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

Attached. A and D are circular. Find the orbit with largest angular momentum, largest total energy, and largest maximum speed.

2. Relevant equations

E is proportional to -1/a (elliptical; a is semimajor axis)

U is proportional to -1/r

K is proportional to 1/r (circular only)

dA/dt is proportional to L

T^2 is proportional to a^3

3. The attempt at a solution

I want to see somebody work it out the 'right' way, since I'm more or less fooling around with no idea what I'm doing.

(a) I have (not sure) that L is proportional to sqrt(r) for circular orbits, so A is higher than D. Since C and B are going slower than A at aphelion, A beats them too. So the answer is A?

(b) is A since it has the largest semimajor axis.

(c) No idea; I know it's not D, but then I'm not sure on the rest. A has highest energy, B has much less but makes a much closer approach.

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# Comparing angular momentum/energy of orbits

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