Calculating Orbital Velocity Ratios for Planets A and B

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Planet A and Planet B are in circular orbits around a star, with Planet A being 8.5 times farther from the star than Planet B. The initial approach to calculate their velocity ratio using the force equation F=1/r^2 is incorrect, as it does not account for the relationship between velocity and radius in circular motion. The correct method indicates that the square of the orbital velocity is inversely proportional to the radius of the orbit. Therefore, the velocity ratio Va/Vb can be calculated as the square root of the inverse of their distance ratio, resulting in Va/Vb = Sqrt(1/8.5), which equals approximately 0.35. This highlights the importance of understanding the dynamics of circular orbits in gravitational fields.
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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