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JEE Main2014PhysicsGravitationActual

India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M . If the semi-major axis of Earth's orbit is a e = 1.5 × 1 0 1 1 m , that of Mar's orbit a m = 2.28 × 1 0 1 1 m , taking Kepler's laws, give the estimate of time for Mangalyan to reach Mars from Earth.

Options

  1. A220 days.
  2. B500 days.
  3. C260 days.
  4. D320 days.

Correct answer

C. 260 days.

Step-by-step solution

Semi major axis of mangalyan, a Mn = a e + a m 2 = 1.89 × 1 0 1 1 m From Kepler's law, T 2 ∝ R 3 ∴    T Mn Te 2 = R M   R e 3 ∴    T Mn ≈ 51 8  days ∴ Required time = 5 1 8 2 = 2 6 0  days .

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