Q: The mass of a spaceship is 1000 kg. It is to be launched from the earth surface out into free space. The value of ‘g’ and ‘R’ are 10 ms^(-2) and 6400 km respectively. The required energy for this work will be

Sol: to launch the spaceship out into free space, from energy conservation

$\large -\frac{G M m}{R} + E = 0 $

$\large E = \frac{G M m}{R} $

$\large E = \frac{G M}{R^2} (m R) = m g R $

= 6.4 × 10^{10} J