Question

A 4000 kg lunar lander is in orbit 70 km above the surface of the moon. It needs to move out to a 500 km -high orbit in order to link up with the mother ship that willtake the astronauts home.

How much work must the thrusters do?

Answer 1

The work will be :

W=-GMm/r evaluted from 70 to 500

W=-GMm/500 + GMm/70

G=6.673x10^-11 (gravitationl constant)

M=7.36x10²² (mass of moon)

m=4000 (mass of lander)

Pluggin those values in gives:

W=2.414x10¹⁴ joules

Hope that helps

Answer 2

solved a similar question already with different numbers.. i put the question and the answer.. hope it helps!! :) kindly rate a lifesaver :)

"A 3000 lunar lander is in orbit 70 above the surface of the moon. It needs to move out to a 300 -high orbit in order to link up with the mother shipthat will take the astronauts home. How much work do the thrusters do?"

ANSWER:

You should read what you paste into a question! Apparently when you copied the page the units were in graphic form (italics, greeks, whatever) anddidn't get pasted. This happens all the time in these questions. So is it 3000 kg, lb, slug, what? 70 and 300 m, km, mi, nmi, feet, what? Too manypossibilities to give a numeric answer for all of them.
So you get the equations instead, actually a more useful answer.
Rmoon is moon radius = 1738090 m
R = Rmoon + altitude in m
m isspacecraft massin kg
μ is moon grav. constant = 4902780000000 m^3/s^2
PE/m = -μ/R (specificpotential energy)
v = sqrt(μ/R)
KE/m = v^2/2 (specific kinetic energy)
Energy of spacecraft in a given orbit = m(PE/m + KE/m)
Energies are in J.
Thrusters' work is the difference between energies of the two orbits.