def __init__(self):
self.rEarth = vector.Vector(1,0,0)
self.vEarth = vector.Vector(0,2*math.pi,0)
self.rMars = vector.Vector(1.5,0,0)
self.vMars = vector.Vector(0,2*math.pi/math.sqrt(1.5),0)
self.max_steps = 10000
self. solver = Solver.RK4(0.01)
self.physics = Physics.CentralGravity(self.solver,G=4*math.pi**2,M=1)
def run(self):
'''Orbits'''
for v0 in self.v0_list:
for dt in self.dt_list:
r = vector.Vector(self.AU, 0, 0) #starting position in AU
v = vector.Vector(0, v0, 0)
earth = Body.GravBody(1, r, v)
solver = Solver.RK4(dt)
physics = Physics.CentralGravity(solver, G=4 * math.pi**2,
M=1) # M is 1 solar mass
sim = Simulation.OrbitSim(self.stop, physics, earth)
time, bodies = sim.get_results()
y = [b[0].position.y for b in bodies]
x = [b[0].position.x for b in bodies]
energy = physics.energy(bodies)
errors = self.error(energy)
if v0 == math.pi * 2:
plt.figure(1)
plt.plot(x, y, '.')
plt.title("Circular Orbits of Earth Around Sun")
plt.ylabel("Position in y [AU]")
plt.xlabel("Position in x [AU]")
plt.legend(["dt=0.003", "dt=0.002", "dt=0.001"])
plt.figure(2)
plt.plot(time, errors)
plt.title("Error in Energy vs Time")
plt.ylabel("Percent Error")
plt.xlabel("Time [Years]")
plt.legend(["dt=0.003", "dt=0.002", "dt=0.001"])
else:
plt.figure(3)
plt.plot(x, y, '.')
plt.title("Elliptical Orbits of Earth Around Sun")
plt.ylabel("Position in y [AU]")
plt.xlabel("Position in x [AU]")
plt.legend(["dt=0.003", "dt=0.002", "dt=0.001"])
plt.figure(4)
plt.plot(time, errors)
plt.title("Error in Energy vs Time")
plt.ylabel("Percent Error")
plt.xlabel("Time [Years]")
plt.legend(["dt=0.003", "dt=0.002", "dt=0.001"])
"""Kepler"""
r_list = [0.9, 1, 1.1]
v_list = [2 * math.pi, 2 * 0.9 * math.pi, 2 * 1.1 * math.pi]
for r in r_list:
for v in v_list:
r0 = vector.Vector(r, 0, 0)
v0 = vector.Vector(0, v, 0)
earth = Body.GravBody(1, r0, v0)
solver = Solver.RK4(0.001)
physics = Physics.CentralGravity(solver, G=4 * math.pi**2,
M=1) # M is 1 solar mass
sim = Simulation.OrbitSim(self.stop, physics, earth)
time, bodies = sim.get_results()
a = sim.semimajor_axis()
p = sim.period()
plt.figure(5)
plt.plot(a, p, '.')
plt.figure(5)
a = np.arange(0, 2, 0.001)
p = a**(3. / 2.)
plt.plot(a, p)
plt.title("Semi Major Axis vs Period")
plt.ylabel("Orbital Period [Years]")
plt.xlabel("Semi Major Axis [AU]")