# Homework Help: Mass of invisible binary companion

1. Dec 2, 2009

### Kinetic

Hey guys, got this question that's been giving me some trouble.

The spectral lines in a low-mass main sequence star are observed to show sinusoidal velocity variations with an amplitude of 500km/s and a period of ten hours. Calculate the lower mass limit of the unseen binary companion.

Here's how far i've managed to get:

I started with newton's adaptation of kepler's third law

1. M1+M2=(4(PI)2a3)/(GP2)

where 'a' is the seperation of the two masses

2. a=r1+r2

I don't know the radius of either orbit but i do know the velocity of one and the period.

3. V1=(2(PI)r1)/P
4. V2=(2(PI)r2)/P

I then rearranged 3 and 4 to get r in terms of P and V and substituted into 2 to get

5. a=(P/2(PI))*(V1+V2)

Then substituting 5 into 1 gives

6. M1+M2=(P/2(PI)G)*(V1+V2)3

I now want to get rid of the V2.

V2/V1=r2/r1=M1/M2

So i make V2= V1*(M1/M2)

Substitute this into 6 and with a bit of fiddling i get

7. M23/(M1+M2)2=(PV13)/(2(PI)G)

I've been told the visible star is a 'low-mass main sequence star' so i can make a rough estimate of M1. Now my only unknown is M2...
However! I've been playing with 7 for ages and simply cannot isolate M2 :uhh:

So i've either messed up somewhere along the way to 7 or my algebra is failing me.

Any suggestions or help would be great guys!

Kinetic