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## Homework Statement

**(b) For a mass m1 in circular orbit with velocity v1, and a mass m2 orbiting with velocity**

v2 (about a common center of mass), the following holds: m1/m2 = v2/v1. Use this

relation to derive an expression relating the mass and velocity of a star with the period

and mass of an orbiting planet.

v2 (about a common center of mass), the following holds: m1/m2 = v2/v1. Use this

relation to derive an expression relating the mass and velocity of a star with the period

and mass of an orbiting planet.

(c) The planet in (a) orbits with a period of 1 month. If the velocity of the star as a

result of this is 100 m s−1, calculate the density of the planet. Is this an Earth-type

planet, or a gaseous giant ?

## Homework Equations

## The Attempt at a Solution

I can't figure out part (b) and I need it to do part (c) and I think part (d) which I haven't shown here.

Here's what I've tried so far

(star)<--r

_{star}-->com<------r

_{planet}------>(planet)

let mass and velocity of star be M and V

let mass and velocity of planet be m and v

MV-mv=0

Mr

_{star}-mr

_{planet}=0

MV-mv=Mr

_{star}-mr

_{planet}

MV-Mr

_{star}=mv-mr

_{planet}

Period:

2pi*r

_{star}=PV

2pi*r

_{planet}=Pv

r

_{star}=PV/2pi

r

_{planet}=Pv/2pi

MV-MPV/2pi=mv-mPv/2pi

As you can probably see, that brings me back around to square 1.

I just can't seem to work it out in such a way that I won't need at least 1 of the distances and as you can see in part (c) I'm only given two values to calculate the density so...

Please help

I'll thank, anyone who helps me, in advance because if I leave it too long I won't want to bump this thread, so thank you in advance