Question: Use the conservation of angular momentum to estimate the difference in

Question

Question: Use the conservation of angular momentum to estimate the difference in Earth's orbital speed from perihelion to aphelion.
Have:

Perihelion Dist. = 147 x 109 m

Aphelion Dist.   = 152 x 109 m

Mass of Sun.    = 1.99 x 1030 Kg

G = 6.67 x 10-11 N M2/Kg2

If I use v2= GM/R, I get:

Perihelion: 30 055.81 m/s

Aphelion: 29 557.33 m/s

Diference: 498.47 m/s

The appendix in my textbook shows that Earth's orbital speed is 30 000 m/s.

However, I did not use conservation of angular momentum, L=I.

Is this correct?

Explanation / Answer

You may use v^2=GM/R for one of the distances, but note then that you can use conservation of momentum to determine the other speed as well: m*v1*r1=m*v2*r2 since the direction of the radius and the velocity are perpendicular at aphelion and perihelion. then v2=v1*(r1/r2) So having solved for one of the speeds, determine the other and subtract for the difference.

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