- #1

Kinetic

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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. M

_{1}+M

_{2}=(4(PI)

^{2}a

^{3})/(GP

^{2})

where 'a' is the separation of the two masses

2. a=r

_{1}+r

_{2}

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

3. V

_{1}=(2(PI)r

_{1})/P

4. V

_{2}=(2(PI)r

_{2})/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))*(V

_{1}+V

_{2})

Then substituting 5 into 1 gives

6. M

_{1}+M

_{2}=(P/2(PI)G)*(V

_{1}+V

_{2})

^{3}

I now want to get rid of the V

_{2}.

V

_{2}/V

_{1}=r

_{2}/r

_{1}=M

_{1}/M

_{2}

So i make V

_{2}= V

_{1}*(M

_{1}/M

_{2})

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

7. M

_{2}

^{3}/(M

_{1}+M

_{2})

^{2}=(PV

_{1}

^{3})/(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 M

_{1}. Now my only unknown is M

_{2}...

However! I've been playing with 7 for ages and simply cannot isolate M

_{2}

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