How to efficently predict an object orbit?

Question

I've implemented the Newton's Law of gravitation to all the GameObject in the scene. I'm trying to simulate the game "Orbit":Sample Video

As you can see in the video, the orbit is real-time predicted, and it gets updated as other objects influence it.

To reproduce the orbit prediction I thought about running a simulation of the entire system every second, but I don't know how to handle it because I'm using the Rigidbody physichs to create gravitational attraction.

Any idea?

Answer 1

Question already answered on stackoverflow:

https://stackoverflow.com/questions/57996836/how-does-spaceflight-simulator-predict-flight-paths/57998714#57998714

Basically you can very easily simulate forces frame-by-frame for a single object, simply by incrementing and applying the velocity:

 var currentPos = _rigidBody.position;
 var prevPos = currentPos;
 var currentVelocity = _rigidBody.velocity;
 var planetCords = gameObject.transform.position;
 
 for (int i = 0; i < stepCount; i++)
 {
     var distance = planetCords - currentPos;
 
     var forceMag = Gravity / distance.sqrMagnitude;
     forces = distance.normalized * forceMag;
     currentVelocity  += forces * Time.fixedDeltaTime;
 
     currentPos += currentVelocity * Time.fixedDeltaTime;
 
     //Replace by a TrailRenderer or LineRenderer you reset each frame
     Debug.DrawLine(prevPos, currentPos, Color.Red, Time.deltaTime);
     prevPos = currentPos;
 }

Answer 2

Answer by ristophonics · Aug 01, 2020 at 07:51 AM

@lucadome On the same problem for a few years ... and still going. For a [game][1] too.

I have dug up the math to do this.

You need to solve Kepler's equations with Newton's iteration. Most of the math is here:

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How to efficently predict an object orbit?

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