Question

If T is the time period of satellite in an orbit of radius r, then the time period in an orbit of radius 3r is:

Hint:

A useful shortcut for Kepler's 3rd law problems where radius increases by a factor $k$ ($r_2 = kr_1$): the new time period will be $k^{3/2} \times T_1$ or $k\sqrt{k} \times T_1$. Here $k=3$, so $T_{new} = 3\sqrt{3} T$.

Answer 1