The gravitational potential energy of a uniform spherical object of mass M and radius R is

,

in which G is the gravitational constant. (a) We have to use this expression to find the maximum energy that could be released by a spherical object, initially of infinite radius, in shrinking to the present size of the Sun . (b) Assuming that during this shrinking the Sun radiated Energy at its present rate; we have to calculate the age of the Sun based on the hypothesis that the Sun derives its energy from gravitational contraction.

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The gravitational potential energy of a uniform spherical object of mass M and radius R is

,

in which G is the gravitational constant. The change in potential energy when the object shrinks from infinite radius to the present radius R will be

(b)

The Sun is radiating energy at the rate of . The time in which it would have radiated of energy will be