How can I accurately simulate orbits in Unity?

Question

I would like to create a space simulation with realistic gravity.

This means planets in 3d space which act as central gravity sources and multiple objects which are attracted by those planets gravity so that they orbit them in physically correct orbits (like in Kerbal Space Program, for example).

How can I implement such gravity sources with C# script?

Answer 1

You can learn about the gravity formula, Fg = G((Mass1 * Mass2)/distance^2), the distance is

d = sqrt( (x1 -x2)^2 + (y1 -y2)^2 + (z1 -z2)^2 )

now you can calculate the distance and use it in the Gravity formula.

after that you need to calculate the acceleration for each axi,

float aX = (x / hip) * tmp; // tmp is the gravity force and x is the object                  
                            // to go less the origin object
float aY = (y / hip) * tmp; //the same
float aZ = (z / hip) * tmp; //the same

so now add this to a variable x, y and z that represent the speed and upload all of this every frame * Time.deltaTime

Answer 2

Here is a C# script for a GravitySource component.

It requires a Collider attached to the same game object with the "Is Trigger" checkbox set. This collider represents the zone of influence of the bodies gravity. Any Rigidbodys inside of that collider will be affected.

The public property gravity needs to be set in the inspector. It represents the strength of the gravity source. The ideal value depends on the time-scale and space-scale of your simulation.

using UnityEngine;
using System.Collections;

public class GravitySource : MonoBehaviour {

    public float gravity;

    void OnTriggerStay(Collider other) {
        Rigidbody otherRigidbody = other.gameObject.GetComponent<Rigidbody>()
        if (otherRigidbody) {
            Vector3 difference = this.gameObject.transform.position - other.gameObject.transform.position;

            float dist = difference.magnitude;
            Vector3 gravityDirection = difference.normalized;
            Vector3 gravityVector = (gravityDirection * gravity) / (dist * dist) ;

            otherRigidbody.AddForce(gravityVector, ForceMode.Acceleration);

        }
    }
}