The required work done to move to the higher orbit will be "2.37 × 10^9 Joule".
According to the question,
Mass of spaceship = 3500 kg
Higher orbit moved = 360 km
Earth's mass = 5.97 × 10²⁴
We know the relation,
Work done, W = Satellite's difference in total energy
= [tex]E_f -E_i[/tex]
= [tex][-\frac{GMm}{2r_2} ] - [-\frac{GMm}{2r_1} ][/tex]
By taking common, we get
= [tex]\frac{GMm}{2} [\frac{1}{r_1} -\frac{1}{r_2} ][/tex]
By substituting the values,
= [tex]\frac{6.67\times 10^{-11}\times 5.97\times 10^{24}\times 3500}{2} [\frac{1}{6591\times 10^3} -\frac{1}{6741\times 10^3} ][/tex]
= 69684 × 10¹³ [0.1517 × 10⁻⁶ - 0.1483 × 10⁻⁶]
= 236.9 × 10⁷ or,
= 2.37 × 10⁹ Joule
Thus the above response is correct.
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