How to efficently predict an object orbit?

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;
 }

@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:

• http://www.braeunig.us/space/orbmech.htm

• https://www.csun.edu/~hcmth017/master/node16.html

• https://youtu.be/7XeCKKPL8Lo

• https://youtu.be/tcBr2pyGVQs