Let be the 3 -dimensional sphere of radius 1 centred at be the sphere of radius centred at and be the sphere of radius centred at . The eccentrically shaped planet Zog is composed of rock of uniform density occupying the region within and outside and . The regions inside and are empty. Give an expression for Zog's gravitational potential at a general coordinate that is outside . Is there a point in the interior of where a test particle would remain stably at rest? Justify your answer.
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