A planet has two satellite moons. Moon X has an orbital period of 2.13 days. Moon Y has an orbital period of about 3.53 days. Both moons have nearly circular orbits. Use Kepler's third law to find the distance of each satellite from the planet's center. The planet's mass is 2.0 10^26 kg.

Question

A planet has two satellite moons. Moon X has an orbital period of 2.13 days. Moon Y has an orbital period of about 3.53 days. Both moons have nearly circular orbits. Use Kepler's third law to find the distance of each satellite from the planet's center. The planet's mass is 2.0 10^26 kg.
Moon X km?
Moon Y km?

I have posted this earlier but didn't get a respond am sorry to re-post it but I really need help with this!

Physics - drwls, Sunday, February 19, 2012 at 12:27pm

The Kepler's law formula you need to use is:

T²/R³ = 4π²/(GM)

M is the mass of the planet, in kg
    G is the universal constant of gravity, which is easily found online.

T is the period in seconds
    Tx = 1.840*10^5 s
    Ty = 3.050*10^5 s
    R is the orbit radius in meters. Do the calculations of R for planets X and Y, one at a time.

Ok i tried this but i still cant get the answer right I don't understand it :(

bobpursley · Answer

T^2/R^3=4PI^2/GM R= cubrt ( T^2 G*mass/4PI^2) solve for R, knowing period T, G, Mass. Do that for each moon.

Angelina · Answer

Ok so this is what i did cubrt(2.13^2(6.67x10^-11)(2.0x10^26))/(4pi2)=R which is 1159307512 but then that's wrong so i don't know what i am doing wrong?