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Angular Momentum and Orbits

  • #1

Homework Statement


A planet has an eccentricity of 0.006800 and a semimajor axis of 0.7233 AU, find the ratio of ortibal speed at perihelion to that at aphelion.


Homework Equations



d=e x a
L=mvrsin[tex]\theta[/tex]

The Attempt at a Solution


I plugged in and solved for the distance between the foci (0.004918)
and then set the angular momentum constants equal to each other:
m v(p) rmin sin[tex]\theta[/tex]=m v(a) rmax sin[tex]\theta[/tex]
the masses and sin[tex]\theta[/tex] cancel out, so
v(p) x r min = v(a) x r max
and so the ratio is:
v(p) / v(a) = r max / r min

r max is the semimajor axis, and r min is the semimajor axis minus the d as found above:
So, it should be .7233/.718382 which gives me 1.00685, but this was incorrect according to my online homework, could you tell me what I did wrong?
 

Answers and Replies

  • #2
Filip Larsen
Gold Member
1,237
169
The relation vp/va = ra/rp is correct, but ra and rp are the aphelion and perihelion distances, respectively, and are given by ra = a(1+e) and rp = a(1-e).
 

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