Pygame Make A Circle Rotate Around Another

I would like to make some kind of solar system in pygame. I've managed to do a fixed one but I thought it would be more interesting to do one with planets moving around the sun and

Solution 1:

You can implement gravity with Newton's Law of Universal Gravitation and Newton's Second Law to get the accelerations of the planets. Give each planet an initial position, velocity and mass. Acceleration is change in velocity a = v * dt, velocity is change in position v = r * dt, so we can integrate to find velocity and position.

Universal gravitation: F = G * m1 * m2 / r ** 2 where F is the magnitude of the force on the object, G is the gravitational constant, m1 and m2 are the masses of the objects and r is the distance between the two objects.

Newton's Second Law: F = m1 * a where a is the acceleration.

dt = 0.01# size of time step
G = 100# gravitational constant defcalcGravity(sun, planet): 
  'Returns acceleration of planet with respect to the sun' 
  diff_x = sun.x - planet.x 
  diff_y = sun.y - planet.y 
  acceleration = G * sun.mass / (diff_x ** 2 + diff_y ** 2) 
  accel_x = acceleration * diff_x / (diff_x ** 2 + diff_y ** 2)
  accel_y = acceleration * diff_y / (diff_x ** 2 + diff_y ** 2)
  return accel_x, accel_y

whileTrue: 
  # update position based on velocity 
  planet.x += planet.vel_x * dt 
  planet.y += planet.vel_y * dt 

  # update velocity based on acceleration
  accel_x, accel_y = calcGravity(sun, planet)
  planet.vel_x += accel_x * dt
  planet.vel_y += accel_y * dt 

This can produce circular and elliptical orbits. Creating an orbiting moon requires a very small timestep (dt) for the numeric integration.

Note: this approach is subtly inaccurate due to the limits of numeric integration.

Sample implementation in pygame here, including three planets revolving around a sun, a moon, and a basic orbital transfer. https://github.com/c2huc2hu/orbital_mechanics