Simulating Gravitational Interactions in a Particle System

[Jozefina Gramatikova]

I have a project to make the solar system. I am trying to start from somwhere. On the notes it says that we need to start by creating a System of Particles

• Two-body simulation (Circular motion)
• Implement Gravitational acceleration
  Each particle (planet) could have its own field.
  • I.e. Each particle loops over all the other bodies to get the effect of all the other fields on it.
• Extend to three body system

Need to create all accelerations in one step before updating the positions and velocities.
I have to use the Euler's method.

I have my code from last week where we had to simulate a projectile with constant acceleration.
Here is my code:

import numpy as np

class Particle:

position = np.array([0,0,0])
velocity = np.array([0,0,0])
acceleration = np.array([0,0,0])

def __init__(self, initialPosition, initialVelocity, initialAcceleration, Name, mass):
    self.position = initialPosition
    self.velocity = initialVelocity
    self.acceleration = initialAcceleration
    self.Name = Name
    self.mass = mass

def update(self, deltaT):
    self.position = self.position + self.velocity*deltaT
    self.velocity = self.velocity + self.acceleration*deltaT
def __repr__(self):
    return 'Particle: %10s, Mass: %.5e, Position: %s, Velocity: %s, Acceleration:%s'%
                   (self.Name,self.mass,self.position, self.velocity,self.acceleration)

Pls help!

 

[jedishrfu]

This is not a trivial request. Have you done some research with Google?

There are many examples of similar problems solved with Python that you could look at and learn how to write your own.

 

[Jozefina Gramatikova]

I have done my research. I am sorry, but couldn't find something like this.

 

[DaveC426913]

What exactly do you need help with?
Is your sim not doing what it's supposed to?

 

[ChrisVer]

OK, that is a good beginning for a particle. But a particle in a gravitational field, does not have a constant acceleration. The acceleration experienced by a particle of mass $m$ under the influence of an external force $F$, is given by the 2nd law of Newton:
$\vec{a} = \vec{F}/m$
The force your particle will experience will be the gravitational one from the other particle 2, and will be the gravitational law:
$\vec{F}= -\frac{G m_1 m_2}{|r_1-r_2|^2} \hat{r_{12}} = -\frac{G m_1 m_2}{|\vec{r_1} - \vec{r_2}|^3} (\vec{r}_1 - \vec{r}_2)$, (where $\hat{r_{12}}$ the unit vector pointing from the particle 2>1).

and so you can see that the force depends on the relative distance between the particle 1 and 2 (and so it's not constant). Start from defining a way to measure the distance between your particles then. That distance can be used to determine the vector of acceleration per unit of time and the latter will affect the movement of your particles.