Question

let the period of revolution of a planet at a distance R from a star be T .prove that if it was at a distance of 2r from the star its period of revolution will be √8 T​

Answer 1

Explanation:

$F = g \frac{mM}{ {r}^{2} } = m \omega {}^{2} r = m( \frac{2\pi}{T}) {}^{2} r \\ gM. {T}^{2} = 4 {\pi}^{2} {r}^{3} \\ T{}^{2} \: \: \: \alpha \: \: \: \: \: {r}^{3}$

so when distance is twice T will be

${2}^{ \frac{3}{2} } = \sqrt{8} \: times$