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AP EAMCET20225 Jul 2022Evening ShiftPhysicsGravitationActual

Two planets, A and B orbit around a star such that time period of A is 8 times the time period of B . The ratio of orbital velocities of the planets A and B is

Options

  1. A4: 1
  2. B1: 4
  3. C2: 1
  4. D1: 2

Correct answer

D. 1: 2

Step-by-step solution

T _ A =8 ~T _ B T _ A ^2=64 ~T _ B ^2 R _ A ^3=64 R _ B ^3 [ T ^2 R ^3 ] R_A=4 R_B Now, V= 2 R T V _ A V _ B = R _ A T _ A T _ B R _ B = R _ A R _ B T _ B T _ A =4 1 8 = 1 2

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