Make GameObject/Model orbit a sphere

You can use either RotateAround as dhendrix mentioned, or you can create an empty GameObject and use this as a pivot for the orbitting GameObject. In Update rotate the pivot around its center and then move your GameObject "distance" along pivot's z-axis.

To do it using physics, you would apply force toward the sphere inside FixedUpdate.

Example:

pseudocode:

FixedUpdate()
{
    Vector3 diff = sphere.transomform.position - object.transform.position;
    Vector3 direction = diff.normalized;
    float gravitationalForce = (sphere.mass * object.mass * gravitationalConstant) / diff.sqrMagnitude;
    object.rigidBody.addForce( direction * gravitationalForce );
}

Gravitation equation taken from: http://www.school-for-champions.com/science/gravitation.htm