When a star of mass M is devoid of a nuclear energy source it will keep the same luminosity L for quite a while by consu

[answerhappygod]

When a star of mass M is devoid of a nuclear energy source it
will keep the same luminosity L for quite a while by consuming its
gravitational energy through contraction. Assume the star can
remain in a state of hydrostatic equilibrium and its gravitational
energy is given by: Ω = −α(GM^2)/ R where G is the gravitational
constant, α is a constant and R is the radius of the star. Prove
that the rate of contraction of its radius R can be expressed by:
dR/dt =R=-(R0/τ)/`[1+ (t /τ)]^2 where R0 is the star’s initial
radius when it starts to contract and: τ = α(GM^2)/(2R0L)