Question

A planet of mass $M$ and a single satellite of mass $M/10$ revolve in circular orbits about their stationary centre of mass, being held together by their gravitational attraction. The distance between their centres is $D$. The period of this orbital motion is (ignore spin of planet and satellite)

• A. $2\pi \sqrt{\frac{D^3}{Gm}}$
• B. $2\pi \sqrt{\frac{D^3}{11Gm}}$
• C. $2\pi \sqrt{\frac{9D^3}{11Gm}}$
• D. $2\pi \sqrt{\frac{10D^3}{11Gm}}$

Answer 1

The correct option is D $2\pi \sqrt{\frac{10D^3}{11Gm}}$

$T=2\pi \sqrt{\frac{a^3}{GM}}$

$T=2\pi \sqrt{\frac{D^3}{G(M+M/10)}}$

$T=2\pi \sqrt{\frac{10D^3}{11GM)}}$