Answer to Question #21825 in Mechanics | Relativity for amar kumar mishra

Question

what is the minimum work that has to be performed to bring a spaceship of mass 2000kg from the surface of earth to moon?

Answer 1

m=2000kg
Potential energy of the ship on the earth surface is

E1 = G* M*m/r1

where r1 is radius of earth and M is its mass

E1 = 6.67*10^(-11)*5.9742*10^(24)*2000/( 6378.1* 10^(3)) = 1.24952302 × 1011& J

Potential energy of the ship on the Moon surface is

E2 = G*M*m/r2
where r2 is distance to Moon
E2 = 6.67*10^(-11)*5.9742*10^(24)*2000/( 384000*10^(3)) = 2.07541219 × 109J

So minimal work should be
E1-E2 =1.2219818 × 1011& J

here we neglect Moon's gravitation