Show that a moon orbiting a planet of mass in a circular orbit of radius has a period…

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

Problem

1. Show that a moon orbiting a planet of mass

M

in a circular orbit of radius

r

has a period

T

given by

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

. (1) Show that a moon orbiting a planet of mass

M

in a circular orbit of radius

r

has a period

T

given by

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

. (2) Europa is a moon of Jupiter with an orbit radius

6.7 \times 10^5 \text{ km}

and period 3.6 days. Triton is a moon of Neptune with an orbital radius

3.5 \times 10^5 \text{ km}

and period 5.9 days. What is the ratio of the mass of Jupiter to that of Neptune?