gravitation:}

orbital speed at a distance 'r' from the centre of the earth is given by v=\sqrt{\frac{GM}{r}}

K.E. = 12mv² = GMm2r
P.E. = - GMmr
total mechanical energy = K.E.+P.E. = - GMm2r

now dEdt = - F.v
or GMm2r²(drdt) = - av³
GMm2r²(drdt) = - a (GMr)\sqrt{\frac{GM}{r}}

\frac{a}{m}\int_{0}^{t}{dt}=-\frac{1}{2}\sqrt{\frac{1}{GM}}\int_{r_{i}}^{r_{f}}{r^{-1/2}}dr

\frac{a}{m}t=-\frac{1}{2}\sqrt{\frac{1}{GM}}\int_{nR}^{R}{r^{-1/2}}dr

t = \frac{m}{a}\sqrt{\frac{R}{GM}}(\sqrt{n}-1)
hence the answer [1]