Question

(13% ) Problem 5: A 4500-kg spaceship is in a circular orbit 170 km above the surface of Earth. It needs to be moved into a higher circular orbit of 390 km to link up with the space station at that altitude a How much work, in joules, do the spaceship's engines have to perform to move to the higher orbit? Ignore any change of mass due to fuel consumption. Grade Summary 0%

Answer 1

5)

given

m = 4500 kg
h1 = 170 km
h2 = 390 km

we know,
Re = 6.37*10^6 m
Me = 5.98*10^24 kg

so,

r1 = Re + h1 = 6.37*10^6 + 0.17*10^6 = 6.54*10^6 m
r2 = Re + h2 = 6.37*10^6 + 0.39*10^6 = 6.76*10^6 m

we know total energy of saceship, E1 = -G*Me*m/(2*r)

Workdone = change in mechanical energy

W = E2 - E1

= -G*Me*m/(2*r2) - ( -G*Me*m/(2*r1))

= G*Me*m*(1/r1 - 1/r2)

= 6.67*10^-11*5.98*10^24*4500*(1/(6.54*10^6) - 1/(6.76*10^6) )/2

= 4.47*10^9 J