Question

A research team has discovered that a moon is circling a planet of our solar system: The moonorbits the planet once every 7 hours on a nearly circular orbit in a distance R of 48000 km fromthe centre of the planet. Unfortunately, the mass m of the moon is not known. Use Newton’s lawof gravitation with G = 6.67 · 10−11 m3/(kg·s²) to approach the following questions:F = G ^. mM R2
(a) Based on the observations, determine the total mass M of the planet.(b) Which moon and planet of our solar system is the team observing? (Use literature.)

Answer 1

a) $R^3=\frac{GT^2}{4\pi^2}M$

$(48\cdot10^{6})^3=\frac{(6.67\cdot10^{-11})(7\cdot3600)^2}{4\pi^2}M$

$M=1.03\cdot10^{26}kg$

b) The observed planet is Neptune.