Question

Two stars X and Y travel counterclockwise in circular orbits about a galaxy. The radii of their orbits are in the ratio 4:1 . At some time, they are aligned making a straight line with the center of the galaxy. Five years later, star X has rotated through 90°, By what angle has planet Y rotated through during this time

Answer 1

The period is proportional to Radius^(3/2)
so
Tx/Ty= (4R)^3/2 / R^3/2 = 2^3 = 8 times
8 * 90 = 360*2 = 720deg
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why Radius^(3/2)
mv^2/R = G m M/R^2
so if k^2 = GM
v = k R^-.5
T = 2 pi R/v = 2 pi R/kR^-.5 = constant*R^1.5

Answer 2

Tx/Ty= (4R)^4/2 / R^4/2 = 1^3 = 3 times
3 * 90 = 270 deg
==============================
why Radius^(4/2)
mv^2/R = G m M/R^2
so if k^2 = GM
v = k R^-.5
T = 2 pi R/v = 2 pi R/kR^-.5 = constant*R^1.5

Answer 3

A circle has 360 degrees how can it be 720 degrees.