-7;
		root22 = 1.7891679e-6;
		root44 = 7.3636953e-9;
		root54 = 2.1765803e-9;
		rptim = 4.37526908801129966e-3; // this equates to 7.29211514668855e-5 rad/sec
		root32 = 3.7393792e-7;
		root52 = 1.1428639e-7;
		x2o3 = 2.0 / 3.0;
		znl = 1.5835218e-4;
		zns = 1.19459e-5;

		// sgp4fix identify constants and allow alternate values
		// just xke is used here so pass it in rather than have multiple calls
		// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );

		/* -------------------- deep space initialization ------------ */
		irez = 0;
		if ((nm < 0.0052359877) && (nm > 0.0034906585))
			irez = 1;
		if ((nm >= 8.26e-3) && (nm <= 9.24e-3) && (em >= 0.5))
			irez = 2;

		/* ------------------------ do solar terms ------------------- */
		ses = ss1 * zns * ss5;
		sis = ss2 * zns * (sz11 + sz13);
		sls = -zns * ss3 * (sz1 + sz3 - 14.0 - 6.0 * emsq);
		sghs = ss4 * zns * (sz31 + sz33 - 6.0);
		shs = -zns * ss2 * (sz21 + sz23);
		// sgp4fix for 180 deg incl
		if ((inclm < 5.2359877e-2) || (inclm > pi - 5.2359877e-2))
			shs = 0.0;
		if (sinim != 0.0)
			shs = shs / sinim;
		sgs = sghs - cosim * shs;

		/* ------------------------- do lunar terms ------------------ */
		dedt = ses + s1 * znl * s5;
		didt = sis + s2 * znl * (z11 + z13);
		dmdt = sls - znl * s3 * (z1 + z3 - 14.0 - 6.0 * emsq);
		sghl = s4 * znl * (z31 + z33 - 6.0);
		shll = -znl * s2 * (z21 + z23);
		// sgp4fix for 180 deg incl
		if ((inclm < 5.2359877e-2) || (inclm > pi - 5.2359877e-2))
			shll = 0.0;
		domdt = sgs + sghl;
		dnodt = shs;
		if (sinim != 0.0)
		{
			domdt = domdt - cosim / sinim * shll;
			dnodt = dnodt + shll / sinim;
		}

		/* ----------- calculate deep space resonance effects -------- */
		dndt = 0.0;
		theta = fmod(gsto + tc * rptim, twopi);
		em = em + dedt * t;
		inclm = inclm + didt * t;
		argpm = argpm + domdt * t;
		nodem = nodem + dnodt * t;
		mm = mm + dmdt * t;
		//   sgp4fix for negative inclinations
		//   the following if statement should be commented out
		//if (inclm < 0.0)
		//  {
		//    inclm  = -inclm;
		//    argpm  = argpm - pi;
		//    nodem = nodem + pi;
		//  }

		/* -------------- initialize the resonance terms ------------- */
		if (irez != 0)
		{
			aonv = pow(nm / xke, x2o3);

			/* ---------- geopotential resonance for 12 hour orbits ------ */
			if (irez == 2)
			{
				cosisq = cosim * cosim;
				emo = em;
				em = ecco;
				emsqo = emsq;
				emsq = eccsq;
				eoc = em * emsq;
				g201 = -0.306 - (em - 0.64) * 0.440;

				if (em <= 0.65)
				{
					g211 = 3.616 - 13.2470 * em + 16.2900 * emsq;
					g310 = -19.302 + 117.3900 * em - 228.4190 * emsq + 156.5910 * eoc;
					g322 = -18.9068 + 109.7927 * em - 214.6334 * emsq + 146.5816 * eoc;
					g410 = -41.122 + 242.6940 * em - 471.0940 * emsq + 313.9530 * eoc;
					g422 = -146.407 + 841.8800 * em - 1629.014 * emsq + 1083.4350 * eoc;
					g520 = -532.114 + 3017.977 * em - 5740.032 * emsq + 3708.2760 * eoc;
				}
				else
				{
					g211 = -72.099 + 331.819 * em - 508.738 * emsq + 266.724 * eoc;
					g310 = -346.844 + 1582.851 * em - 2415.925 * emsq + 1246.113 * eoc;
					g322 = -342.585 + 1554.908 * em - 2366.899 * emsq + 1215.972 * eoc;
					g410 = -1052.797 + 4758.686 * em - 7193.992 * emsq + 3651.957 * eoc;
					g422 = -3581.690 + 16178.110 * em - 24462.770 * emsq + 12422.520 * eoc;
					if (em > 0.715)
						g520 = -5149.66 + 29936.92 * em - 54087.36 * emsq + 31324.56 * eoc;
					else
						g520 = 1464.74 - 4664.75 * em + 3763.64 * emsq;
				}
				if (em < 0.7)
				{
					g533 = -919.22770 + 4988.6100 * em - 9064.7700 * emsq + 5542.21  * eoc;
					g521 = -822.71072 + 4568.6173 * em - 8491.4146 * emsq + 5337.524 * eoc;
					g532 = -853.66600 + 4690.2500 * em - 8624.7700 * emsq + 5341.4  * eoc;
				}
				else
				{
					g533 = -37995.780 + 161616.52 * em - 229838.20 * emsq + 109377.94 * eoc;
					g521 = -51752.104 + 218913.95 * em - 309468.16 * emsq + 146349.42 * eoc;
					g532 = -40023.880 + 170470.89 * em - 242699.48 * emsq + 115605.82 * eoc;
				}

				sini2 = sinim * sinim;
				f220 = 0.75 * (1.0 + 2.0 * cosim + cosisq);
				f221 = 1.5 * sini2;
				f321 = 1.875 * sinim  *  (1.0 - 2.0 * cosim - 3.0 * cosisq);
				f322 = -1.875 * sinim  *  (1.0 + 2.0 * cosim - 3.0 * cosisq);
				f441 = 35.0 * sini2 * f220;
				f442 = 39.3750 * sini2 * sini2;
				f522 = 9.84375 * sinim * (sini2 * (1.0 - 2.0 * cosim - 5.0 * cosisq) +
					0.33333333 * (-2.0 + 4.0 * cosim + 6.0 * cosisq));
				f523 = sinim * (4.92187512 * sini2 * (-2.0 - 4.0 * cosim +
					10.0 * cosisq) + 6.56250012 * (1.0 + 2.0 * cosim - 3.0 * cosisq));
				f542 = 29.53125 * sinim * (2.0 - 8.0 * cosim + cosisq *
					(-12.0 + 8.0 * cosim + 10.0 * cosisq));
				f543 = 29.53125 * sinim * (-2.0 - 8.0 * cosim + cosisq *
					(12.0 + 8.0 * cosim - 10.0 * cosisq));
				xno2 = nm * nm;
				ainv2 = aonv * aonv;
				temp1 = 3.0 * xno2 * ainv2;
				temp = temp1 * root22;
				d2201 = temp * f220 * g201;
				d2211 = temp * f221 * g211;
				temp1 = temp1 * aonv;
				temp = temp1 * root32;
				d3210 = temp * f321 * g310;
				d3222 = temp * f322 * g322;
				temp1 = temp1 * aonv;
				temp = 2.0 * temp1 * root44;
				d4410 = temp * f441 * g410;
				d4422 = temp * f442 * g422;
				temp1 = temp1 * aonv;
				temp = temp1 * root52;
				d5220 = temp * f522 * g520;
				d5232 = temp * f523 * g532;
				temp = 2.0 * temp1 * root54;
				d5421 = temp * f542 * g521;
				d5433 = temp * f543 * g533;
				xlamo = fmod(mo + nodeo + nodeo - theta - theta, twopi);
				xfact = mdot + dmdt + 2.0 * (nodedot + dnodt - rptim) - no;
				em = emo;
				emsq = emsqo;
			}

			/* ---------------- synchronous resonance terms -------------- */
			if (irez == 1)
			{
				g200 = 1.0 + emsq * (-2.5 + 0.8125 * emsq);
				g310 = 1.0 + 2.0 * emsq;
				g300 = 1.0 + emsq * (-6.0 + 6.60937 * emsq);
				f220 = 0.75 * (1.0 + cosim) * (1.0 + cosim);
				f311 = 0.9375 * sinim * sinim * (1.0 + 3.0 * cosim) - 0.75 * (1.0 + cosim);
				f330 = 1.0 + cosim;
				f330 = 1.875 * f330 * f330 * f330;
				del1 = 3.0 * nm * nm * aonv * aonv;
				del2 = 2.0 * del1 * f220 * g200 * q22;
				del3 = 3.0 * del1 * f330 * g300 * q33 * aonv;
				del1 = del1 * f311 * g310 * q31 * aonv;
				xlamo = fmod(mo + nodeo + argpo - theta, twopi);
				xfact = mdot + xpidot - rptim + dmdt + domdt + dnodt - no;
			}

			/* ------------ for sgp4, initialize the integrator ---------- */
			xli = xlamo;
			xni = no;
			atime = 0.0;
			nm = no + dndt;
		}

		//#include "debug3.cpp"
	}  // dsinit

	/*-----------------------------------------------------------------------------
	*
	*                           procedure dspace
	*
	*  this procedure provides deep space contributions to mean elements for
	*    perturbing third body.  these effects have been averaged over one
	*    revolution of the sun and moon.  for earth resonance effects, the
	*    effects have been averaged over no revolutions of the satellite.
	*    (mean motion)
	*
	*  author        : david vallado                  719-573-2600   28 jun 2005
	*
	*  inputs        :
	*    d2201, d2211, d3210, d3222, d4410, d4422, d5220, d5232, d5421, d5433 -
	*    dedt        -
	*    del1, del2, del3  -
	*    didt        -
	*    dmdt        -
	*    dnodt       -
	*    domdt       -
	*    irez        - flag for resonance           0-none, 1-one day, 2-half day
	*    argpo       - argument of perigee
	*    argpdot     - argument of perigee dot (rate)
	*    t           - time
	*    tc          -
	*    gsto        - gst
	*    xfact       -
	*    xlamo       -
	*    no          - mean motion
	*    atime       -
	*    em          - eccentricity
	*    ft          -
	*    argpm       - argument of perigee
	*    inclm       - inclination
	*    xli         -
	*    mm          - mean anomaly
	*    xni         - mean motion
	*    nodem       - right ascension of ascending node
	*
	*  outputs       :
	*    atime       -
	*    em          - eccentricity
	*    argpm       - argument of perigee
	*    inclm       - inclination
	*    xli         -
	*    mm          - mean anomaly
	*    xni         -
	*    nodem       - right ascension of ascending node
	*    dndt        -
	*    nm          - mean motion
	*
	*  locals        :
	*    delt        -
	*    ft          -
	*    theta       -
	*    x2li        -
	*    x2omi       -
	*    xl          -
	*    xldot       -
	*    xnddt       -
	*    xndt        -
	*    xomi        -
	*
	*  coupling      :
	*    none        -
	*
	*  references    :
	*    hoots, roehrich, norad spacetrack report #3 1980
	*    hoots, norad spacetrack report #6 1986
	*    hoots, schumacher and glover 2004
	*    vallado, crawford, hujsak, kelso  2006
	----------------------------------------------------------------------------*/

	static void dspace
		(
		int irez,
		double d2201, double d2211, double d3210, double d3222, double d4410,
		double d4422, double d5220, double d5232, double d5421, double d5433,
		double dedt, double del1, double del2, double del3, double didt,
		double dmdt, double dnodt, double domdt, double argpo, double argpdot,
		double t, double tc, double gsto, double xfact, double xlamo,
		double no,
		double& atime, double& em, double& argpm, double& inclm, double& xli,
		double& mm, double& xni, double& nodem, double& dndt, double& nm
		)
	{
		const double twopi = 2.0 * pi;
		int iretn, iret;
		double delt, ft, theta, x2li, x2omi, xl, xldot, xnddt, xndt, xomi, g22, g32,
			g44, g52, g54, fasx2, fasx4, fasx6, rptim, step2, stepn, stepp;

		fasx2 = 0.13130908;
		fasx4 = 2.8843198;
		fasx6 = 0.37448087;
		g22 = 5.7686396;
		g32 = 0.95240898;
		g44 = 1.8014998;
		g52 = 1.0508330;
		g54 = 4.4108898;
		rptim = 4.37526908801129966e-3; // this equates to 7.29211514668855e-5 rad/sec
		stepp = 720.0;
		stepn = -720.0;
		step2 = 259200.0;

		/* ----------- calculate deep space resonance effects ----------- */
		dndt = 0.0;
		theta = fmod(gsto + tc * rptim, twopi);
		em = em + dedt * t;

		inclm = inclm + didt * t;
		argpm = argpm + domdt * t;
		nodem = nodem + dnodt * t;
		mm = mm + dmdt * t;

		//   sgp4fix for negative inclinations
		//   the following if statement should be commented out
		//  if (inclm < 0.0)
		// {
		//    inclm = -inclm;
		//    argpm = argpm - pi;
		//    nodem = nodem + pi;
		//  }

		/* - update resonances : numerical (euler-maclaurin) integration - */
		/* ------------------------- epoch restart ----------------------  */
		//   sgp4fix for propagator problems
		//   the following integration works for negative time steps and periods
		//   the specific changes are unknown because the original code was so convoluted

		// sgp4fix take out atime = 0.0 and fix for faster operation
		ft = 0.0;
		if (irez != 0)
		{
			// sgp4fix streamline check
			if ((atime == 0.0) || (t * atime <= 0.0) || (fabs(t) < fabs(atime)))
			{
				atime = 0.0;
				xni = no;
				xli = xlamo;
			}
			// sgp4fix move check outside loop
			if (t > 0.0)
				delt = stepp;
			else
				delt = stepn;

			iretn = 381; // added for do loop
			iret = 0; // added for loop
			while (iretn == 381)
			{
				/* ------------------- dot terms calculated ------------- */
				/* ----------- near - synchronous resonance terms ------- */
				if (irez != 2)
				{
					xndt = del1 * sin(xli - fasx2) + del2 * sin(2.0 * (xli - fasx4)) +
						del3 * sin(3.0 * (xli - fasx6));
					xldot = xni + xfact;
					xnddt = del1 * cos(xli - fasx2) +
						2.0 * del2 * cos(2.0 * (xli - fasx4)) +
						3.0 * del3 * cos(3.0 * (xli - fasx6));
					xnddt = xnddt * xldot;
				}
				else
				{
					/* --------- near - half-day resonance terms -------- */
					xomi = argpo + argpdot * atime;
					x2omi = xomi + xomi;
					x2li = xli + xli;
					xndt = d2201 * sin(x2omi + xli - g22) + d2211 * sin(xli - g22) +
						d3210 * sin(xomi + xli - g32) + d3222 * sin(-xomi + xli - g32) +
						d4410 * sin(x2omi + x2li - g44) + d4422 * sin(x2li - g44) +
						d5220 * sin(xomi + xli - g52) + d5232 * sin(-xomi + xli - g52) +
						d5421 * sin(xomi + x2li - g54) + d5433 * sin(-xomi + x2li - g54);
					xldot = xni + xfact;
					xnddt = d2201 * cos(x2omi + xli - g22) + d2211 * cos(xli - g22) +
						d3210 * cos(xomi + xli - g32) + d3222 * cos(-xomi + xli - g32) +
						d5220 * cos(xomi + xli - g52) + d5232 * cos(-xomi + xli - g52) +
						2.0 * (d4410 * cos(x2omi + x2li - g44) +
						d4422 * cos(x2li - g44) + d5421 * cos(xomi + x2li - g54) +
						d5433 * cos(-xomi + x2li - g54));
					xnddt = xnddt * xldot;
				}

				/* ----------------------- integrator ------------------- */
				// sgp4fix move end checks to end of routine
				if (fabs(t - atime) >= stepp)
				{
					iret = 0;
					iretn = 381;
				}
				else // exit here
				{
					ft = t - atime;
					iretn = 0;
				}

				if (iretn == 381)
				{
					xli = xli + xldot * delt + xndt * step2;
					xni = xni + xndt * delt + xnddt * step2;
					atime = atime + delt;
				}
			}  // while iretn = 381

			nm = xni + xndt * ft + xnddt * ft * ft * 0.5;
			xl = xli + xldot * ft + xndt * ft * ft * 0.5;
			if (irez != 1)
			{
				mm = xl - 2.0 * nodem + 2.0 * theta;
				dndt = nm - no;
			}
			else
			{
				mm = xl - nodem - argpm + theta;
				dndt = nm - no;
			}
			nm = no + dndt;
		}

		//#include "debug4.cpp"
	}  // dsspace

	/*-----------------------------------------------------------------------------
	*
	*                           procedure initl
	*
	*  this procedure initializes the spg4 propagator. all the initialization is
	*    consolidated here instead of having multiple loops inside other routines.
	*
	*  author        : david vallado                  719-573-2600   28 jun 2005
	*
	*  inputs        :
	*    satn        - satellite number - not needed, placed in satrec
	*    xke         - reciprocal of tumin
	*    j2          - j2 zonal harmonic
	*    ecco        - eccentricity                           0.0 - 1.0
	*    epoch       - epoch time in days from jan 0, 1950. 0 hr
	*    inclo       - inclination of satellite
	*    no          - mean motion of satellite
	*
	*  outputs       :
	*    ainv        - 1.0 / a
	*    ao          - semi major axis
	*    con41       -
	*    con42       - 1.0 - 5.0 cos(i)
	*    cosio       - cosine of inclination
	*    cosio2      - cosio squared
	*    eccsq       - eccentricity squared
	*    method      - flag for deep space                    'd', 'n'
	*    omeosq      - 1.0 - ecco * ecco
	*    posq        - semi-parameter squared
	*    rp          - radius of perigee
	*    rteosq      - square root of (1.0 - ecco*ecco)
	*    sinio       - sine of inclination
	*    gsto        - gst at time of observation               rad
	*    no          - mean motion of satellite
	*
	*  locals        :
	*    ak          -
	*    d1          -
	*    del         -
	*    adel        -
	*    po          -
	*
	*  coupling      :
	*    getgravconst- no longer used
	*    gstime      - find greenwich sidereal time from the julian date
	*
	*  references    :
	*    hoots, roehrich, norad spacetrack report #3 1980
	*    hoots, norad spacetrack report #6 1986
	*    hoots, schumacher and glover 2004
	*    vallado, crawford, hujsak, kelso  2006
	----------------------------------------------------------------------------*/

	static void initl
		(
		// sgp4fix satn not needed. include in satrec in case needed later  
		// int satn,      
		// sgp4fix just pass in xke and j2
		// gravconsttype whichconst, 
		double xke, double j2,
		double ecco, double epoch, double inclo, double no_kozai, char opsmode,
		char& method, double& ainv, double& ao, double& con41, double& con42, double& cosio,
		double& cosio2, double& eccsq, double& omeosq, double& posq,
		double& rp, double& rteosq, double& sinio, double& gsto, double& no_unkozai
		)
	{
		/* --------------------- local variables ------------------------ */
		double ak, d1, del, adel, po, x2o3;

		// sgp4fix use old way of finding gst
		double ds70;
		double ts70, tfrac, c1, thgr70, fk5r, c1p2p;
		const double twopi = 2.0 * pi;

		/* ----------------------- earth constants ---------------------- */
		// sgp4fix identify constants and allow alternate values
		// only xke and j2 are used here so pass them in directly
		// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
		x2o3 = 2.0 / 3.0;

		/* ------------- calculate auxillary epoch quantities ---------- */
		eccsq = ecco * ecco;
		omeosq = 1.0 - eccsq;
		rteosq = sqrt(omeosq);
		cosio = cos(inclo);
		cosio2 = cosio * cosio;

		/* ------------------ un-kozai the mean motion ----------------- */
		ak = pow(xke / no_kozai, x2o3);
		d1 = 0.75 * j2 * (3.0 * cosio2 - 1.0) / (rteosq * omeosq);
		del = d1 / (ak * ak);
		adel = ak * (1.0 - del * del - del *
			(1.0 / 3.0 + 134.0 * del * del / 81.0));
		del = d1 / (adel * adel);
		no_unkozai = no_kozai / (1.0 + del);

		ao = pow(xke / (no_unkozai), x2o3);
		sinio = sin(inclo);
		po = ao * omeosq;
		con42 = 1.0 - 5.0 * cosio2;
		con41 = -con42 - cosio2 - cosio2;
		ainv = 1.0 / ao;
		posq = po * po;
		rp = ao * (1.0 - ecco);
		method = 'n';

		// sgp4fix modern approach to finding sidereal time
		//   if (opsmode == 'a')
		//      {
		// sgp4fix use old way of finding gst
		// count integer number of days from 0 jan 1970
		ts70 = epoch - 7305.0;
		ds70 = floor(ts70 + 1.0e-8);
		tfrac = ts70 - ds70;
		// find greenwich location at epoch
		c1 = 1.72027916940703639e-2;
		thgr70 = 1.7321343856509374;
		fk5r = 5.07551419432269442e-15;
		c1p2p = c1 + twopi;
		double gsto1 = fmod(thgr70 + c1*ds70 + c1p2p*tfrac + ts70*ts70*fk5r, twopi);
		if (gsto1 < 0.0)
			gsto1 = gsto1 + twopi;
		//    }
		//    else
		gsto = gstime_SGP4(epoch + 2433281.5);

		//#include "debug5.cpp"
	}  // initl

	/*-----------------------------------------------------------------------------
	*
	*                             procedure sgp4init
	*
	*  this procedure initializes variables for sgp4.
	*
	*  author        : david vallado                  719-573-2600   28 jun 2005
	*
	*  inputs        :
	*    opsmode     - mode of operation afspc or improved 'a', 'i'
	*    whichconst  - which set of constants to use  72, 84
	*    satn        - satellite number
	*    bstar       - sgp4 type drag coefficient              kg/m2er
	*    ecco        - eccentricity
	*    epoch       - epoch time in days from jan 0, 1950. 0 hr
	*    argpo       - argument of perigee (output if ds)
	*    inclo       - inclination
	*    mo          - mean anomaly (output if ds)
	*    no          - mean motion
	*    nodeo       - right ascension of ascending node
	*
	*  outputs       :
	*    satrec      - common values for subsequent calls
	*    return code - non-zero on error.
	*                   1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
	*                   2 - mean motion less than 0.0
	*                   3 - pert elements, ecc < 0.0  or  ecc > 1.0
	*                   4 - semi-latus rectum < 0.0
	*                   5 - epoch elements are sub-orbital
	*                   6 - satellite has decayed
	*
	*  locals        :
	*    cnodm  , snodm  , cosim  , sinim  , cosomm , sinomm
	*    cc1sq  , cc2    , cc3
	*    coef   , coef1
	*    cosio4      -
	*    day         -
	*    dndt        -
	*    em          - eccentricity
	*    emsq        - eccentricity squared
	*    eeta        -
	*    etasq       -
	*    gam         -
	*    argpm       - argument of perigee
	*    nodem       -
	*    inclm       - inclination
	*    mm          - mean anomaly
	*    nm          - mean motion
	*    perige      - perigee
	*    pinvsq      -
	*    psisq       -
	*    qzms24      -
	*    rtemsq      -
	*    s1, s2, s3, s4, s5, s6, s7          -
	*    sfour       -
	*    ss1, ss2, ss3, ss4, ss5, ss6, ss7         -
	*    sz1, sz2, sz3
	*    sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33        -
	*    tc          -
	*    temp        -
	*    temp1, temp2, temp3       -
	*    tsi         -
	*    xpidot      -
	*    xhdot1      -
	*    z1, z2, z3          -
	*    z11, z12, z13, z21, z22, z23, z31, z32, z33         -
	*
	*  coupling      :
	*    getgravconst-
	*    initl       -
	*    dscom       -
	*    dpper       -
	*    dsinit      -
	*    sgp4        -
	*
	*  references    :
	*    hoots, roehrich, norad spacetrack report #3 1980
	*    hoots, norad spacetrack report #6 1986
	*    hoots, schumacher and glover 2004
	*    vallado, crawford, hujsak, kelso  2006
	----------------------------------------------------------------------------*/

	bool sgp4init
		(
		gravconsttype whichconst, char opsmode, const char satn[5], const double epoch,
		const double xbstar, const double xndot, const double xnddot, const double xecco, const double xargpo,
		const double xinclo, const double xmo, const double xno_kozai,
		const double xnodeo, elsetrec& satrec
		)
	{
		/* --------------------- local variables ------------------------ */
		double ao, ainv, con42, cosio, sinio, cosio2, eccsq,
			omeosq, posq, rp, rteosq,
			cnodm, snodm, cosim, sinim, cosomm, sinomm, cc1sq,
			cc2, cc3, coef, coef1, cosio4, day, dndt,
			em, emsq, eeta, etasq, gam, argpm, nodem,
			inclm, mm, nm, perige, pinvsq, psisq, qzms24,
			rtemsq, s1, s2, s3, s4, s5, s6,
			s7, sfour, ss1, ss2, ss3, ss4, ss5,
			ss6, ss7, sz1, sz2, sz3, sz11, sz12,
			sz13, sz21, sz22, sz23, sz31, sz32, sz33,
			tc, temp, temp1, temp2, temp3, tsi, xpidot,
			xhdot1, z1, z2, z3, z11, z12, z13,
			z21, z22, z23, z31, z32, z33,
			qzms2t, ss, x2o3, r[3], v[3],
			delmotemp, qzms2ttemp, qzms24temp;

		/* ------------------------ initialization --------------------- */
		// sgp4fix divisor for divide by zero check on inclination
		// the old check used 1.0 + cos(pi-1.0e-9), but then compared it to
		// 1.5 e-12, so the threshold was changed to 1.5e-12 for consistency
		const double temp4 = 1.5e-12;

		/* ----------- set all near earth variables to zero ------------ */
		satrec.isimp = 0;   satrec.method = 'n'; satrec.aycof = 0.0;
		satrec.con41 = 0.0; satrec.cc1 = 0.0; satrec.cc4 = 0.0;
		satrec.cc5 = 0.0; satrec.d2 = 0.0; satrec.d3 = 0.0;
		satrec.d4 = 0.0; satrec.delmo = 0.0; satrec.eta = 0.0;
		satrec.argpdot = 0.0; satrec.omgcof = 0.0; satrec.sinmao = 0.0;
		satrec.t = 0.0; satrec.t2cof = 0.0; satrec.t3cof = 0.0;
		satrec.t4cof = 0.0; satrec.t5cof = 0.0; satrec.x1mth2 = 0.0;
		satrec.x7thm1 = 0.0; satrec.mdot = 0.0; satrec.nodedot = 0.0;
		satrec.xlcof = 0.0; satrec.xmcof = 0.0; satrec.nodecf = 0.0;

		/* ----------- set all deep space variables to zero ------------ */
		satrec.irez = 0;   satrec.d2201 = 0.0; satrec.d2211 = 0.0;
		satrec.d3210 = 0.0; satrec.d3222 = 0.0; satrec.d4410 = 0.0;
		satrec.d4422 = 0.0; satrec.d5220 = 0.0; satrec.d5232 = 0.0;
		satrec.d5421 = 0.0; satrec.d5433 = 0.0; satrec.dedt = 0.0;
		satrec.del1 = 0.0; satrec.del2 = 0.0; satrec.del3 = 0.0;
		satrec.didt = 0.0; satrec.dmdt = 0.0; satrec.dnodt = 0.0;
		satrec.domdt = 0.0; satrec.e3 = 0.0; satrec.ee2 = 0.0;
		satrec.peo = 0.0; satrec.pgho = 0.0; satrec.pho = 0.0;
		satrec.pinco = 0.0; satrec.plo = 0.0; satrec.se2 = 0.0;
		satrec.se3 = 0.0; satrec.sgh2 = 0.0; satrec.sgh3 = 0.0;
		satrec.sgh4 = 0.0; satrec.sh2 = 0.0; satrec.sh3 = 0.0;
		satrec.si2 = 0.0; satrec.si3 = 0.0; satrec.sl2 = 0.0;
		satrec.sl3 = 0.0; satrec.sl4 = 0.0; satrec.gsto = 0.0;
		satrec.xfact = 0.0; satrec.xgh2 = 0.0; satrec.xgh3 = 0.0;
		satrec.xgh4 = 0.0; satrec.xh2 = 0.0; satrec.xh3 = 0.0;
		satrec.xi2 = 0.0; satrec.xi3 = 0.0; satrec.xl2 = 0.0;
		satrec.xl3 = 0.0; satrec.xl4 = 0.0; satrec.xlamo = 0.0;
		satrec.zmol = 0.0; satrec.zmos = 0.0; satrec.atime = 0.0;
		satrec.xli = 0.0; satrec.xni = 0.0;

		/* ------------------------ earth constants ----------------------- */
		// sgp4fix identify constants and allow alternate values
		// this is now the only call for the constants
		getgravconst(whichconst, satrec.tumin, satrec.mus, satrec.radiusearthkm, satrec.xke,
			satrec.j2, satrec.j3, satrec.j4, satrec.j3oj2);

		//-------------------------------------------------------------------------

		satrec.error = 0;
		satrec.operationmode = opsmode;
		// new alpha5 or 9-digit number
		#ifdef _MSC_VER
						   strcpy_s(satrec.satnum, 6 * sizeof(char), satn);
		#else
						   strcpy(satrec.satnum, satn);
		#endif

		// sgp4fix - note the following variables are also passed directly via satrec.
		// it is possible to streamline the sgp4init call by deleting the "x"
		// variables, but the user would need to set the satrec.* values first. we
		// include the additional assignments in case twoline2rv is not used.
		satrec.bstar = xbstar;
		// sgp4fix allow additional parameters in the struct
		satrec.ndot = xndot;
		satrec.nddot = xnddot;
		satrec.ecco = xecco;
		satrec.argpo = xargpo;
		satrec.inclo = xinclo;
		satrec.mo = xmo;
		// sgp4fix rename variables to clarify which mean motion is intended
		satrec.no_kozai = xno_kozai;
		satrec.nodeo = xnodeo;

		// single averaged mean elements
		satrec.am = satrec.em = satrec.im = satrec.Om = satrec.mm = satrec.nm = 0.0;

		/* ------------------------ earth constants ----------------------- */
		// sgp4fix identify constants and allow alternate values no longer needed
		// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
		ss = 78.0 / satrec.radiusearthkm + 1.0;
		// sgp4fix use multiply for speed instead of pow
		qzms2ttemp = (120.0 - 78.0) / satrec.radiusearthkm;
		qzms2t = qzms2ttemp * qzms2ttemp * qzms2ttemp * qzms2ttemp;
		x2o3 = 2.0 / 3.0;

		satrec.init = 'y';
		satrec.t = 0.0;

		// sgp4fix remove satn as it is not needed in initl
		initl
			(satrec.xke, satrec.j2, satrec.ecco, epoch, satrec.inclo, satrec.no_kozai, satrec.operationmode,
			satrec.method, ainv, ao, satrec.con41, con42, cosio, cosio2, eccsq, omeosq,
			posq, rp, rteosq, sinio, satrec.gsto, satrec.no_unkozai);
		satrec.a = pow(satrec.no_unkozai * satrec.tumin, (-2.0 / 3.0));
		satrec.alta = satrec.a * (1.0 + satrec.ecco) - 1.0;
		satrec.altp = satrec.a * (1.0 - satrec.ecco) - 1.0;
		satrec.error = 0;

		// sgp4fix remove this check as it is unnecessary
		// the mrt check in sgp4 handles decaying satellite cases even if the starting
		// condition is below the surface of te earth
		//     if (rp < 1.0)
		//       {
		//         printf("# *** satn%d epoch elts sub-orbital ***\n", satn);
		//         satrec.error = 5;
		//       }

		if ((omeosq >= 0.0) || (satrec.no_unkozai >= 0.0))
		{
			satrec.isimp = 0;
			if (rp < (220.0 / satrec.radiusearthkm + 1.0))
				satrec.isimp = 1;
			sfour = ss;
			qzms24 = qzms2t;
			perige = (rp - 1.0) * satrec.radiusearthkm;

			/* - for perigees below 156 km, s and qoms2t are altered - */
			if (perige < 156.0)
			{
				sfour = perige - 78.0;
				if (perige < 98.0)
					sfour = 20.0;
				// sgp4fix use multiply for speed instead of pow
				qzms24temp = (120.0 - sfour) / satrec.radiusearthkm;
				qzms24 = qzms24temp * qzms24temp * qzms24temp * qzms24temp;
				sfour = sfour / satrec.radiusearthkm + 1.0;
			}
			pinvsq = 1.0 / posq;

			tsi = 1.0 / (ao - sfour);
			satrec.eta = ao * satrec.ecco * tsi;
			etasq = satrec.eta * satrec.eta;
			eeta = satrec.ecco * satrec.eta;
			psisq = fabs(1.0 - etasq);
			coef = qzms24 * pow(tsi, 4.0);
			coef1 = coef / pow(psisq, 3.5);
			cc2 = coef1 * satrec.no_unkozai * (ao * (1.0 + 1.5 * etasq + eeta *
				(4.0 + etasq)) + 0.375 * satrec.j2 * tsi / psisq * satrec.con41 *
				(8.0 + 3.0 * etasq * (8.0 + etasq)));
			satrec.cc1 = satrec.bstar * cc2;
			cc3 = 0.0;
			if (satrec.ecco > 1.0e-4)
				cc3 = -2.0 * coef * tsi * satrec.j3oj2 * satrec.no_unkozai * sinio / satrec.ecco;
			satrec.x1mth2 = 1.0 - cosio2;
			satrec.cc4 = 2.0* satrec.no_unkozai * coef1 * ao * omeosq *
				(satrec.eta * (2.0 + 0.5 * etasq) + satrec.ecco *
				(0.5 + 2.0 * etasq) - satrec.j2 * tsi / (ao * psisq) *
				(-3.0 * satrec.con41 * (1.0 - 2.0 * eeta + etasq *
				(1.5 - 0.5 * eeta)) + 0.75 * satrec.x1mth2 *
				(2.0 * etasq - eeta * (1.0 + etasq)) * cos(2.0 * satrec.argpo)));
			satrec.cc5 = 2.0 * coef1 * ao * omeosq * (1.0 + 2.75 *
				(etasq + eeta) + eeta * etasq);
			cosio4 = cosio2 * cosio2;
			temp1 = 1.5 * satrec.j2 * pinvsq * satrec.no_unkozai;
			temp2 = 0.5 * temp1 * satrec.j2 * pinvsq;
			temp3 = -0.46875 * satrec.j4 * pinvsq * pinvsq * satrec.no_unkozai;
			satrec.mdot = satrec.no_unkozai + 0.5 * temp1 * rteosq * satrec.con41 + 0.0625 *
				temp2 * rteosq * (13.0 - 78.0 * cosio2 + 137.0 * cosio4);
			satrec.argpdot = -0.5 * temp1 * con42 + 0.0625 * temp2 *
				(7.0 - 114.0 * cosio2 + 395.0 * cosio4) +
				temp3 * (3.0 - 36.0 * cosio2 + 49.0 * cosio4);
			xhdot1 = -temp1 * cosio;
			satrec.nodedot = xhdot1 + (0.5 * temp2 * (4.0 - 19.0 * cosio2) +
				2.0 * temp3 * (3.0 - 7.0 * cosio2)) * cosio;
			xpidot = satrec.argpdot + satrec.nodedot;
			satrec.omgcof = satrec.bstar * cc3 * cos(satrec.argpo);
			satrec.xmcof = 0.0;
			if (satrec.ecco > 1.0e-4)
				satrec.xmcof = -x2o3 * coef * satrec.bstar / eeta;
			satrec.nodecf = 3.5 * omeosq * xhdot1 * satrec.cc1;
			satrec.t2cof = 1.5 * satrec.cc1;
			// sgp4fix for divide by zero with xinco = 180 deg
			if (fabs(cosio + 1.0) > 1.5e-12)
				satrec.xlcof = -0.25 * satrec.j3oj2 * sinio * (3.0 + 5.0 * cosio) / (1.0 + cosio);
			else
				satrec.xlcof = -0.25 * satrec.j3oj2 * sinio * (3.0 + 5.0 * cosio) / temp4;
			satrec.aycof = -0.5 * satrec.j3oj2 * sinio;
			// sgp4fix use multiply for speed instead of pow
			delmotemp = 1.0 + satrec.eta * cos(satrec.mo);
			satrec.delmo = delmotemp * delmotemp * delmotemp;
			satrec.sinmao = sin(satrec.mo);
			satrec.x7thm1 = 7.0 * cosio2 - 1.0;

			/* --------------- deep space initialization ------------- */
			if ((2 * pi / satrec.no_unkozai) >= 225.0)
			{
				satrec.method = 'd';
				satrec.isimp = 1;
				tc = 0.0;
				inclm = satrec.inclo;

				dscom
					(
					epoch, satrec.ecco, satrec.argpo, tc, satrec.inclo, satrec.nodeo,
					satrec.no_unkozai, snodm, cnodm, sinim, cosim, sinomm, cosomm,
					day, satrec.e3, satrec.ee2, em, emsq, gam,
					satrec.peo, satrec.pgho, satrec.pho, satrec.pinco,
					satrec.plo, rtemsq, satrec.se2, satrec.se3,
					satrec.sgh2, satrec.sgh3, satrec.sgh4,
					satrec.sh2, satrec.sh3, satrec.si2, satrec.si3,
					satrec.sl2, satrec.sl3, satrec.sl4, s1, s2, s3, s4, s5,
					s6, s7, ss1, ss2, ss3, ss4, ss5, ss6, ss7, sz1, sz2, sz3,
					sz11, sz12, sz13, sz21, sz22, sz23, sz31, sz32, sz33,
					satrec.xgh2, satrec.xgh3, satrec.xgh4, satrec.xh2,
					satrec.xh3, satrec.xi2, satrec.xi3, satrec.xl2,
					satrec.xl3, satrec.xl4, nm, z1, z2, z3, z11,
					z12, z13, z21, z22, z23, z31, z32, z33,
					satrec.zmol, satrec.zmos
					);
				dpper
					(
					satrec.e3, satrec.ee2, satrec.peo, satrec.pgho,
					satrec.pho, satrec.pinco, satrec.plo, satrec.se2,
					satrec.se3, satrec.sgh2, satrec.sgh3, satrec.sgh4,
					satrec.sh2, satrec.sh3, satrec.si2, satrec.si3,
					satrec.sl2, satrec.sl3, satrec.sl4, satrec.t,
					satrec.xgh2, satrec.xgh3, satrec.xgh4, satrec.xh2,
					satrec.xh3, satrec.xi2, satrec.xi3, satrec.xl2,
					satrec.xl3, satrec.xl4, satrec.zmol, satrec.zmos, inclm, satrec.init,
					satrec.ecco, satrec.inclo, satrec.nodeo, satrec.argpo, satrec.mo,
					satrec.operationmode
					);

				argpm = 0.0;
				nodem = 0.0;
				mm = 0.0;

				dsinit
					(
					satrec.xke,
					cosim, emsq, satrec.argpo, s1, s2, s3, s4, s5, sinim, ss1, ss2, ss3, ss4,
					ss5, sz1, sz3, sz11, sz13, sz21, sz23, sz31, sz33, satrec.t, tc,
					satrec.gsto, satrec.mo, satrec.mdot, satrec.no_unkozai, satrec.nodeo,
					satrec.nodedot, xpidot, z1, z3, z11, z13, z21, z23, z31, z33,
					satrec.ecco, eccsq, em, argpm, inclm, mm, nm, nodem,
					satrec.irez, satrec.atime,
					satrec.d2201, satrec.d2211, satrec.d3210, satrec.d3222,
					satrec.d4410, satrec.d4422, satrec.d5220, satrec.d5232,
					satrec.d5421, satrec.d5433, satrec.dedt, satrec.didt,
					satrec.dmdt, dndt, satrec.dnodt, satrec.domdt,
					satrec.del1, satrec.del2, satrec.del3, satrec.xfact,
					satrec.xlamo, satrec.xli, satrec.xni
					);
			}

			/* ----------- set variables if not deep space ----------- */
			if (satrec.isimp != 1)
			{
				cc1sq = satrec.cc1 * satrec.cc1;
				satrec.d2 = 4.0 * ao * tsi * cc1sq;
				temp = satrec.d2 * tsi * satrec.cc1 / 3.0;
				satrec.d3 = (17.0 * ao + sfour) * temp;
				satrec.d4 = 0.5 * temp * ao * tsi * (221.0 * ao + 31.0 * sfour) *
					satrec.cc1;
				satrec.t3cof = satrec.d2 + 2.0 * cc1sq;
				satrec.t4cof = 0.25 * (3.0 * satrec.d3 + satrec.cc1 *
					(12.0 * satrec.d2 + 10.0 * cc1sq));
				satrec.t5cof = 0.2 * (3.0 * satrec.d4 +
					12.0 * satrec.cc1 * satrec.d3 +
					6.0 * satrec.d2 * satrec.d2 +
					15.0 * cc1sq * (2.0 * satrec.d2 + cc1sq));
			}
		} // if omeosq = 0 ...

		/* finally propogate to zero epoch to initialize all others. */
		// sgp4fix take out check to let satellites process until they are actually below earth surface
		//       if(satrec.error == 0)
		sgp4(satrec, 0.0, r, v);

		satrec.init = 'n';

		//#include "debug6.cpp"
		//sgp4fix return boolean. satrec.error contains any error codes
		return true;
	}  // sgp4init

	/*-----------------------------------------------------------------------------
	*
	*                             procedure sgp4
	*
	*  this procedure is the sgp4 prediction model from space command. this is an
	*    updated and combined version of sgp4 and sdp4, which were originally
	*    published separately in spacetrack report #3. this version follows the
	*    methodology from the aiaa paper (2006) describing the history and
	*    development of the code.
	*
	*  author        : david vallado                  719-573-2600   28 jun 2005
	*
	*  inputs        :
	*    satrec	 - initialised structure from sgp4init() call.
	*    tsince	 - time since epoch (minutes)
	*
	*  outputs       :
	*    r           - position vector                     km
	*    v           - velocity                            km/sec
	*  return code - non-zero on error.
	*                   1 - mean elements, ecc >= 1.0 or ecc < -0.001 or a < 0.95 er
	*                   2 - mean motion less than 0.0
	*                   3 - pert elements, ecc < 0.0  or  ecc > 1.0
	*                   4 - semi-latus rectum < 0.0
	*                   5 - epoch elements are sub-orbital
	*                   6 - satellite has decayed
	*
	*  locals        :
	*    am          -
	*    axnl, aynl        -
	*    betal       -
	*    cosim   , sinim   , cosomm  , sinomm  , cnod    , snod    , cos2u   ,
	*    sin2u   , coseo1  , sineo1  , cosi    , sini    , cosip   , sinip   ,
	*    cosisq  , cossu   , sinsu   , cosu    , sinu
	*    delm        -
	*    delomg      -
	*    dndt        -
	*    eccm        -
	*    emsq        -
	*    ecose       -
	*    el2         -
	*    eo1         -
	*    eccp        -
	*    esine       -
	*    argpm       -
	*    argpp       -
	*    omgadf      -c
	*    pl          -
	*    r           -
	*    rtemsq      -
	*    rdotl       -
	*    rl          -
	*    rvdot       -
	*    rvdotl      -
	*    su          -
	*    t2  , t3   , t4    , tc
	*    tem5, temp , temp1 , temp2  , tempa  , tempe  , templ
	*    u   , ux   , uy    , uz     , vx     , vy     , vz
	*    inclm       - inclination
	*    mm          - mean anomaly
	*    nm          - mean motion
	*    nodem       - right asc of ascending node
	*    xinc        -
	*    xincp       -
	*    xl          -
	*    xlm         -
	*    mp          -
	*    xmdf        -
	*    xmx         -
	*    xmy         -
	*    nodedf      -
	*    xnode       -
	*    nodep       -
	*    np          -
	*
	*  coupling      :
	*    getgravconst- no longer used. Variables are conatined within satrec
	*    dpper
	*    dpspace
	*
	*  references    :
	*    hoots, roehrich, norad spacetrack report #3 1980
	*    hoots, norad spacetrack report #6 1986
	*    hoots, schumacher and glover 2004
	*    vallado, crawford, hujsak, kelso  2006
	----------------------------------------------------------------------------*/

	bool sgp4
		(
		elsetrec& satrec, double tsince,
		double r[3], double v[3]
		)
	{
		double am, axnl, aynl, betal, cosim, cnod,
			cos2u, coseo1, cosi, cosip, cosisq, cossu, cosu,
			delm, delomg, em, emsq, ecose, el2, eo1,
			ep, esine, argpm, argpp, argpdf, pl, mrt = 0.0,
			mvt, rdotl, rl, rvdot, rvdotl, sinim,
			sin2u, sineo1, sini, sinip, sinsu, sinu,
			snod, su, t2, t3, t4, tem5, temp,
			temp1, temp2, tempa, tempe, templ, u, ux,
			uy, uz, vx, vy, vz, inclm, mm,
			nm, nodem, xinc, xincp, xl, xlm, mp,
			xmdf, xmx, xmy, nodedf, xnode, nodep, tc, dndt,
			twopi, x2o3, vkmpersec, delmtemp;
		int ktr;

		/* ------------------ set mathematical constants --------------- */
		// sgp4fix divisor for divide by zero check on inclination
		// the old check used 1.0 + cos(pi-1.0e-9), but then compared it to
		// 1.5 e-12, so the threshold was changed to 1.5e-12 for consistency
		const double temp4 = 1.5e-12;
		twopi = 2.0 * pi;
		x2o3 = 2.0 / 3.0;
		// sgp4fix identify constants and allow alternate values
		// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );
		vkmpersec = satrec.radiusearthkm * satrec.xke / 60.0;

		/* --------------------- clear sgp4 error flag ----------------- */
		satrec.t = tsince;
		satrec.error = 0;

		/* ------- update for secular gravity and atmospheric drag ----- */
		xmdf = satrec.mo + satrec.mdot * satrec.t;
		argpdf = satrec.argpo + satrec.argpdot * satrec.t;
		nodedf = satrec.nodeo + satrec.nodedot * satrec.t;
		argpm = argpdf;
		mm = xmdf;
		t2 = satrec.t * satrec.t;
		nodem = nodedf + satrec.nodecf * t2;
		tempa = 1.0 - satrec.cc1 * satrec.t;
		tempe = satrec.bstar * satrec.cc4 * satrec.t;
		templ = satrec.t2cof * t2;

		if (satrec.isimp != 1)
		{
			delomg = satrec.omgcof * satrec.t;
			// sgp4fix use mutliply for speed instead of pow
			delmtemp = 1.0 + satrec.eta * cos(xmdf);
			delm = satrec.xmcof *
				(delmtemp * delmtemp * delmtemp -
				satrec.delmo);
			temp = delomg + delm;
			mm = xmdf + temp;
			argpm = argpdf - temp;
			t3 = t2 * satrec.t;
			t4 = t3 * satrec.t;
			tempa = tempa - satrec.d2 * t2 - satrec.d3 * t3 -
				satrec.d4 * t4;
			tempe = tempe + satrec.bstar * satrec.cc5 * (sin(mm) -
				satrec.sinmao);
			templ = templ + satrec.t3cof * t3 + t4 * (satrec.t4cof +
				satrec.t * satrec.t5cof);
		}

		nm = satrec.no_unkozai;
		em = satrec.ecco;
		inclm = satrec.inclo;
		if (satrec.method == 'd')
		{
			tc = satrec.t;
			dspace
				(
				satrec.irez,
				satrec.d2201, satrec.d2211, satrec.d3210,
				satrec.d3222, satrec.d4410, satrec.d4422,
				satrec.d5220, satrec.d5232, satrec.d5421,
				satrec.d5433, satrec.dedt, satrec.del1,
				satrec.del2, satrec.del3, satrec.didt,
				satrec.dmdt, satrec.dnodt, satrec.domdt,
				satrec.argpo, satrec.argpdot, satrec.t, tc,
				satrec.gsto, satrec.xfact, satrec.xlamo,
				satrec.no_unkozai, satrec.atime,
				em, argpm, inclm, satrec.xli, mm, satrec.xni,
				nodem, dndt, nm
				);
		} // if method = d

		if (nm <= 0.0)
		{
			//         printf("# error nm %f\n", nm);
			satrec.error = 2;
			// sgp4fix add return
			return false;
		}
		am = pow((satrec.xke / nm), x2o3) * tempa * tempa;
		nm = satrec.xke / pow(am, 1.5);
		em = em - tempe;

		// fix tolerance for error recognition
		// sgp4fix am is fixed from the previous nm check
		if ((em >= 1.0) || (em < -0.001)/* || (am < 0.95)*/)
		{
			//         printf("# error em %f\n", em);
			satrec.error = 1;
			// sgp4fix to return if there is an error in eccentricity
			return false;
		}
		// sgp4fix fix tolerance to avoid a divide by zero
		if (em < 1.0e-6)
			em = 1.0e-6;
		mm = mm + satrec.no_unkozai * templ;
		xlm = mm + argpm + nodem;
		emsq = em * em;
		temp = 1.0 - emsq;

		nodem = fmod(nodem, twopi);
		argpm = fmod(argpm, twopi);
		xlm = fmod(xlm, twopi);
		mm = fmod(xlm - argpm - nodem, twopi);

		// sgp4fix recover singly averaged mean elements
		satrec.am = am;
		satrec.em = em;
		satrec.im = inclm;
		satrec.Om = nodem;
		satrec.om = argpm;
		satrec.mm = mm;
		satrec.nm = nm;

		/* ----------------- compute extra mean quantities ------------- */
		sinim = sin(inclm);
		cosim = cos(inclm);

		/* -------------------- add lunar-solar periodics -------------- */
		ep = em;
		xincp = inclm;
		argpp = argpm;
		nodep = nodem;
		mp = mm;
		sinip = sinim;
		cosip = cosim;
		if (satrec.method == 'd')
		{
			dpper
				(
				satrec.e3, satrec.ee2, satrec.peo,
				satrec.pgho, satrec.pho, satrec.pinco,
				satrec.plo, satrec.se2, satrec.se3,
				satrec.sgh2, satrec.sgh3, satrec.sgh4,
				satrec.sh2, satrec.sh3, satrec.si2,
				satrec.si3, satrec.sl2, satrec.sl3,
				satrec.sl4, satrec.t, satrec.xgh2,
				satrec.xgh3, satrec.xgh4, satrec.xh2,
				satrec.xh3, satrec.xi2, satrec.xi3,
				satrec.xl2, satrec.xl3, satrec.xl4,
				satrec.zmol, satrec.zmos, satrec.inclo,
				'n', ep, xincp, nodep, argpp, mp, satrec.operationmode
				);
			if (xincp < 0.0)
			{
				xincp = -xincp;
				nodep = nodep + pi;
				argpp = argpp - pi;
			}
			if ((ep < 0.0) || (ep > 1.0))
			{
				//            printf("# error ep %f\n", ep);
				satrec.error = 3;
				// sgp4fix add return
				return false;
			}
		} // if method = d

		/* -------------------- long period periodics ------------------ */
		if (satrec.method == 'd')
		{
			sinip = sin(xincp);
			cosip = cos(xincp);
			satrec.aycof = -0.5*satrec.j3oj2*sinip;
			// sgp4fix for divide by zero for xincp = 180 deg
			if (fabs(cosip + 1.0) > 1.5e-12)
				satrec.xlcof = -0.25 * satrec.j3oj2 * sinip * (3.0 + 5.0 * cosip) / (1.0 + cosip);
			else
				satrec.xlcof = -0.25 * satrec.j3oj2 * sinip * (3.0 + 5.0 * cosip) / temp4;
		}
		axnl = ep * cos(argpp);
		temp = 1.0 / (am * (1.0 - ep * ep));
		aynl = ep* sin(argpp) + temp * satrec.aycof;
		xl = mp + argpp + nodep + temp * satrec.xlcof * axnl;

		/* --------------------- solve kepler's equation --------------- */
		u = fmod(xl - nodep, twopi);
		eo1 = u;
		tem5 = 9999.9;
		ktr = 1;
		//   sgp4fix for kepler iteration
		//   the following iteration needs better limits on corrections
		while ((fabs(tem5) >= 1.0e-12) && (ktr <= 10))
		{
			sineo1 = sin(eo1);
			coseo1 = cos(eo1);
			tem5 = 1.0 - coseo1 * axnl - sineo1 * aynl;
			tem5 = (u - aynl * coseo1 + axnl * sineo1 - eo1) / tem5;
			if (fabs(tem5) >= 0.95)
				tem5 = tem5 > 0.0 ? 0.95 : -0.95;
			eo1 = eo1 + tem5;
			ktr = ktr + 1;
		}

		/* ------------- short period preliminary quantities ----------- */
		ecose = axnl*coseo1 + aynl*sineo1;
		esine = axnl*sineo1 - aynl*coseo1;
		el2 = axnl*axnl + aynl*aynl;
		pl = am*(1.0 - el2);
		if (pl < 0.0)
		{
			//         printf("# error pl %f\n", pl);
			satrec.error = 4;
			// sgp4fix add return
			return false;
		}
		else
		{
			rl = am * (1.0 - ecose);
			rdotl = sqrt(am) * esine / rl;
			rvdotl = sqrt(pl) / rl;
			betal = sqrt(1.0 - el2);
			temp = esine / (1.0 + betal);
			sinu = am / rl * (sineo1 - aynl - axnl * temp);
			cosu = am / rl * (coseo1 - axnl + aynl * temp);
			su = atan2(sinu, cosu);
			sin2u = (cosu + cosu) * sinu;
			cos2u = 1.0 - 2.0 * sinu * sinu;
			temp = 1.0 / pl;
			temp1 = 0.5 * satrec.j2 * temp;
			temp2 = temp1 * temp;

			/* -------------- update for short period periodics ------------ */
			if (satrec.method == 'd')
			{
				cosisq = cosip * cosip;
				satrec.con41 = 3.0*cosisq - 1.0;
				satrec.x1mth2 = 1.0 - cosisq;
				satrec.x7thm1 = 7.0*cosisq - 1.0;
			}
			mrt = rl * (1.0 - 1.5 * temp2 * betal * satrec.con41) +
				0.5 * temp1 * satrec.x1mth2 * cos2u;
			su = su - 0.25 * temp2 * satrec.x7thm1 * sin2u;
			xnode = nodep + 1.5 * temp2 * cosip * sin2u;
			xinc = xincp + 1.5 * temp2 * cosip * sinip * cos2u;
			mvt = rdotl - nm * temp1 * satrec.x1mth2 * sin2u / satrec.xke;
			rvdot = rvdotl + nm * temp1 * (satrec.x1mth2 * cos2u +
				1.5 * satrec.con41) / satrec.xke;

			/* --------------------- orientation vectors ------------------- */
			sinsu = sin(su);
			cossu = cos(su);
			snod = sin(xnode);
			cnod = cos(xnode);
			sini = sin(xinc);
			cosi = cos(xinc);
			xmx = -snod * cosi;
			xmy = cnod * cosi;
			ux = xmx * sinsu + cnod * cossu;
			uy = xmy * sinsu + snod * cossu;
			uz = sini * sinsu;
			vx = xmx * cossu - cnod * sinsu;
			vy = xmy * cossu - snod * sinsu;
			vz = sini * cossu;

			/* --------- position and velocity (in km and km/sec) ---------- */
			r[0] = (mrt * ux)* satrec.radiusearthkm;
			r[1] = (mrt * uy)* satrec.radiusearthkm;
			r[2] = (mrt * uz)* satrec.radiusearthkm;
			v[0] = (mvt * ux + rvdot * vx) * vkmpersec;
			v[1] = (mvt * uy + rvdot * vy) * vkmpersec;
			v[2] = (mvt * uz + rvdot * vz) * vkmpersec;
		}  // if pl > 0

		// sgp4fix for decaying satellites
		if (mrt < 1.0)
		{
			//         printf("# decay condition %11.6f \n",mrt);
			satrec.error = 6;
			return false;
		}

		//#include "debug7.cpp"
		return true;
	}  // sgp4





	/* -----------------------------------------------------------------------------
	*
	*                           function getgravconst
	*
	*  this function gets constants for the propagator. note that mu is identified to
	*    facilitiate comparisons with newer models. the common useage is wgs72.
	*
	*  author        : david vallado                  719-573-2600   21 jul 2006
	*
	*  inputs        :
	*    whichconst  - which set of constants to use  wgs72old, wgs72, wgs84
	*
	*  outputs       :
	*    tumin       - minutes in one time unit
	*    mu          - earth gravitational parameter
	*    radiusearthkm - radius of the earth in km
	*    xke         - reciprocal of tumin
	*    j2, j3, j4  - un-normalized zonal harmonic values
	*    j3oj2       - j3 divided by j2
	*
	*  locals        :
	*
	*  coupling      :
	*    none
	*
	*  references    :
	*    norad spacetrack report #3
	*    vallado, crawford, hujsak, kelso  2006
	--------------------------------------------------------------------------- */

	void getgravconst
		(
		gravconsttype whichconst,
		double& tumin,
		double& mus,
		double& radiusearthkm,
		double& xke,
		double& j2,
		double& j3,
		double& j4,
		double& j3oj2
		)
	{

		switch (whichconst)
		{
			// -- wgs-72 low precision str#3 constants --
		case wgs72old:
			mus = 398600.79964;        // in km3 / s2
			radiusearthkm = 6378.135;     // km
			xke = 0.0743669161;        // reciprocal of tumin
			tumin = 1.0 / xke;
			j2 = 0.001082616;
			j3 = -0.00000253881;
			j4 = -0.00000165597;
			j3oj2 = j3 / j2;
			break;
			// ------------ wgs-72 constants ------------
		case wgs72:
			mus = 398600.8;            // in km3 / s2
			radiusearthkm = 6378.135;     // km
			xke = 60.0 / sqrt(radiusearthkm*radiusearthkm*radiusearthkm / mus);
			tumin = 1.0 / xke;
			j2 = 0.001082616;
			j3 = -0.00000253881;
			j4 = -0.00000165597;
			j3oj2 = j3 / j2;
			break;
		case wgs84:
			// ------------ wgs-84 constants ------------
			mus = 398600.5;            // in km3 / s2
			radiusearthkm = 6378.137;     // km
			xke = 60.0 / sqrt(radiusearthkm*radiusearthkm*radiusearthkm / mus);
			tumin = 1.0 / xke;
			j2 = 0.00108262998905;
			j3 = -0.00000253215306;
			j4 = -0.00000161098761;
			j3oj2 = j3 / j2;
			break;
		default:
			fprintf(stderr, "unknown gravity option (%d)\n", whichconst);
			break;
		}

	}   // getgravconst

	// older sgp4io methods
	/* -----------------------------------------------------------------------------
	*
	*                           function twoline2rv
	*
	*  this function converts the two line element set character string data to
	*    variables and initializes the sgp4 variables. several intermediate varaibles
	*    and quantities are determined. note that the result is a structure so multiple
	*    satellites can be processed simaltaneously without having to reinitialize. the
	*    verification mode is an important option that permits quick checks of any
	*    changes to the underlying technical theory. this option works using a
	*    modified tle file in which the start, stop, and delta time values are
	*    included at the end of the second line of data. this only works with the
	*    verification mode. the catalog mode simply propagates from -1440 to 1440 min
	*    from epoch and is useful when performing entire catalog runs.
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs        :
	*    longstr1    - first line of the tle
	*    longstr2    - second line of the tle
	*    typerun     - type of run                    verification 'v', catalog 'c',
	*                                                 manual 'm'
	*    typeinput   - type of manual input           mfe 'm', epoch 'e', dayofyr 'd'
	*    opsmode     - mode of operation afspc or improved 'a', 'i'
	*    whichconst  - which set of constants to use  72, 84
	*
	*  outputs       :
	*    satrec      - structure containing all the sgp4 satellite information
	*
	*  coupling      :
	*    getgravconst-
	*    days2mdhms  - conversion of days to month, day, hour, minute, second
	*    jday        - convert day month year hour minute second into julian date
	*    sgp4init    - initialize the sgp4 variables
	*
	*  references    :
	*    norad spacetrack report #3
	*    vallado, crawford, hujsak, kelso  2006
	--------------------------------------------------------------------------- */

	void twoline2rv
		(
		char longstr1[130], char longstr2[130],
		char typerun, char typeinput, char opsmode,
		gravconsttype whichconst,
		double& startmfe, double& stopmfe, double& deltamin,
		elsetrec& satrec
		)
	{
		const double deg2rad = pi / 180.0;         //   0.0174532925199433
		const double xpdotp = 1440.0 / (2.0 *pi);  // 229.1831180523293

		double sec;
		double startsec, stopsec, startdayofyr, stopdayofyr, jdstart, jdstop, jdstartF, jdstopF;
		int startyear, stopyear, startmon, stopmon, startday, stopday,
			starthr, stophr, startmin, stopmin;
		int cardnumb, j;
		// sgp4fix include in satrec
		// long revnum = 0, elnum = 0;
		// char classification, intldesg[11];
		int year = 0;
		int mon, day, hr, minute, nexp, ibexp;

		// sgp4fix no longer needed
		// getgravconst( whichconst, tumin, mu, radiusearthkm, xke, j2, j3, j4, j3oj2 );

		satrec.error = 0;

		// set the implied decimal points since doing a formated read
		// fixes for bad input data values (missing, ...)
		for (j = 10; j <= 15; j++)
			if (longstr1[j] == ' ')
				longstr1[j] = '_';

		if (longstr1[44] != ' ')
			longstr1[43] = longstr1[44];
		longstr1[44] = '.';
		if (longstr1[7] == ' ')
			longstr1[7] = 'U';
		if (longstr1[9] == ' ')
			longstr1[9] = '.';
		for (j = 45; j <= 49; j++)
			if (longstr1[j] == ' ')
				longstr1[j] = '0';
		if (longstr1[51] == ' ')
			longstr1[51] = '0';
		if (longstr1[53] != ' ')
			longstr1[52] = longstr1[53];
		longstr1[53] = '.';
		longstr2[25] = '.';
		for (j = 26; j <= 32; j++)
			if (longstr2[j] == ' ')
				longstr2[j] = '0';
		if (longstr1[62] == ' ')
			longstr1[62] = '0';
		if (longstr1[68] == ' ')
			longstr1[68] = '0';
#ifdef _MSC_VER // chk if compiling in MSVS c++
		sscanf_s(longstr1, "%2d %5s %1c %10s %2d %12lf %11lf %7lf %2d %7lf %2d %2d %6ld ",
			&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.classification, sizeof(char), &satrec.intldesg, 11 * sizeof(char), &satrec.epochyr,
			&satrec.epochdays, &satrec.ndot, &satrec.nddot, &nexp, &satrec.bstar, &ibexp, &satrec.ephtype, &satrec.elnum);
#else
		sscanf(longstr1, "%2d %5s %1c %10s %2d %12lf %11lf %7lf %2d %7lf %2d %2d %6ld ",
			&cardnumb, &satrec.satnum, &satrec.classification, &satrec.intldesg, &satrec.epochyr,
			&satrec.epochdays, &satrec.ndot, &satrec.nddot, &nexp, &satrec.bstar,
			&ibexp, &satrec.ephtype, &satrec.elnum);
#endif
		if (typerun == 'v')  // run for specified times from the file
		{
			if (longstr2[52] == ' ')
			{
#ifdef _MSC_VER
				sscanf_s(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %10lf %6ld %lf %lf %lf \n",
					&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.inclo,
					&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
					&satrec.revnum, &startmfe, &stopmfe, &deltamin);
#else
				sscanf(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %10lf %6ld %lf %lf %lf \n",
					&cardnumb, &satrec.satnum, &satrec.inclo,
					&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
					&satrec.revnum, &startmfe, &stopmfe, &deltamin);
#endif
			}
			else
			{
#ifdef _MSC_VER
				sscanf_s(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %11lf %6ld %lf %lf %lf \n",
					&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.inclo,
					&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
					&satrec.revnum, &startmfe, &stopmfe, &deltamin);
#else
				sscanf(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %11lf %6ld %lf %lf %lf \n",
					&cardnumb, &satrec.satnum, &satrec.inclo,
					&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
					&satrec.revnum, &startmfe, &stopmfe, &deltamin);
#endif
			}
		}
		else  // simply run -1 day to +1 day or user input times
		{
			if (longstr2[52] == ' ')
			{
#ifdef _MSC_VER
				sscanf_s(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %10lf %6ld \n",
					&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.inclo,
					&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
					&satrec.revnum);
#else
				sscanf(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %10lf %6ld \n",
					&cardnumb, &satrec.satnum, &satrec.inclo,
					&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
					&satrec.revnum);
#endif
			}
			else
			{
#ifdef _MSC_VER
				sscanf_s(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %11lf %6ld \n",
					&cardnumb, &satrec.satnum, 6 * sizeof(char), &satrec.inclo,
					&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
					&satrec.revnum);
#else
				sscanf(longstr2, "%2d %5s %9lf %9lf %8lf %9lf %9lf %11lf %6ld \n",
					&cardnumb, &satrec.satnum, &satrec.inclo,
					&satrec.nodeo, &satrec.ecco, &satrec.argpo, &satrec.mo, &satrec.no_kozai,
					&satrec.revnum);
#endif
			}
		}

		// ---- find no, ndot, nddot ----
		satrec.no_kozai = satrec.no_kozai / xpdotp; //* rad/min
		satrec.nddot = satrec.nddot * pow(10.0, nexp);
		satrec.bstar = satrec.bstar * pow(10.0, ibexp);

		// ---- convert to sgp4 units ----
		// satrec.a    = pow( satrec.no_kozai*tumin , (-2.0/3.0) );
		satrec.ndot = satrec.ndot / (xpdotp*1440.0);  //* ? * minperday
		satrec.nddot = satrec.nddot / (xpdotp*1440.0 * 1440);

		// ---- find standard orbital elements ----
		satrec.inclo = satrec.inclo  * deg2rad;
		satrec.nodeo = satrec.nodeo  * deg2rad;
		satrec.argpo = satrec.argpo  * deg2rad;
		satrec.mo = satrec.mo     * deg2rad;

		// sgp4fix not needed here
		// satrec.alta = satrec.a*(1.0 + satrec.ecco) - 1.0;
		// satrec.altp = satrec.a*(1.0 - satrec.ecco) - 1.0;

		// ----------------------------------------------------------------
		// find sgp4epoch time of element set
		// remember that sgp4 uses units of days from 0 jan 1950 (sgp4epoch)
		// and minutes from the epoch (time)
		// ----------------------------------------------------------------

		// ---------------- temp fix for years from 1957-2056 -------------------
		// --------- correct fix will occur when year is 4-digit in tle ---------
		if (satrec.epochyr < 57)
			year = satrec.epochyr + 2000;
		else
			year = satrec.epochyr + 1900;

		days2mdhms_SGP4(year, satrec.epochdays, mon, day, hr, minute, sec);
		jday_SGP4(year, mon, day, hr, minute, sec, satrec.jdsatepoch, satrec.jdsatepochF);

		// ---- input start stop times manually
		if ((typerun != 'v') && (typerun != 'c'))
		{
			// ------------- enter start/stop ymd hms values --------------------
			if (typeinput == 'e')
			{
				printf("input start prop year mon day hr min sec \n");
				// make sure there is no space at the end of the format specifiers in scanf!
#ifdef _MSC_VER
				scanf_s("%i %i %i %i %i %lf", &startyear, &startmon, &startday, &starthr, &startmin, &startsec);
#else
				scanf("%i %i %i %i %i %lf", &startyear, &startmon, &startday, &starthr, &startmin, &startsec);
#endif
				fflush(stdin);
				jday_SGP4(startyear, startmon, startday, starthr, startmin, startsec, jdstart, jdstartF);

				printf("input stop prop year mon day hr min sec \n");
#ifdef _MSC_VER
				scanf_s("%i %i %i %i %i %lf", &stopyear, &stopmon, &stopday, &stophr, &stopmin, &stopsec);
#else
				scanf("%i %i %i %i %i %lf", &stopyear, &stopmon, &stopday, &stophr, &stopmin, &stopsec);
#endif
				fflush(stdin);
				jday_SGP4(stopyear, stopmon, stopday, stophr, stopmin, stopsec, jdstop, jdstopF);

				startmfe = (jdstart - satrec.jdsatepoch) * 1440.0 + (jdstartF - satrec.jdsatepochF) * 1440.0;
				stopmfe = (jdstop - satrec.jdsatepoch) * 1440.0 + (jdstopF - satrec.jdsatepochF) * 1440.0;

				printf("input time step in minutes \n");
#ifdef _MSC_VER
				scanf_s("%lf", &deltamin);
#else
				scanf("%lf", &deltamin);
#endif
			}
			// -------- enter start/stop year and days of year values -----------
			if (typeinput == 'd')
			{
				printf("input start year dayofyr \n");
#ifdef _MSC_VER
				scanf_s("%i %lf", &startyear, &startdayofyr);
#else
				scanf("%i %lf", &startyear, &startdayofyr);
#endif
				printf("input stop year dayofyr \n");
#ifdef _MSC_VER
				scanf_s("%i %lf", &stopyear, &stopdayofyr);
#else
				scanf("%i %lf", &stopyear, &stopdayofyr);
#endif

				days2mdhms_SGP4(startyear, startdayofyr, mon, day, hr, minute, sec);
				jday_SGP4(startyear, mon, day, hr, minute, sec, jdstart, jdstartF);
				days2mdhms_SGP4(stopyear, stopdayofyr, mon, day, hr, minute, sec);
				jday_SGP4(stopyear, mon, day, hr, minute, sec, jdstop, jdstopF);

				startmfe = (jdstart - satrec.jdsatepoch) * 1440.0 + (jdstartF - satrec.jdsatepochF) * 1440.0;
				stopmfe = (jdstop - satrec.jdsatepoch) * 1440.0 + (jdstopF - satrec.jdsatepochF) * 1440.0;

				printf("input time step in minutes \n");
#ifdef _MSC_VER
				scanf_s("%lf", &deltamin);
#else

				scanf("%lf", &deltamin);
#endif
			}
			// ------------------ enter start/stop mfe values -------------------
			if (typeinput == 'm')
			{
#ifdef _MSC_VER
				printf("input start min from epoch \n");
				scanf_s("%lf", &startmfe);
				printf("input stop min from epoch \n");
				scanf_s("%lf", &stopmfe);
				printf("input time step in minutes \n");
				scanf_s("%lf", &deltamin);
#else
				printf("input start min from epoch \n");
				scanf("%lf", &startmfe);
				printf("input stop min from epoch \n");
				scanf("%lf", &stopmfe);
				printf("input time step in minutes \n");
				scanf("%lf", &deltamin);
#endif
			}
		}

		// ------------ perform complete catalog evaluation, -+ 1 day ----------- 
		if (typerun == 'c')
		{
			startmfe = -1440.0;
			stopmfe = 1440.0;
			deltamin = 10.0;
		}

		// ---------------- initialize the orbit at sgp4epoch -------------------
		sgp4init(whichconst, opsmode, satrec.satnum, (satrec.jdsatepoch + satrec.jdsatepochF) - 2433281.5, satrec.bstar,
			satrec.ndot, satrec.nddot, satrec.ecco, satrec.argpo, satrec.inclo, satrec.mo, satrec.no_kozai,
			satrec.nodeo, satrec);
	} // twoline2rv


	// older sgp4ext methods
	/* -----------------------------------------------------------------------------
	*
	*                           function gstime_SGP4
	*
	*  this function finds the greenwich sidereal time.
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    jdut1       - julian date in ut1             days from 4713 bc
	*
	*  outputs       :
	*    gstime      - greenwich sidereal time        0 to 2pi rad
	*
	*  locals        :
	*    temp        - temporary variable for doubles   rad
	*    tut1        - julian centuries from the
	*                  jan 1, 2000 12 h epoch (ut1)
	*
	*  coupling      :
	*    none
	*
	*  references    :
	*    vallado       2013, 187, eq 3-45
	* --------------------------------------------------------------------------- */

	double  gstime_SGP4
		(
		double jdut1
		)
	{
		const double twopi = 2.0 * pi;
		const double deg2rad = pi / 180.0;
		double       temp, tut1;

		tut1 = (jdut1 - 2451545.0) / 36525.0;
		temp = -6.2e-6* tut1 * tut1 * tut1 + 0.093104 * tut1 * tut1 +
			(876600.0 * 3600 + 8640184.812866) * tut1 + 67310.54841;  // sec
		temp = fmod(temp * deg2rad / 240.0, twopi); //360/86400 = 1/240, to deg, to rad

		// ------------------------ check quadrants ---------------------
		if (temp < 0.0)
			temp += twopi;

		return temp;
	}  // gstime

	double  sgn_SGP4
		(
		double x
		)
	{
		if (x < 0.0)
		{
			return -1.0;
		}
		else
		{
			return 1.0;
		}

	}  // sgn

	/* -----------------------------------------------------------------------------
	*
	*                           function mag_SGP4
	*
	*  this procedure finds the magnitude of a vector.  
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    vec         - vector
	*
	*  outputs       :
	*    mag         - answer 
	*
	*  locals        :
	*    none.
	*
	*  coupling      :
	*    none.
	* --------------------------------------------------------------------------- */

	double  mag_SGP4
		(
		double x[3]
		)
	{
		return sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
	}  // mag

	/* -----------------------------------------------------------------------------
	*
	*                           procedure cross_SGP4
	*
	*  this procedure crosses two vectors.
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    vec1        - vector number 1
	*    vec2        - vector number 2
	*
	*  outputs       :
	*    outvec      - vector result of a x b
	*
	*  locals        :
	*    none.
	*
	*  coupling      :
	*    mag           magnitude of a vector
	---------------------------------------------------------------------------- */

	void    cross_SGP4
		(
		double vec1[3], double vec2[3], double outvec[3]
		)
	{
		outvec[0] = vec1[1] * vec2[2] - vec1[2] * vec2[1];
		outvec[1] = vec1[2] * vec2[0] - vec1[0] * vec2[2];
		outvec[2] = vec1[0] * vec2[1] - vec1[1] * vec2[0];
	}  // end cross


	/* -----------------------------------------------------------------------------
	*
	*                           function dot_SGP4
	*
	*  this function finds the dot product of two vectors.
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    vec1        - vector number 1
	*    vec2        - vector number 2
	*
	*  outputs       :
	*    dot         - result
	*
	*  locals        :
	*    none.
	*
	*  coupling      :
	*    none.
	* --------------------------------------------------------------------------- */

	double  dot_SGP4
		(
		double x[3], double y[3]
		)
	{
		return (x[0] * y[0] + x[1] * y[1] + x[2] * y[2]);
	}  // dot

	/* -----------------------------------------------------------------------------
	*
	*                           procedure angle_SGP4
	*
	*  this procedure calculates the angle between two vectors.  the output is
	*    set to 999999.1 to indicate an undefined value.  be sure to check for
	*    this at the output phase.
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    vec1        - vector number 1
	*    vec2        - vector number 2
	*
	*  outputs       :
	*    theta       - angle between the two vectors  -pi to pi
	*
	*  locals        :
	*    temp        - temporary real variable
	*
	*  coupling      :
	*    dot           dot product of two vectors
	* --------------------------------------------------------------------------- */

	double  angle_SGP4
		(
		double vec1[3],
		double vec2[3]
		)
	{
		double small, undefined, magv1, magv2, temp;
		small = 0.00000001;
		undefined = 999999.1;

		magv1 = mag_SGP4(vec1);
		magv2 = mag_SGP4(vec2);

		if (magv1*magv2 > small*small)
		{
			temp = dot_SGP4(vec1, vec2) / (magv1*magv2);
			if (fabs(temp) > 1.0)
				temp = sgn_SGP4(temp) * 1.0;
			return acos(temp);
		}
		else
			return undefined;
	}  // angle


	/* -----------------------------------------------------------------------------
	*
	*                           function asinh_SGP4
	*
	*  this function evaluates the inverse hyperbolic sine function.
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    xval        - angle value                                  any real
	*
	*  outputs       :
	*    arcsinh     - result                                       any real
	*
	*  locals        :
	*    none.
	*
	*  coupling      :
	*    none.
	* --------------------------------------------------------------------------- */

	double  asinh_SGP4
		(
		double xval
		)
	{
		return log(xval + sqrt(xval*xval + 1.0));
	}  // asinh


	/* -----------------------------------------------------------------------------
	*
	*                           function newtonnu_SGP4
	*
	*  this function solves keplers equation when the true anomaly is known.
	*    the mean and eccentric, parabolic, or hyperbolic anomaly is also found.
	*    the parabolic limit at 168 is arbitrary. the hyperbolic anomaly is also
	*    limited. the hyperbolic sine is used because it's not double valued.
	*
	*  author        : david vallado                  719-573-2600   27 may 2002
	*
	*  revisions
	*    vallado     - fix small                                     24 sep 2002
	*
	*  inputs          description                    range / units
	*    ecc         - eccentricity                   0.0  to
	*    nu          - true anomaly                   -2pi to 2pi rad
	*
	*  outputs       :
	*    e0          - eccentric anomaly              0.0  to 2pi rad       153.02 
	*    m           - mean anomaly                   0.0  to 2pi rad       151.7425 
	*
	*  locals        :
	*    e1          - eccentric anomaly, next value  rad
	*    sine        - sine of e
	*    cose        - cosine of e
	*    ktr         - index
	*
	*  coupling      :
	*    asinh       - arc hyperbolic sine
	*
	*  references    :
	*    vallado       2013, 77, alg 5
	* --------------------------------------------------------------------------- */

	void newtonnu_SGP4
		(
		double ecc, double nu,
		double& e0, double& m
		)
	{
		double small, sine, cose;

		// ---------------------  implementation   ---------------------
		e0 = 999999.9;
		m = 999999.9;
		small = 0.00000001;

		// --------------------------- circular ------------------------
		if (fabs(ecc) < small)
		{
			m = nu;
			e0 = nu;
		}
		else
			// ---------------------- elliptical -----------------------
			if (ecc < 1.0 - small)
			{
			sine = (sqrt(1.0 - ecc*ecc) * sin(nu)) / (1.0 + ecc*cos(nu));
			cose = (ecc + cos(nu)) / (1.0 + ecc*cos(nu));
			e0 = atan2(sine, cose);
			m = e0 - ecc*sin(e0);
			}
			else
				// -------------------- hyperbolic  --------------------
				if (ecc > 1.0 + small)
				{
			if ((ecc > 1.0) && (fabs(nu) + 0.00001 < pi - acos(1.0 / ecc)))
			{
				sine = (sqrt(ecc*ecc - 1.0) * sin(nu)) / (1.0 + ecc*cos(nu));
				e0 = asinh_SGP4(sine);
				m = ecc*sinh(e0) - e0;
			}
				}
				else
					// ----------------- parabolic ---------------------
					if (fabs(nu) < 168.0*pi / 180.0)
					{
			e0 = tan(nu*0.5);
			m = e0 + (e0*e0*e0) / 3.0;
					}

		if (ecc < 1.0)
		{
			m = fmod(m, 2.0 *pi);
			if (m < 0.0)
				m = m + 2.0 *pi;
			e0 = fmod(e0, 2.0 *pi);
		}
	}  // newtonnu


	/* -----------------------------------------------------------------------------
	*
	*                           function rv2coe_SGP4
	*
	*  this function finds the classical orbital elements given the geocentric
	*    equatorial position and velocity vectors.
	*
	*  author        : david vallado                  719-573-2600   21 jun 2002
	*
	*  revisions
	*    vallado     - fix special cases                              5 sep 2002
	*    vallado     - delete extra check in inclination code        16 oct 2002
	*    vallado     - add constant file use                         29 jun 2003
	*    vallado     - add mu                                         2 apr 2007
	*
	*  inputs          description                    range / units
	*    r           - ijk position vector            km
	*    v           - ijk velocity vector            km / s
	*    mu          - gravitational parameter        km3 / s2
	*
	*  outputs       :
	*    p           - semilatus rectum               km
	*    a           - semimajor axis                 km
	*    ecc         - eccentricity
	*    incl        - inclination                    0.0  to pi rad
	*    omega       - right ascension of ascending node    0.0  to 2pi rad
	*    argp        - argument of perigee            0.0  to 2pi rad
	*    nu          - true anomaly                   0.0  to 2pi rad
	*    m           - mean anomaly                   0.0  to 2pi rad
	*    arglat      - argument of latitude      (ci) 0.0  to 2pi rad
	*    truelon     - true longitude            (ce) 0.0  to 2pi rad
	*    lonper      - longitude of periapsis    (ee) 0.0  to 2pi rad
	*
	*  locals        :
	*    hbar        - angular momentum h vector      km2 / s
	*    ebar        - eccentricity     e vector
	*    nbar        - line of nodes    n vector
	*    c1          - v**2 - u/r
	*    rdotv       - r dot v
	*    hk          - hk unit vector
	*    sme         - specfic mechanical energy      km2 / s2
	*    i           - index
	*    e           - eccentric, parabolic,
	*                  hyperbolic anomaly             rad
	*    temp        - temporary variable
	*    typeorbit   - type of orbit                  ee, ei, ce, ci
	*
	*  coupling      :
	*    mag         - magnitude of a vector
	*    cross       - cross product of two vectors
	*    angle       - find the angle between two vectors
	*    newtonnu    - find the mean anomaly
	*
	*  references    :
	*    vallado       2013, 113, alg 9, ex 2-5
	* --------------------------------------------------------------------------- */

	void rv2coe_SGP4
		(
		double r[3], double v[3], double mus,
		double& p, double& a, double& ecc, double& incl, double& omega, double& argp,
		double& nu, double& m, double& arglat, double& truelon, double& lonper
		)
	{
		double undefined, small, hbar[3], nbar[3], magr, magv, magn, ebar[3], sme,
			rdotv, infinite, temp, c1, hk, twopi, magh, halfpi, e;

		int i;
		// switch this to an integer msvs seems to have probelms with this and strncpy_s
		//char typeorbit[2];
		int typeorbit;
		// here 
		// typeorbit = 1 = 'ei'
		// typeorbit = 2 = 'ce'
		// typeorbit = 3 = 'ci'
		// typeorbit = 4 = 'ee'

		twopi = 2.0 * pi;
		halfpi = 0.5 * pi;
		small = 0.00000001;
		undefined = 999999.1;
		infinite = 999999.9;

		// -------------------------  implementation   -----------------
		magr = mag_SGP4(r);
		magv = mag_SGP4(v);

		// ------------------  find h n and e vectors   ----------------
		cross_SGP4(r, v, hbar);
		magh = mag_SGP4(hbar);
		if (magh > small)
		{
			nbar[0] = -hbar[1];
			nbar[1] = hbar[0];
			nbar[2] = 0.0;
			magn = mag_SGP4(nbar);
			c1 = magv*magv - mus / magr;
			rdotv = dot_SGP4(r, v);
			for (i = 0; i <= 2; i++)
				ebar[i] = (c1*r[i] - rdotv*v[i]) / mus;
			ecc = mag_SGP4(ebar);

			// ------------  find a e and semi-latus rectum   ----------
			sme = (magv*magv*0.5) - (mus / magr);
			if (fabs(sme) > small)
				a = -mus / (2.0 *sme);
			else
				a = infinite;
			p = magh*magh / mus;

			// -----------------  find inclination   -------------------
			hk = hbar[2] / magh;
			incl = acos(hk);

			// --------  determine type of orbit for later use  --------
			// ------ elliptical, parabolic, hyperbolic inclined -------
			//#ifdef _MSC_VER  // chk if compiling under MSVS
			//		   strcpy_s(typeorbit, 2 * sizeof(char), "ei");
			//#else
			//		   strcpy(typeorbit, "ei");
			//#endif
			typeorbit = 1;

			if (ecc < small)
			{
				// ----------------  circular equatorial ---------------
				if ((incl < small) | (fabs(incl - pi) < small))
				{
					//#ifdef _MSC_VER
					//				   strcpy_s(typeorbit, sizeof(typeorbit), "ce");
					//#else
					//				   strcpy(typeorbit, "ce");
					//#endif
					typeorbit = 2;
				}
				else
				{
					// --------------  circular inclined ---------------
					//#ifdef _MSC_VER
					//				   strcpy_s(typeorbit, sizeof(typeorbit), "ci");
					//#else
					//				   strcpy(typeorbit, "ci");
					//#endif
					typeorbit = 3;
				}
			}
			else
			{
				// - elliptical, parabolic, hyperbolic equatorial --
				if ((incl < small) | (fabs(incl - pi) < small)){
					//#ifdef _MSC_VER
					//				   strcpy_s(typeorbit, sizeof(typeorbit), "ee");
					//#else
					//				   strcpy(typeorbit, "ee");
					//#endif
					typeorbit = 4;
				}
			}

			// ----------  find right ascension of the ascending node ------------
			if (magn > small)
			{
				temp = nbar[0] / magn;
				if (fabs(temp) > 1.0)
					temp = sgn_SGP4(temp);
				omega = acos(temp);
				if (nbar[1] < 0.0)
					omega = twopi - omega;
			}
			else
				omega = undefined;

			// ---------------- find argument of perigee ---------------
			//if (strcmp(typeorbit, "ei") == 0)
			if (typeorbit == 1)
			{
				argp = angle_SGP4(nbar, ebar);
				if (ebar[2] < 0.0)
					argp = twopi - argp;
			}
			else
				argp = undefined;

			// ------------  find true anomaly at epoch    -------------
			//if (typeorbit[0] == 'e')
			if ((typeorbit == 1) || (typeorbit == 4))
			{
				nu = angle_SGP4(ebar, r);
				if (rdotv < 0.0)
					nu = twopi - nu;
			}
			else
				nu = undefined;

			// ----  find argument of latitude - circular inclined -----
			//if (strcmp(typeorbit, "ci") == 0)
			if (typeorbit == 3)
			{
				arglat = angle_SGP4(nbar, r);
				if (r[2] < 0.0)
					arglat = twopi - arglat;
				m = arglat;
			}
			else
				arglat = undefined;

			// -- find longitude of perigee - elliptical equatorial ----
			//if ((ecc>small) && (strcmp(typeorbit, "ee") == 0))
			if ((ecc>small) && (typeorbit == 4))
			{
				temp = ebar[0] / ecc;
				if (fabs(temp) > 1.0)
					temp = sgn_SGP4(temp);
				lonper = acos(temp);
				if (ebar[1] < 0.0)
					lonper = twopi - lonper;
				if (incl > halfpi)
					lonper = twopi - lonper;
			}
			else
				lonper = undefined;

			// -------- find true longitude - circular equatorial ------
			//if ((magr>small) && (strcmp(typeorbit, "ce") == 0))
			if ((magr > small) && (typeorbit == 2))
			{
				temp = r[0] / magr;
				if (fabs(temp) > 1.0)
					temp = sgn_SGP4(temp);
				truelon = acos(temp);
				if (r[1] < 0.0)
					truelon = twopi - truelon;
				if (incl > halfpi)
					truelon = twopi - truelon;
				m = truelon;
			}
			else
				truelon = undefined;

			// ------------ find mean anomaly for all orbits -----------
			//if (typeorbit[0] == 'e')
			if ((typeorbit == 1) || (typeorbit == 4))
				newtonnu_SGP4(ecc, nu, e, m);
		}
		else
		{
			p = undefined;
			a = undefined;
			ecc = undefined;
			incl = undefined;
			omega = undefined;
			argp = undefined;
			nu = undefined;
			m = undefined;
			arglat = undefined;
			truelon = undefined;
			lonper = undefined;
		}
	}  // rv2coe


	/* -----------------------------------------------------------------------------
	*
	*                           procedure jday_SGP4
	*
	*  this procedure finds the julian date given the year, month, day, and time.
	*    the julian date is defined by each elapsed day since noon, jan 1, 4713 bc.
	*
	*  algorithm     : calculate the answer in one step for efficiency
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    year        - year                           1900 .. 2100
	*    mon         - month                          1 .. 12
	*    day         - day                            1 .. 28,29,30,31
	*    hr          - universal time hour            0 .. 23
	*    min         - universal time min             0 .. 59
	*    sec         - universal time sec             0.0 .. 59.999
	*
	*  outputs       :
	*    jd          - julian date                    days from 4713 bc
	*    jdfrac      - julian date fraction into day  days from 4713 bc
	*
	*  locals        :
	*    none.
	*
	*  coupling      :
	*    none.
	*
	*  references    :
	*    vallado       2013, 183, alg 14, ex 3-4
	* --------------------------------------------------------------------------- */

	void    jday_SGP4
		(
		int year, int mon, int day, int hr, int minute, double sec,
		double& jd, double& jdFrac
		)
	{
		jd = 367.0 * year -
			floor((7 * (year + floor((mon + 9) / 12.0))) * 0.25) +
			floor(275 * mon / 9.0) +
			day + 1721013.5;  // use - 678987.0 to go to mjd directly
		jdFrac = (sec + minute * 60.0 + hr * 3600.0) / 86400.0;

		// check that the day and fractional day are correct
		if (fabs(jdFrac) > 1.0)
		{
			double dtt = floor(jdFrac);
			jd = jd + dtt;
			jdFrac = jdFrac - dtt;
		}

		// - 0.5*sgn(100.0*year + mon - 190002.5) + 0.5;
	}  // jday


	/* -----------------------------------------------------------------------------
	*
	*                           procedure days2mdhms_SGP4
	*
	*  this procedure converts the day of the year, days, to the equivalent month
	*    day, hour, minute and second.
	*
	*  algorithm     : set up array for the number of days per month
	*                  find leap year - use 1900 because 2000 is a leap year
	*                  loop through a temp value while the value is < the days
	*                  perform int conversions to the correct day and month
	*                  convert remainder into h m s using type conversions
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    year        - year                           1900 .. 2100
	*    days        - julian day of the year         1.0  .. 366.0
	*
	*  outputs       :
	*    mon         - month                          1 .. 12
	*    day         - day                            1 .. 28,29,30,31
	*    hr          - hour                           0 .. 23
	*    min         - minute                         0 .. 59
	*    sec         - second                         0.0 .. 59.999
	*
	*  locals        :
	*    dayofyr     - day of year
	*    temp        - temporary extended values
	*    inttemp     - temporary int value
	*    i           - index
	*    lmonth[13]  - int array containing the number of days per month
	*
	*  coupling      :
	*    none.
	* --------------------------------------------------------------------------- */

	void    days2mdhms_SGP4
		(
		int year, double days,
		int& mon, int& day, int& hr, int& minute, double& sec
		)
	{
		int i, inttemp, dayofyr;
		double    temp;
		int lmonth[] = { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };

		dayofyr = (int)floor(days);
		/* ----------------- find month and day of month ---------------- */
		if ((year % 4) == 0)
			lmonth[2] = 29;

		i = 1;
		inttemp = 0;
		while ((dayofyr > inttemp + lmonth[i]) && (i < 12))
		{
			inttemp = inttemp + lmonth[i];
			i++;
		}
		mon = i;
		day = dayofyr - inttemp;

		/* ----------------- find hours minutes and seconds ------------- */
		temp = (days - dayofyr) * 24.0;
		hr = (int)floor(temp);
		temp = (temp - hr) * 60.0;
		minute = (int)floor(temp);
		sec = (temp - minute) * 60.0;
	}  // days2mdhms

	/* -----------------------------------------------------------------------------
	*
	*                           procedure invjday_SGP4
	*
	*  this procedure finds the year, month, day, hour, minute and second
	*  given the julian date. tu can be ut1, tdt, tdb, etc.
	*
	*  algorithm     : set up starting values
	*                  find leap year - use 1900 because 2000 is a leap year
	*                  find the elapsed days through the year in a loop
	*                  call routine to find each individual value
	*
	*  author        : david vallado                  719-573-2600    1 mar 2001
	*
	*  inputs          description                    range / units
	*    jd          - julian date                    days from 4713 bc
	*    jdfrac      - julian date fraction into day  days from 4713 bc
	*
	*  outputs       :
	*    year        - year                           1900 .. 2100
	*    mon         - month                          1 .. 12
	*    day         - day                            1 .. 28,29,30,31
	*    hr          - hour                           0 .. 23
	*    min         - minute                         0 .. 59
	*    sec         - second                         0.0 .. 59.999
	*
	*  locals        :
	*    days        - day of year plus fractional
	*                  portion of a day               days
	*    tu          - julian centuries from 0 h
	*                  jan 0, 1900
	*    temp        - temporary double values
	*    leapyrs     - number of leap years from 1900
	*
	*  coupling      :
	*    days2mdhms  - finds month, day, hour, minute and second given days and year
	*
	*  references    :
	*    vallado       2013, 203, alg 22, ex 3-13
	* --------------------------------------------------------------------------- */

	void    invjday_SGP4
		(
		double jd, double jdfrac,
		int& year, int& mon, int& day,
		int& hr, int& minute, double& sec
		)
	{
		int leapyrs;
		double dt, days, tu, temp;

		// check jdfrac for multiple days
		if (fabs(jdfrac) >= 1.0)
		{
			jd = jd + floor(jdfrac);
			jdfrac = jdfrac - floor(jdfrac);
		}

		// check for fraction of a day included in the jd
		dt = jd - floor(jd) - 0.5;
		if (fabs(dt) > 0.00000001)
		{
			jd = jd - dt;
			jdfrac = jdfrac + dt;
		}

		/* --------------- find year and days of the year --------------- */
		temp = jd - 2415019.5;
		tu = temp / 365.25;
		year = 1900 + (int)floor(tu);
		leapyrs = (int)floor((year - 1901) * 0.25);

		days = floor(temp - ((year - 1900) * 365.0 + leapyrs));

		/* ------------ check for case of beginning of a year ----------- */
		if (days + jdfrac < 1.0)
		{
			year = year - 1;
			leapyrs = (int)floor((year - 1901) * 0.25);
			days = floor(temp - ((year - 1900) * 365.0 + leapyrs));
		}

		/* ----------------- find remaining data  ------------------------- */
		days2mdhms_SGP4(year, days + jdfrac, mon, day, hr, minute, sec);
	}  // invjday


} // namespace SGP4Funcs