What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an alti - Physics MCQ JEE Main 2026 | ExamTest.live

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What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2 R ?

Solution & Step-by-step Explanation

1. Energy at the surface E_{i} = - \frac{G m M}{R} + K_{i} = - \frac{G m M}{R} (since we need "minimum energy required" to be provided).2. Energy in the circular orbit at distance r = R + 2 R = 3 R is E_{f} .For a circular orbit, E_{f} = - \frac{G m M}{2 r} = - \frac{G m M}{2 ( 3 R )} = - \frac{G m M}{6 R} .3. Energy required Δ E = E_{f} - (Initial Potential Energy) Δ E = - \frac{G m M}{6 R} - (- \frac{G m M}{R}) = \frac{G m M}{R} - \frac{G m M}{6 R} = \frac{5 G m M}{6 R} .

Try it yourself before checking the explanation above.

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2 R ?

\frac{2GmM}{3R}

\frac{GmM}{2R}

\frac{GmM}{3R}

\frac{5GmM}{6R}

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