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Question 30774
JEE Physics · Hard

Gravitation: Advanced — Vis-Viva Equation MCQ

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Advanced — Vis-Viva EquationHardQuestion 30774

Question

The vis-viva equation for a satellite at radius r in an ellipse (semi-major axis a) is:
  1. A
    v² = GM(2/r − 1/a)
    Correct
  2. B
    v² = GM/r
  3. C
    v² = 2GM/r − GM/a
  4. D
    v² = GM(1/r − 2/a)

Correct answer

v² = GM(2/r − 1/a)

Explanation

The vis-viva equation: v² = GM(2/r − 1/a). For circular orbit (r = a): v² = GM/r. For escape (a = ∞): v² = 2GM/r. It unifies circular, elliptical, and escape trajectories.

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