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Physics · GRAVITATION
हिन्दीA satellite of mass \( 400\text{ kg} \) is in a circular orbit of radius \( 2 R_E \) about the Earth. How much energy is required to transfer it into a circular orbit of radius \( 4 R_E \)? (Take \( g = 9.81\text{ m s}^{-2} \) and \( R_E = 6.37 \times 10^6\text{ m} \))
Correct answer · Option 3
\( 3.13 \times 10^9\text{ J} \)
Explanation
\( \Delta E = E_f - E_i = -\frac{G M_E m}{8 R_E} - (-\frac{G M_E m}{4 R_E}) = \frac{G M_E m}{8 R_E} = \frac{m g R_E}{8} = \frac{400 \times 9.81 \times 6.37 \times 10^6}{8} \approx 3.13 \times 10^9\text{ J} \).
