Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 320 / 3 / c

Table of contents
- Solution c

Solution

If

M_{s}

is constant, the frictional acceleration instead scales as

r_{o}^{- 2}

. The angular-momentum equation gives

\frac{d r _{o}}{d t} = - K_{c} r_{o}^{- 3/2}, K_{c} = \frac{4 G M _{s} L}{3 C} .

Therefore

r_{o} (t) = [r_{o 0}^{5/2} - \frac{5}{2} K_{c} t]^{2/5} .

The orbit again reaches the centre in finite time, but its inward speed accelerates without the strong tidal-mass suppression present in part b.

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