India's Mangalyan was sent to the Mars by launching it into a...

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 ${\text{a}}_{\text{e}} = \text{1.5} \times 1 {0}^{1 1} \text{m}$ , that of Mar's orbit ${\text{a}}_{\text{m}} = \text{2.28} \times 1 {0}^{1 1} \text{m}$ , taking Kepler's laws, give the estimate of time for Mangalyan to reach Mars from Earth.
India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at

Options

A $220$ days.
B $500$ days.
C $260$ days.
D $320$ days.

Correct answer

C. $260$ days.

Step-by-step solution

Semi major axis of mangalyan,

{\text{a}}_{\text{Mn}} = \dfrac{{\text{a}}_{\text{e}} + {\text{a}}_{\text{m}}}{2}

= \text{1.89} \times 1 {0}^{1 1} \text{m}

From Kepler's law,

{\text{T}}^{2} ∝ {\text{R}}^{3}

∴ {\left(\dfrac{{\text{T}}_{\text{Mn}}}{\text{Te}}\right)}^{2} = {\left(\dfrac{{\text{R}}_{\text{M}}}{{\text{R}}_{\text{e}}}\right)}^{3}

∴ {\text{T}}_{\text{Mn}}\text{\approx}518\text{days}

∴

Required time

= \dfrac{5 1 8}{2} = 2 6 0 \text{days}

Practice Gravitation on Quantrex Academy →

More from Gravitation

A particle of mass m , and angular momentum ℓ is moving in a circular orbit of radius r_0… JEE Advanced 2026 A body of mass m is taken from the surface of earth to a height equal to twice the radius… JEE Main 2026 When one moves from a point 16 km below the earth's surface to a point 16 km above the… JEE Main 2026 The height in terms of radius of the earth (R) , at which the acceleration due to gravity… JEE Main 2026 If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and… JEE Main 2026 A planet (P_1) is moving around the star of mass 2M in the orbit of radius R . Another… JEE Main 2026 Three masses 200 ~kg, 300 ~kg and 400 kg are placed at the vertices of an equilateral… JEE Main 2026 Given below are two statements: Statement I : A satellite is moving around earth in the… JEE Main 2026 Full Gravitation list All JEE Main PYQs