2024 GravitationEnergy to Launch a Satellite into Orbit Hard Question 7 of 66 in Gravitation

The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$ from the surface of the earth is:

A $\frac{GmM}{2R}$
B $\frac{GmM}{3R}$
C $\frac{5GmM}{6R}$
D $\frac{2GmM}{3R}$

The answer is C.

Solution

Orbital radius = R + 2R = 3R Energy on the surface $E_1 = -\frac{GMm}{R}$; total energy in orbit $E_2 = -\frac{GMm}{2 \times 3R}$ $W = E_2 - E_1 = -\frac{GMm}{6R} + \frac{GMm}{R} = \frac{-GMm + 6GMm}{6R}$ $W = \frac{5GMm}{6R}$

Concept Minimum energy for orbital insertion at a given altitude

Gravitation in past papers

66 questions from this chapter have appeared across 26 exam years.