Distance and Masses...

Question

Deimos orbits mars at a distance of 23,000km with a period of 1.3 days. Charon is estimated to orbit Pluto at about the same distance but with a period of 6.5 days. Use this information to compare the masses of Pluto and Mars.

Answer 1

Taking Earth as 1.0, the table I consulted gives Mars as  0.11 and Pluto as 0.002. (On the same scale Jupiter has 318 times Earth's mass.)

That would suggest Mars has 55 times the mass of Pluto, but I have no idea how it relates to orbital distances of satellites, their masses, and periods.

Answer 2

You need to use Kepler's 3rd law: P2 = ka3

where k = 4 pi-square/G(M1+m2)

in the case of a moon orbiting a planet - the moon mass is small so can be ignored and the k simplfies to 4 pi-square/GM, where M is the mass of the planet.

Since you know the orbital radius (= semimajor axis = a) and you know the period P you can calculate the mass.

But you don;t even need to go that far. The "a"s are the same, so you just need to get the relationship between mass and oeriod to figure out how much more massive Mars is than Pluto!