# How does mass affect orbital period?

Apr 19, 2018

When one object orbits another due to gravity (i.e. planet around a sun) we say that the centripetal force is brought around by the force of gravity:

$\frac{m {v}^{2}}{r} = \frac{G M m}{r} ^ 2$

${v}^{2} / r = \frac{G M}{r} ^ 2$

$v = \frac{2 \pi r}{t}$

$\frac{4 {\pi}^{2} {r}^{2}}{2 r {t}^{2}} = \frac{G M}{r} ^ 2$

${t}^{2} = \frac{2 {\pi}^{2} {r}^{3}}{G M}$

$t = \sqrt{\frac{2 {\pi}^{2} {r}^{3}}{G M}}$

An increase in the mass of he orbited body causes a decrease in the orbital period.