# Velocity of a planet around the sun

#### hs764

1. Asking because the answer I got seems too simple...a planet of mass m moves in an elliptical orbit about the sun. The minimum and maximum distances of the planet from the sun are called the perihelion and aphelion respectively. If the speed of the planet at p is vp, what is its speed at a? Assume the distances rp and ra are known.

2. Relevant equations

dA/dt = 1/2r2ω, ω=v/r

3. The attempt at a solution

dA/dt is constant, so 1/2rp2ωp = 1/2ra2ωa. Substitute v = ωr, that gives 1/2rpvp = 1/2rava, va = rpvp/ra. Is this correct?

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#### Simon Bridge

Science Advisor
Homework Helper
Try verifying the result from another rule - like conservation of momentum and energy...

#### hs764

So using conservation of momentum I got the same thing...dA/dt = L/2m = mr2ω/2m. Given that ω = v/r, rpvp/2 = rava/2, va = rpvp/ra.

#### Dick

Science Advisor
Homework Helper
So using conservation of momentum I got the same thing...dA/dt = L/2m = mr2ω/2m. Given that ω = v/r, rpvp/2 = rava/2, va = rpvp/ra.
Yes, it is the same thing as Kepler's law. Good job.

#### hs764

Great, thank you!

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