Question

The ratio of KE required to be given to the satellite to escape earth's gravitational field to the KE required to be given, so that the satellite moves in a circular orbit just above earth's atmosphere is :

• A. 1
• B. \( \frac{1}{2} \)
• C. 2
• D. infinity

Hint:

Escape velocity is \(\sqrt{2}\) times orbital velocity $\Rightarrow$ KE ratio = 2.

Answer 1

The Correct Option is C

Concept: Escape velocity: \[ v_e = \sqrt{\frac{2GM}{R}}, \quad v_o = \sqrt{\frac{GM}{R}} \]

Step 1: Kinetic energies.
\[ KE_e = \frac{1}{2} m v_e^2 = \frac{GMm}{R} \] \[ KE_o = \frac{1}{2} m v_o^2 = \frac{GMm}{2R} \]

Step 2: Ratio.
\[ \frac{KE_e}{KE_o} = \frac{GMm/R}{GMm/2R} = 2 \]