1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
|
# The Computer Language Shootout
# http://shootout.alioth.debian.org
#
# Optimized for Ruby by Jesse Millikan
# From version ported by Michael Neumann from the C gcc version,
# which was written by Christoph Bauer.
SOLAR_MASS = 4 * Math::PI**2
DAYS_PER_YEAR = 365.24
class Planet
attr_accessor :x, :y, :z, :vx, :vy, :vz, :mass
def initialize(x, y, z, vx, vy, vz, mass)
@x, @y, @z = x, y, z
@vx, @vy, @vz = vx * DAYS_PER_YEAR, vy * DAYS_PER_YEAR, vz * DAYS_PER_YEAR
@mass = mass * SOLAR_MASS
end
def move_from_i(bodies, nbodies, dt, i)
while i < nbodies
b2 = bodies[i]
dx = @x - b2.x
dy = @y - b2.y
dz = @z - b2.z
distance = Math.sqrt(dx * dx + dy * dy + dz * dz)
mag = dt / (distance * distance * distance)
b_mass_mag, b2_mass_mag = @mass * mag, b2.mass * mag
@vx -= dx * b2_mass_mag
@vy -= dy * b2_mass_mag
@vz -= dz * b2_mass_mag
b2.vx += dx * b_mass_mag
b2.vy += dy * b_mass_mag
b2.vz += dz * b_mass_mag
i += 1
end
@x += dt * @vx
@y += dt * @vy
@z += dt * @vz
end
end
def energy(bodies)
e = 0.0
nbodies = bodies.size
for i in 0 ... nbodies
b = bodies[i]
e += 0.5 * b.mass * (b.vx * b.vx + b.vy * b.vy + b.vz * b.vz)
for j in (i + 1) ... nbodies
b2 = bodies[j]
dx = b.x - b2.x
dy = b.y - b2.y
dz = b.z - b2.z
distance = Math.sqrt(dx * dx + dy * dy + dz * dz)
e -= (b.mass * b2.mass) / distance
end
end
e
end
def offset_momentum(bodies)
px, py, pz = 0.0, 0.0, 0.0
for b in bodies
m = b.mass
px += b.vx * m
py += b.vy * m
pz += b.vz * m
end
b = bodies[0]
b.vx = - px / SOLAR_MASS
b.vy = - py / SOLAR_MASS
b.vz = - pz / SOLAR_MASS
end
BODIES = [
# sun
Planet.new(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0),
# jupiter
Planet.new(
4.84143144246472090e+00,
-1.16032004402742839e+00,
-1.03622044471123109e-01,
1.66007664274403694e-03,
7.69901118419740425e-03,
-6.90460016972063023e-05,
9.54791938424326609e-04),
# saturn
Planet.new(
8.34336671824457987e+00,
4.12479856412430479e+00,
-4.03523417114321381e-01,
-2.76742510726862411e-03,
4.99852801234917238e-03,
2.30417297573763929e-05,
2.85885980666130812e-04),
# uranus
Planet.new(
1.28943695621391310e+01,
-1.51111514016986312e+01,
-2.23307578892655734e-01,
2.96460137564761618e-03,
2.37847173959480950e-03,
-2.96589568540237556e-05,
4.36624404335156298e-05),
# neptune
Planet.new(
1.53796971148509165e+01,
-2.59193146099879641e+01,
1.79258772950371181e-01,
2.68067772490389322e-03,
1.62824170038242295e-03,
-9.51592254519715870e-05,
5.15138902046611451e-05)
]
n = Integer(ARGV[0])
offset_momentum(BODIES)
puts "%.9f" % energy(BODIES)
nbodies = BODIES.size
dt = 0.01
n.times do
i = 0
while i < nbodies
b = BODIES[i]
b.move_from_i(BODIES, nbodies, dt, i + 1)
i += 1
end
end
puts "%.9f" % energy(BODIES)
|
