Orbital Gravity 2D - A demonstration of Orbital Gravity in a 2D Unity Game. Unity's standard physics engine implements gravity only in the vertical axis. Here's a demo of orbital gravity for space type games. It allows for one object (spaceship, satellite, etc.) to achieve a stable organic orbit around another object (planet, moon, star, etc.)

orbital_gravity_2d.cs

using UnityEngine;
using UnityEngine.UI;
using System.Collections;

// Intended to be attached to a GameObject in order for that object to have its own gravity.
// Standard Unity Gravity is disabled on objects implementing this class
// This class is pared down from the original WorldBodyController used Oliver Holmberg's game Apogee to simply demonstrate orbital gravity.

public class OrbitalGravityObject : MonoBehaviour { 

	// Physics settings
	public float mass;     			// The relative mass of the object
	public int soiRadius;			// The radius of the "sphere of influence" This can be set to infinity (or a very large number) for more realistic gravity.
	public int proximityModifier = 195;	// Used to alter (unatuarally) the coorelation between the proximity of the objects to the severity of the attraction.  Tweak to make orbits easier to achieve or more intersting.

	
	void Start() {
		mass = mass * 100000; // Mass ^ 5 in order to allow the relative mass input to be more readable
	}
	
	public void OnDrawGizmos() { // Creates a visual representation of the sphere of indluence in the editor
		// Show the Object's Sphere Of Influence
		Gizmos.DrawWireSphere (transform.position, soiRadius);
	}
	
	void FixedUpdate () { // Runs continuously during gameplay

		// Get all objects that will be affected by gravity (Game objects are tagged in order to be influenced by gravity)
		GameObject[] objectsAffectedByGravity;objectsAffectedByGravity = GameObject.FindGameObjectsWithTag ("affectedByPlanetGravity");
		
		foreach (GameObject gravBody in objectsAffectedByGravity) { // Iterate through objects affected by gravity
				
			Rigidbody2D gravRigidBody = gravBody.GetComponent<Rigidbody2D> (); // Get the object's Rigid Body Component
			
			float orbitalDistance = Vector3.Distance (transform.position, gravRigidBody.transform.position); // Get the object's distance from the World Body
			
			if (orbitalDistance < soiRadius) { // If the object is in the sphere of influence (close enough to be affected by the gravity of this object)

				// Get info about the object in the sphere of influence

				Vector3 objectOffset = transform.position - gravRigidBody.transform.position; // Get the object's 2d offset relative to this World Body
				objectOffset.z = 0;
				
				Vector3 objectTrajectory = gravRigidBody.velocity; // Get object's trajectory vector
				
				float angle = Vector3.Angle (objectOffset, objectTrajectory); // Calculate object's angle of attack ( Not used here, but potentially insteresting to have )
				
				float magsqr = objectOffset.sqrMagnitude; // Square Magnitude of the object's offset
				
				if ( magsqr > 0.0001f ) { // If object's force is significant

					// Apply gravitational force to the object
					Vector3 gravityVector = ( mass * objectOffset.normalized / magsqr ) * gravRigidBody.mass;
					gravRigidBody.AddForce ( gravityVector * ( orbitalDistance/proximityModifier) );
					
				}
			} 
		}
	}
}