class SolarSystem():
def __init__(self, total_time, dt):
self.solver = Solver(total_time, dt)
self.planet = Planet(self.solver, 3e-6, [1, 0], [0, 2 * np.pi])
self.sun = Planet(self.solver, 1, [0, 0], [0, 0])
self.planet.accelerations[0, :] = self.planet.get_acceleration(
[self.sun], 0)
def run(self):
self.solver.velocity_verlet(self.planet, self.sun)
#self.solver.forward_euler(self.planet, self.sun)
plt.plot(self.planet.positions[:, 0], self.planet.positions[:, 1])
plt.xlabel("x [AU]")
plt.ylabel("y [AU]")
plt.legend(["Earth"])
plt.tight_layout()
plt.savefig("circular_orbit.png")
plt.show()
def test_energy_conservation(self):
kinetic_energies = 0.5 * self.planet.mass * (
self.planet.velocities[:, 0]**2 + self.planet.velocities[:, 1]**2)
potential_energies = -4 * np.pi**2 * self.sun.mass * self.planet.mass / np.sqrt(
self.planet.positions[:, 0]**2 + self.planet.positions[:, 1]**2)
angular_momentum = self.planet.mass * np.cross(self.planet.positions,
self.planet.velocities)
x = np.linspace(0, self.solver.total_time, self.solver.time_steps)
plt.plot(x, kinetic_energies, x, potential_energies, x,
angular_momentum)
plt.xlabel("Time[Years]")
plt.ylabel('Energy[$M_\odot AU^2/yr^2$]')
plt.legend(["Kinetic energy", "Potential energy", "Angular momentum"])
plt.tight_layout()
plt.savefig("energy_conservation_elliptic.png")
plt.show()
