(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two individual stars in a binary system (m1=mo, m2=2mo) are in circular orbit about their common centre of mass and are separated by a distance ro. At some stage, the more massive star explodes - resulting in the two stars having equal mass after the explosion

(a)Calculate the total energy, angular momentum and period of the binary star as viewed in the ZMF before the collision.

(b)Calculate the total energy and period of the equivalent single particle system orbit, before the explosion.

(c) Using the equivalent single particle system or otherwise, show that the binary star will remain bound after the explosion.

2. Relevant equations

3. The attempt at a solution

(a)

So is the total energy just the sum of the energy for each star?

I defined PE to equal 0 at one star and found total energy = -Gmo^2/ro

How do you do it for angular momentum? Just find the two individually, note they are in opposite direction, and add?

I worked out T = 2/3 pi ro / (1/3 Gmo/ro)^1/2 Is this right?

(b) Im using F int = ur'' where u is reduced mass, r relative position vector..

Using this method i get E total to be -1/3 Gmo^2/ro..which isn't equal to the above, why?

Also I get T = 2/3pi ro / (Gmo/ro)^1/2 which again isnt equal to the above.. :S

(c) Not sure how to do this...

Thanks!

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# Homework Help: Motion of a Binary Star

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