Question

The kinetic energy of a satellite in its orbit around Earth is \( E \). What should be the kinetic energy of the satellite to escape Earth's gravity?

• A. \( 4E \)
• B. \( 2E \)
• C. \( \sqrt{2}E \)
• D. \( E \)

Hint:

Escape velocity is given by \( v_e = \sqrt{2} v_0 \), where \( v_0 \) is the orbital velocity.

Answer 1

The Correct Option is B

Step 1: {Escape velocity formula}
\[ v_e = \sqrt{2} v_0 \] Step 2: {Find kinetic energy for escape}
\[ KE_{{escape}} = \frac{1}{2} M v_e^2 = \frac{1}{2} M (2 v_0^2) \] \[ = 2E \] Thus, the correct answer is \( 2E \).