Q77 / 90 · JEE Main 2014 (09 Apr Online) · Physics

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.
Figure

  • A
    220 days.
  • B
    500 days.
  • Correct answer
    C
    260 days.
  • D
    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

∴   TMn≈518 days

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

Hence, the correct answer is option: 'C'.

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