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NTA Abhyas JEE Main2020PhysicsGravitationPractice

If a satellite is revolving around a planet of mass M in an elliptical orbit of semi-major axis a , find the orbital speed of the satellite when it is at a distance r from the focus

Options

  1. Av 2 = G M 2 r - 1 a
  2. Bv 2 = G M 2 r 2 - 1 a
  3. Cv 2 = G M 2 r 2 - 1 a 2
  4. Dv 2 = G 2 r - 1 a

Correct answer

A. v 2 = G M 2 r - 1 a

Step-by-step solution

As in case of elliptic orbit of a satellite mechanical energy remains constant, at any position of satellite in the orbit, K E   +   P E   = - G M m 2 a ...(i) Now, if at position r , v is the orbital speed of satellite K E   =   1 2   m v 2   and P E   =   - G M m r ...(ii) So, from Eqs. (i) and (ii), we have 1 2   m v 2 - G M m r = - G M m 2 a ,   i . e . ,   v 2 = G M 2 r - 1 a  

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