India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It…

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.

  1. 220 days.
  2. 500 days.
  3. 260 days.
  4. 320 days.

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

∴   TMn518 days

 Required time = 5 1 8 2 = 2 6 0  days .

Asked in: JEE Main 2014 (09 Apr Online)

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