Solving Planetary Motion: X & Y's Circular Orbits

AI Thread Summary
Planets X and Y orbit a star with a radius ratio of 5:2. After 5 years, planet X has rotated 92.6 degrees, prompting a calculation of how far planet Y has traveled in the same period. The discussion highlights the application of Kepler's third law to relate the angular velocities of the two planets based on their orbital radii. Users express difficulty in applying the radius ratio to angular velocities correctly. The conversation emphasizes the importance of understanding the relationship between gravitational forces and orbital motion.
lempkema
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Homework Statement



Planets X & Y travel in circular orbits around the same star. The ratio of the radii of their orbits is 5:2. 5 years after the planets were aligned, planet x has rotated 92.6 degrees. how many degrees has y traveled in the same amount of time?

Homework Equations



v^2=GM/R

Wx=phix/t; Wy=phiy/t

phix= angular of X after t time
phiy= angular of X after t time

The Attempt at a Solution



I just keep getting the wrong answer. I try transferring the ratio of radii to the angular velocities, but i must be doing it wrong.
 
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Check Kepler's third law.
 
thank you so much, that made to ratio a lot less difficult to apply!
 
Note, that third law can be derived from the F=GMm/r^2.
 

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