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[SOLVED] Ratio of speeds in an elliptic orbit
Hi, I need some clarification on a problem.
The problem is: The diagram shows a view of the earth's elliptic orbit about the sun. (This was the closest picture I could find.) In terms of Ra (the distance between the sun and point A) and Rb (the distance between the sun and point B), what is the ratio Vb/Va?
Using conservation of angular momentum, L = I*w = m*r^2*v/r = m*r*v,
m*rA*vA = m*rB*vB
vB/vA = rA/rB
So the velocity is inversely related to the distance from the sun.
However, the answer given is the square root of rA/rB. I can get this answer by equating Newton's gravitational law with the centripetal force, but doesn't centripetal acceleration only work for circular orbits?
Which answer is correct?
Any help would be appreciated. Thanks!
Hi, I need some clarification on a problem.
The problem is: The diagram shows a view of the earth's elliptic orbit about the sun. (This was the closest picture I could find.) In terms of Ra (the distance between the sun and point A) and Rb (the distance between the sun and point B), what is the ratio Vb/Va?
Using conservation of angular momentum, L = I*w = m*r^2*v/r = m*r*v,
m*rA*vA = m*rB*vB
vB/vA = rA/rB
So the velocity is inversely related to the distance from the sun.
However, the answer given is the square root of rA/rB. I can get this answer by equating Newton's gravitational law with the centripetal force, but doesn't centripetal acceleration only work for circular orbits?
Which answer is correct?
Any help would be appreciated. Thanks!
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