Question

A research team has discovered that a moon is circling a planet of our solar system: The moon orbits the planet once every 7 hours on a nearly circular orbit in a distance R of 48000 km from the centre of the planet. Unfortunately, the mass m of the moon is not known. Use Newton’s law of gravitation with G = 6.67 · 10−11 m3 /(kg·s 2 ) 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.)

PLEASE SOLVE BOTH PARTS

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) It is Neptune.