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 v_p, what is its speed at a? Assume the distances r_p and r_a are known.

Homework Equations

dA/dt = 1/2r²ω, ω=v/r[/B]

The Attempt at a Solution

dA/dt is constant, so 1/2r_p²ω_p = 1/2r_a²ω_a. Substitute v = ωr, that gives 1/2r_pv_p = 1/2r_av_a, v_a = r_pv_p/r_a. Is this correct?[/B]

 

[Simon Bridge]

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, r_pv_p/2 = r_av_a/2, v_a = r_pv_p/r_a.

 

[Dick]

So using conservation of momentum I got the same thing...dA/dt = L/2m = mr²ω/2m. Given that ω = v/r, r_pv_p/2 = r_av_a/2, v_a = r_pv_p/r_a.

Yes, it is the same thing as Kepler's law. Good job.

 

[hs764]

Great, thank you!