- #1

Greywolfe1982

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## 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}=Gm

_{1}m

_{2}/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[tex]\pi[/tex]r/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?