Relative gravity

Question

I've started using jMonkey engine recently, which is very nice. But I got stuck trying to implement relative gravity.

I want to make planets orbiting around each other (not necessarily in perfectly circular orbit, depends on velocity). So every object should affect other objects.

What I have right now:

turning off global gravity

bulletAppState.getPhysicsSpace().setGravity(Vector3f.ZERO);

initializing spheres and adding to physics space

Sphere sphere = new Sphere(50, 50, 5);
Geometry sun = new Geometry("Sun", sphere);

sun.setMaterial(stone_mat);
rootNode.attachChild(sun);
sun.setLocalTranslation(0, 0, 0);

sunPhysics = new RigidBodyControl((float) (50*Math.pow(10, 5)));
sun.addControl(sunPhysics);
bulletAppState.getPhysicsSpace().add(sunPhysics);

Geometry mercury = new Geometry("Mercury", sphere);

mercury.setMaterial(stone_mat);
rootNode.attachChild(mercury);
mercury.setLocalTranslation(15f, 0, 0);

mercuryPhysics = new RigidBodyControl((float) (5));
mercury.addControl(mercuryPhysics);
bulletAppState.getPhysicsSpace().add(mercuryPhysics);

I noticed that there is method setGravity in RigidBodyControl class, but it just sets the direction. So object goes that way until it disappears.

I am really looking forward for answers.

Answer 1

The law of gravitation says F = G (m1 * m2) / r^2 where m1 and m2 are the masses of the two bodies, and r is the distance. G is the gravitational constant.

Newton's second law says F = m * a, so if we put them together, the body with mass m1 would experience an acceleration of a = G * m2 / r^2 from gravitational pull from the body with mass m2.

Now, what you would have to do is: In each step of the simulation, for each body, sum up the as for each other body and apply that acceleration to the body's velocity.

a(body1) = G * sum[ mass(body2) / dist(body1, body2)^2 , for each body2 ]