Question

A 4000kg lunar lander is in orbit 50km above the surface of the moon. It needs to move to a 300km high orbit in order to link up with the mother ship that will take the astronauts home. How much work must the thrusters do?

Answer 1

As per the given question,

Mass of the lunar lander $(M)=4000kg$

Radius of orbit $(R)=50km$

Let the mass of the moon is m

Height =300km

Now,

$\dfrac{v^2}{R}=\dfrac{Gm}{R^2}$

$v=\sqrt{\dfrac{Gm}{R}}$

Now, applying the conservation of energy,

$W=KE-PE=\dfrac{Mv^2}{2}-\dfrac{GMm}{R+300km}$

$=\dfrac{4000\times mG}{2\times50\times 10^{3}}-\dfrac{4000mG}{350\times 10^{3}}$

$=\dfrac{4000mG}{50\times 10^3}(\dfrac{1}{2}-\dfrac{1}{7})$

$=\dfrac{2mG\times 5}{25\times 14}=\dfrac{mG}{35}$