One of Kepler's laws suggests that for moons that have circular orbits around a…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

One of Kepler's laws suggests that for moons that have circular orbits around a planet:

\frac{T^2}{4\pi r^3} = k

where

T

is the orbital period of the moon,

r

is the radius of its circular orbit about the planet, and

k

is a constant. The table gives data relating to the two moons of Mars.

Moon	$T$ / hour	$r$ / Mm
Phobos	7.66	9.38
Deimos	30.4	-

(1) Show that

k = \frac{1}{GM}

. (2) Determine

r

for Deimos.