# Two body problem

#### Mathmos6

1. Homework Statement
Two gravitating particles with masses m1 and m2 start from rest a large distance apart. They are allowed to fall freely towards one another. The particles are given equal and opposite impulses I when they are a distance a apart, such that each impulse is perpendicular to the direction of motion.

Show that the total angular momentum of the two particles about their centre of mass has magnitude aI /µ, where µ is the reduced mass of the system.

2. Homework Equations

Reduced mass=m1m2/(m1+m2)

3. The Attempt at a Solution
Well this is the second last part of quite a long question on the 2-body problem, and I've managed fine until now (showing the position of the centre of mass 'C' - is constant, finding their relative speed etc) but I'm not sure how to go about this part of the question. The two particles are going to be moving in a straight line towards each other before the impulses which should mean 0 angular momentum before, so then the only angular momentum afterwards would be that from the impulses right?

But the impulses are perpendicular to the direction of motion so with the r x p cross product we'd just have angular momentum=dist. from C * impulse in each case wouldn't we? The m2 mass particle should have a distance (m1/(m1+m2))a from C and the m1 particle a distance of (m2/(m1+m2))a, but then clearly I've done something wrong because the sum of the impulses will just be (m1+m2/m1+m2)aI=aI.

Where am I going wrong? Thanks!

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#### Dick

Science Advisor
Homework Helper
That sure seems correct to me. aI/mu doesn't even have the correct units, does it?

#### Mathmos6

Actually that's a fair point, whereas aI does - weird! I'll check with someone else to see if the question is mistyped, but it seems odd that the entire "/µ, where µ is the reduced mass of the system." would be a mistake...

I'll let you know if i find out! Do you think just aI is the correct answer then?

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