Calculating Orbital Velocity Ratios for Planets A and B

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SUMMARY

The discussion focuses on calculating the orbital velocity ratio of two planets, A and B, orbiting a star, where Planet A is 8.5 times farther from the star than Planet B. The initial approach using the formula F=1/r^2 to determine velocity differences is incorrect. Instead, the correct relationship indicates that the square of the velocity is inversely proportional to the radius of the orbit, leading to the conclusion that the velocity ratio can be calculated as Va/Vb = √(1/8.5), resulting in a velocity ratio of approximately 0.35.

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mariners02
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Planet A and planet B are in circular orbits around a distant star. Planet A is 8.5 times farther from the star than is planet B. What is the ratio of their speeds Va/Vb

This problem seems very simple, thought i could just use F=1/r^2, find the difference in forces, which would also be the difference in velocity. Can anyone explain the error in my thinking?
 
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mariners02 said:
Planet A and planet B are in circular orbits around a distant star. Planet A is 8.5 times farther from the star than is planet B. What is the ratio of their speeds Va/Vb

This problem seems very simple, thought i could just use F=1/r^2, find the difference in forces, which would also be the difference in velocity. Can anyone explain the error in my thinking?

The problem is that the force is proportional to the velocity squared divided by the radius. Thus the velocity squared is proportional to the inverse of the radius.
 
So i could just do V=Sqrt(1/8.5)=.35?
 

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