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Two planets X and Y travel counterclockwise in circular orbits about a star, as seen in the figure.
The radii of their orbits are in the ratio 4:3. At some time, they are aligned, as seen in (a), making a straight line with the star. Five years later, planet X has rotated through 88.0°, as seen in (b).
By what angle has planet Y rotated through during this time?

Two planets X and Y travel counterclockwise in circular orbits about a star as seen in the figure The radii of their orbits are in the ratio 43 At some time the class=

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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:

https://brainly.com/question/22247460

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