Question

To shift the lab from first orbit to the second orbit.($R=6400$km, $g=10m/s^2$)

Answer 1

Energy of lab in an orbit is

$E=\frac{1}{2}m{\left(\sqrt{\frac{GM}{r}}\right)}^2-\frac{GMm}{r}=-\frac{GMm}{2r}$

Hence, energy required would be equal to the change i total energy,

$\Delta E=-\frac{GMm}{2\left(3R\right)}+\frac{GMm}{2\left(2R\right)}=\frac{GMm}{12R}=\frac{1}{12}gmR=\frac{1}{12}\times 9.8\times 2000\times 6400000=1.67\times {10}^{10}J$

Answer is $1.67\times {10}^{10}J$.