What Is the Mass of a Planet Given Its Moon's Orbital Period and Radius?

[Greywolfe1982]

Homework Statement

Given: G = 6.67259 × 10^−11 Nm2/kg2
A small Moon of a planet has an orbital period of 2.08 days and an orbital radius of 5.04 × 10^5 km.
From these data, determine the mass of the planet. Answer in units of kg.

Homework Equations

F_G=F_C
F_G=Gm₁m₂/r^2
F_C=mv^2/r

The Attempt at a Solution

First step was to convert into meters/seconds:
2.08 days to 179712 seconds
5.04x10^5km to 5.04x10^8m

Use v=d/t (or v=2\pir/T) and get a velocity of 17621.1m/s. Use Fg=Fc and simplify to Gm/r=v^2, rearrange to v^2r/G=m. I crunched out the numbers and get a mass that's nearly as large as the sun. The problem states it's a planet, so I'm assuming I'm doing something wrong...what is it?

 

[Nabeshin]

I don't see any error in your calculation... What is your final number you get for mass? Note the mass of the sun is about 2*10^30 kg.

 

[Greywolfe1982]

Doh, I guess I should have done half a second of research before I posted this topic.

For some reason I thought the Earth was ...x10^10, rather than x10^24. I got an answer of something (don't have the papers by me now)x10^27, which now seems fairly reasonable.