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n-body.py
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n-body.py
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import numpy as np
import matplotlib.pyplot as plt
class Particle:
""" Class representing a particle in a 2D space
:param x: x-coordinate of the particle
:param y: y-coordinate of the particle
:param vx: x-component of the velocity of the particle
:param vy: y-component of the velocity of the particle
:param mass: mass of the particle
"""
def __init__(self, x: float, y: float, vx: float, vy: float, mass: float):
self.position = np.array([x, y])
self.velocity = np.array([vx, vy])
self.mass = mass
def getAcceleration(self, rhs: 'Particle', softening: float) -> np.array:
""" Returns the acceleration of the particle due to another particle
:param rhs: the other particle
:param softening: softening factor to avoid division by zero
"""
G = 6.67430e-11
dPosition = rhs.position - self.position
return G * rhs.mass * dPosition / (np.dot(dPosition, dPosition) + softening)**1.5
def getPotentialEnergy(self, rhs: 'Particle', softening: float) -> float:
""" Returns the potential energy of the particle due to another particle
:param rhs: the other particle
:param softening: softening factor to avoid division by zero
"""
G = 6.67430e-11
dPosition = rhs.position - self.position
return G * self.mass * rhs.mass / np.sqrt(np.dot(dPosition, dPosition) + softening)
def getKineticEnergy(self) -> float:
""" Returns the kinetic energy of the particle """
return 0.5 * self.mass * np.dot(self.velocity, self.velocity)
def move(self, acceleration: np.array, dt: float) -> None:
""" Moves the particle based on the acceleration and the time step
:param acceleration: the acceleration acting on the particle
:param dt: the time step
"""
self.velocity += acceleration * dt
self.position += self.velocity * dt
class StarSystem:
""" Class representing a system of particles. The softening parameter is calculated based on this paper: https://academic.oup.com/mnras/article/314/3/475/969154
:param particles: list of particles in the system
"""
def __init__(self, particles: list[Particle]):
self.particles = particles
self.n = len(particles)
self.softening = (0.98 * self.n**-0.26)**2
def getAccelerations(self):
""" Returns the accelerations of all particles in the system """
accelerations = []
for i in range(self.n):
acceleration = np.zeros(2)
for j in range(self.n):
if i != j:
acceleration += self.particles[i].getAcceleration(self.particles[j], self.softening)
accelerations.append(acceleration)
return accelerations
def kineticEnergy(self):
""" Returns the total kinetic energy of the system """
energy = 0
for particle in range(self.particles):
energy += particle.getKineticEnergy()
return energy
def potentialEnergy(self):
""" Returns the total potential energy of the system """
energy = 0
for i in range(self.n):
for j in range(i+1, self.n):
energy += self.particles[i].getPotentialEnergy(self.particles[j], self.softening)
return energy
def getTotalEnergy(self):
""" Returns the total energy of the system """
return self.kineticEnergy() + self.potentialEnergy()
def evolve(self, dt: float):
""" Evolves the system based on the time step """
accelerations = self.getAccelerations()
for i in range(self.n):
self.particles[i].move(accelerations[i], dt)
def solarSystem():
""" Returns a list of particles representing the solar system """
sun = Particle(0.0, 0.0, 0.0, 0.0, 1.98847e30)
mercury = Particle(5.79e10, 0.0, 0.0, 4.74e4, 3.3011e23)
venus = Particle(0.0, 1.08e11, 3.50e4, 0, 4.8673e24)
earth = Particle(-1.50e11, 0, 0.0, 2.9783e4, 5.97219e24)
mars = Particle(0.0, -2.28e11, 2.41e4, 0, 6.4169e23)
jupiter = Particle(7.78e11, 0, 0.0, 1.31e4, 1.8981e27)
saturn = Particle(0.0, 1.43e12, 9.64e3, 0, 5.68232e26)
uranus = Particle(-2.88e12, 0.0, 0.0, 6.7991e3, 8.6810e25)
neptune = Particle(0.0, -4.50e12, 5.43e3, 0, 1.0241e26)
return [sun, mercury, venus, earth, mars, jupiter, saturn, uranus, neptune]
def main():
DAY = 24*60*60
MONTH = 30*DAY
YEAR = 12*MONTH
tEnd = 100 * YEAR
dt = 5 * DAY
iterations = int(tEnd/dt)
system = StarSystem(solarSystem())
ax1 = plt.subplot(111)
ax1.set_title('Solar System')
ax1.set_xlabel('x (m)')
ax1.set_ylabel('y (m)')
mercuryTrajectory = ax1.plot([], [], color='gray')
venusTrajectory = ax1.plot([], [], color='orange')
earthTrajectory = ax1.plot([], [], color='blue')
marsTrajectory = ax1.plot([], [], color='red')
jupiterTrajectory = ax1.plot([], [], color='brown')
saturnTrajectory = ax1.plot([], [], color='brown')
uranusTrajectory = ax1.plot([], [], color='blue')
neptuneTrajectory = ax1.plot([], [], color='blue')
plt.sca(ax1)
ax1.set(xlim=(-5e12, 5e12), ylim=(-5e12, 5e12))
ax1.set_aspect('equal', 'box')
for _ in range(iterations):
system.evolve(dt)
mercuryTrajectory[0].set_data(
np.append(mercuryTrajectory[0].get_xdata(), system.particles[1].position[0]),
np.append(mercuryTrajectory[0].get_ydata(), system.particles[1].position[1]))
venusTrajectory[0].set_data(
np.append(venusTrajectory[0].get_xdata(), system.particles[2].position[0]),
np.append(venusTrajectory[0].get_ydata(), system.particles[2].position[1]))
earthTrajectory[0].set_data(
np.append(earthTrajectory[0].get_xdata(), system.particles[3].position[0]),
np.append(earthTrajectory[0].get_ydata(), system.particles[3].position[1]))
marsTrajectory[0].set_data(
np.append(marsTrajectory[0].get_xdata(), system.particles[4].position[0]),
np.append(marsTrajectory[0].get_ydata(), system.particles[4].position[1]))
jupiterTrajectory[0].set_data(
np.append(jupiterTrajectory[0].get_xdata(), system.particles[5].position[0]),
np.append(jupiterTrajectory[0].get_ydata(), system.particles[5].position[1]))
saturnTrajectory[0].set_data(
np.append(saturnTrajectory[0].get_xdata(), system.particles[6].position[0]),
np.append(saturnTrajectory[0].get_ydata(), system.particles[6].position[1]))
uranusTrajectory[0].set_data(
np.append(uranusTrajectory[0].get_xdata(), system.particles[7].position[0]),
np.append(uranusTrajectory[0].get_ydata(), system.particles[7].position[1]))
neptuneTrajectory[0].set_data(
np.append(neptuneTrajectory[0].get_xdata(), system.particles[8].position[0]),
np.append(neptuneTrajectory[0].get_ydata(), system.particles[8].position[1]))
plt.pause(0.000001)
plt.draw()
if __name__== "__main__":
main()