How does mass affect orbital period?

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Answer 1 · 2018-04-19T07:32:42

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:

$(mv^2)/r=(GMm)/r^2$

$v^2/r=(GM)/r^2$

$v=(2pir)/t$

$(4pi^2r^2)/(2rt^2)=(GM)/r^2$

$t^2=(2pi^2r^3)/(GM)$

$t=sqrt((2pi^2r^3)/(GM))$

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