[SF5 7.P.36.] What is the mass of the planet?

Question

(NOTE: Its moon has an orbital period of 1.20 days and an orbital radius equal to 4.35 x 10e5 km.)

_____ kg

This question is from my Web Assignment from http://www.webassign.com/.

Answer 1

Look it up in your book. Clearly this is where you got the question.

Answer 2

Ok, using the same equations from the other question (satellite altitude), we have :

GM/r = v^2

v here is the circular velocity of the moon in you mention. As v = distance/time, we assume the moon has a circular orbit (technically it doesn't, it's elliptical, but I'll assume the eccentricity is negligible), so the distance is = 2pi*r (ie the circumference of the orbit). As we already have t, we know v:

v = 2pi*r/t
now r = 4.35E5km = 4.35E8m (convert km to m)
t = 1.2 days = 1.2*24*60*60 s = 103680s (convert time to seconds)
so v = 2*pi*4.35E8/103680 = 2.64E4 m/s (ie 26,400 m/s)

Rearrange the 1st equation:

M = (rv^2)/G

now put in the values, again with r in metres, and

G = 6.67E-11

M = (4.35E8*2.64E4^2)/6.67E-11
M = 4.55E27kg

Given Earth mass = 5.97E24 kg, this is approx 760 Earth masses - well over twice that of Jupiter!