Question

Two planets X and Y travel counterclockwise in circular orbits about a star, as seen in the figure.

Answer 1

Planet Y has rotated by 135.5° through during this time.

To find the answer, we need to know about the relation between angle and radius of orbit.

What's the expression of angle in terms of radius?

• Angle= arc/radius
• As arc = orbital velocity × time,

            angle= (orbital velocity × time)/radius

• Orbital velocity= √(GM/radius), G= gravitational constant and M = mass of sun
• So, angle = (√(GM)× time)/radius^3/2

What's is the angle rotated by planet Y after 5 years, if ratio of the radius of orbit of planet X and Y is 4:3 and planet X is rotated by 88°?

• Let Ф₁= angle rotated by planet Y, Ф₂= angle rotated by planet X
• As time = 5 years ( a constant)
• Ф₁/Ф₂= (radius of planet X / radius of planet Y)^(3/2)
• Ф₁= (radius of planet X / radius of planet Y)^(3/2) × Ф₂

   = (4/3)^(3/2) × 88°

   = 135.5°

Thus, we can conclude that Planet Y has rotated by 135.5° through during this time.

Learn more about the orbital velocity here:

brainly.com/question/22247460

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