A spacecraft of negligible mass compared to Earth is to be transferred from a…

PHYSICS · Single correct · CBSE · Physics · Gravitation · Gravitation

Problem

A spacecraft of negligible mass compared to Earth is to be transferred from a circular low-Earth orbit of radius

7.0\times10^{6}\,\text{m}

to a geostationary orbit of radius

4.2\times10^{7}\,\text{m}

. Using

GM_{\oplus}=3.99\times10^{14}\,\text{m}^{3}\,\text{s}^{-2}

, the additional mechanical energy required per kilogram of the spacecraft is closest to (a)

4.8\times10^{7}\,\text{J\,kg}^{-1}

(b)

1.2\times10^{7}\,\text{J\,kg}^{-1}

(c)

2.4\times10^{7}\,\text{J\,kg}^{-1}

(d)

-2.4\times10^{7}\,\text{J\,kg}^{-1}