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nbody.py
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149 lines (126 loc) · 6.61 KB
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class NBodySystem(object):
class Body(object):
PI = 3.141592653589793
SOLAR_MASS = 4 * PI * PI
DAYS_PER_YEAR = 365.24
def __init__(self,x,y,z,vx,vy,vz,mass):
self.x = x
self.y = y
self.z = z
self.vx = vx
self.vy = vy
self.vz = vz
self.mass = mass
@classmethod
def Jupiter(cls):
return cls(
x = 4.84143144246472090e+00,
y = -1.16032004402742839e+00,
z = -1.03622044471123109e-01,
vx = 1.66007664274403694e-03 * cls.DAYS_PER_YEAR,
vy = 7.69901118419740425e-03 * cls.DAYS_PER_YEAR,
vz = -6.90460016972063023e-05 * cls.DAYS_PER_YEAR,
mass = 9.54791938424326609e-04 * cls.SOLAR_MASS
)
@classmethod
def Saturn(cls):
return cls(
x = 8.34336671824457987e+00,
y = 4.12479856412430479e+00,
z = -4.03523417114321381e-01,
vx = -2.76742510726862411e-03 * cls.DAYS_PER_YEAR,
vy = 4.99852801234917238e-03 * cls.DAYS_PER_YEAR,
vz = 2.30417297573763929e-05 * cls.DAYS_PER_YEAR,
mass = 2.85885980666130812e-04 * cls.SOLAR_MASS,
)
@classmethod
def Uranus(cls):
return cls(
x = 1.28943695621391310e+01,
y = -1.51111514016986312e+01,
z = -2.23307578892655734e-01,
vx = 2.96460137564761618e-03 * cls.DAYS_PER_YEAR,
vy = 2.37847173959480950e-03 * cls.DAYS_PER_YEAR,
vz = -2.96589568540237556e-05 * cls.DAYS_PER_YEAR,
mass = 4.36624404335156298e-05 * cls.SOLAR_MASS,
)
@classmethod
def Neptune(cls):
return cls(
x = 1.53796971148509165e+01,
y = -2.59193146099879641e+01,
z = 1.79258772950371181e-01,
vx = 2.68067772490389322e-03 * cls.DAYS_PER_YEAR,
vy = 1.62824170038242295e-03 * cls.DAYS_PER_YEAR,
vz = -9.51592254519715870e-05 * cls.DAYS_PER_YEAR,
mass = 5.15138902046611451e-05 * cls.SOLAR_MASS,
)
@classmethod
def Sun(cls):
return cls(
x = 0,
y = 0,
z = 0,
vx = 0,
vy = 0,
vz = 0,
mass = cls.SOLAR_MASS,
)
def offsetMomentum(self, px, py, pz):
self.vx = -px / self.SOLAR_MASS
self.vy = -py / self.SOLAR_MASS
self.vz = -pz / self.SOLAR_MASS
def __init__(self):
self.bodies = [ self.Body.Sun(),
self.Body.Jupiter(),
self.Body.Saturn(),
self.Body.Uranus(),
self.Body.Neptune()]
px, py, pz = 0.0, 0.0, 0.0
for i in range(len(self.bodies)):
px += self.bodies[i].vx * self.bodies[i].mass
py += self.bodies[i].vy * self.bodies[i].mass
pz += self.bodies[i].vz * self.bodies[i].mass
self.bodies[0].offsetMomentum(px, py, pz)
def advance(self, dt):
for i in range(len(self.bodies)):
iBody = self.bodies[i]
for j in range(i + 1, len(self.bodies)):
dx = iBody.x - self.bodies[j].x
dy = iBody.y - self.bodies[j].y
dz = iBody.z - self.bodies[j].z
dSquared = dx*dx + dy*dy + dz*dz
distance = dSquared ** 0.5
mag = dt / (dSquared * distance)
iBody.vx -= dx * self.bodies[j].mass * mag
iBody.vy -= dy * self.bodies[j].mass * mag
iBody.vz -= dz * self.bodies[j].mass * mag
self.bodies[j].vx += dx * iBody.mass * mag
self.bodies[j].vy += dy * iBody.mass * mag
self.bodies[j].vz += dz * iBody.mass * mag
for i in range(len(self.bodies)):
body = self.bodies[i]
body.x = body.x + dt * body.vx
body.y = body.y + dt * body.vy
body.z = body.z + dt * body.vz
def energy(self):
e = 0
for i in range(len(self.bodies)):
iBody = self.bodies[i]
val = 0.5 * iBody.mass * (iBody.vx*iBody.vx + iBody.vy*iBody.vy + iBody.vz*iBody.vz)
e += val
for j in range(i + 1, len(self.bodies)):
jBody = self.bodies[j]
dx = iBody.x - jBody.x
dy = iBody.y - jBody.y
dz = iBody.z - jBody.z
distance = (dx*dx + dy*dy + dz*dz) ** 0.5
val = (iBody.mass * jBody.mass) / distance
e -= val
return e
def run(self, n):
if n < 0:
return 0
for _ in range(n):
self.advance(0.01)
return self.energy()