Question

A 5000 kg lunar lander is in orbit 10 km above the surface of the moon. It needs to move out to a 200 km -high orbit in order to link up with the mother ship that will take the astronauts home.

How much work must the thrusters do?

Express your answer with the appropriate units.

I got 1568.5*10^6 J but it is incorrect

Answer 1

Solution:-

total energy = half of the potential energy


work done = final total energy - initial total energy

= -(1/2)G*M_moon*m/(Rm+h2) - ((-(1/2)G*M_moon*m/(Rm+h1))

=(1/2) G*M_moon*m*( 1/(Rm+h1) - 1/(Rm+h2))

M_moon = 7.35*10^22 kg

Rm = 1737.4 km

W = (1/2)6.67*10^-11*7.35*10^22*5000*(1/(1737.4*10^3+10*10^3) - 1/(1737.4*10^3+200*10^3)

=  (1/2)6.67*10^-11*7.35*10^22*5000[5.612*10^-8)

= 6.88*10^8 J