source code
-- The Computer Language Benchmarks Game
-- https://salsa.debian.org/benchmarksgame-team/benchmarksgame/
-- contributed by Mike Pall
-- modified by Geoff Leyland
local sqrt = math.sqrt
local PI = 3.141592653589793
local SOLAR_MASS = 4 * PI * PI
local DAYS_PER_YEAR = 365.24
local bodies = {
{ -- Sun
x = 0,
y = 0,
z = 0,
vx = 0,
vy = 0,
vz = 0,
mass = SOLAR_MASS
},
{ -- Jupiter
x = 4.84143144246472090e+00,
y = -1.16032004402742839e+00,
z = -1.03622044471123109e-01,
vx = 1.66007664274403694e-03 * DAYS_PER_YEAR,
vy = 7.69901118419740425e-03 * DAYS_PER_YEAR,
vz = -6.90460016972063023e-05 * DAYS_PER_YEAR,
mass = 9.54791938424326609e-04 * SOLAR_MASS
},
{ -- Saturn
x = 8.34336671824457987e+00,
y = 4.12479856412430479e+00,
z = -4.03523417114321381e-01,
vx = -2.76742510726862411e-03 * DAYS_PER_YEAR,
vy = 4.99852801234917238e-03 * DAYS_PER_YEAR,
vz = 2.30417297573763929e-05 * DAYS_PER_YEAR,
mass = 2.85885980666130812e-04 * SOLAR_MASS
},
{ -- Uranus
x = 1.28943695621391310e+01,
y = -1.51111514016986312e+01,
z = -2.23307578892655734e-01,
vx = 2.96460137564761618e-03 * DAYS_PER_YEAR,
vy = 2.37847173959480950e-03 * DAYS_PER_YEAR,
vz = -2.96589568540237556e-05 * DAYS_PER_YEAR,
mass = 4.36624404335156298e-05 * SOLAR_MASS
},
{ -- Neptune
x = 1.53796971148509165e+01,
y = -2.59193146099879641e+01,
z = 1.79258772950371181e-01,
vx = 2.68067772490389322e-03 * DAYS_PER_YEAR,
vy = 1.62824170038242295e-03 * DAYS_PER_YEAR,
vz = -9.51592254519715870e-05 * DAYS_PER_YEAR,
mass = 5.15138902046611451e-05 * SOLAR_MASS
}
}
local function advance(bodies, nbody, dt)
for i=1,nbody do
local bi = bodies[i]
local bix, biy, biz, bimass = bi.x, bi.y, bi.z, bi.mass
local bivx, bivy, bivz = bi.vx, bi.vy, bi.vz
for j=i+1,nbody do
local bj = bodies[j]
local dx, dy, dz = bix-bj.x, biy-bj.y, biz-bj.z
local mag = sqrt(dx*dx + dy*dy + dz*dz)
mag = dt / (mag * mag * mag)
local bm = bj.mass*mag
bivx = bivx - (dx * bm)
bivy = bivy - (dy * bm)
bivz = bivz - (dz * bm)
bm = bimass*mag
bj.vx = bj.vx + (dx * bm)
bj.vy = bj.vy + (dy * bm)
bj.vz = bj.vz + (dz * bm)
end
bi.vx = bivx
bi.vy = bivy
bi.vz = bivz
bi.x = bix + dt * bivx
bi.y = biy + dt * bivy
bi.z = biz + dt * bivz
end
end
local function energy(bodies, nbody)
local e = 0
for i=1,nbody do
local bi = bodies[i]
local vx, vy, vz, bim = bi.vx, bi.vy, bi.vz, bi.mass
e = e + (0.5 * bim * (vx*vx + vy*vy + vz*vz))
for j=i+1,nbody do
local bj = bodies[j]
local dx, dy, dz = bi.x-bj.x, bi.y-bj.y, bi.z-bj.z
local distance = sqrt(dx*dx + dy*dy + dz*dz)
e = e - ((bim * bj.mass) / distance)
end
end
return e
end
local function offsetMomentum(b, nbody)
local px, py, pz = 0, 0, 0
for i=1,nbody do
local bi = b[i]
local bim = bi.mass
px = px + (bi.vx * bim)
py = py + (bi.vy * bim)
pz = pz + (bi.vz * bim)
end
b[1].vx = -px / SOLAR_MASS
b[1].vy = -py / SOLAR_MASS
b[1].vz = -pz / SOLAR_MASS
end
local N = tonumber(arg and arg[1]) or 1000
local nbody = #bodies
offsetMomentum(bodies, nbody)
io.write( string.format("%0.9f",energy(bodies, nbody)), "\n")
for i=1,N do advance(bodies, nbody, 0.01) end
io.write( string.format("%0.9f",energy(bodies, nbody)), "\n")