A5000-kg spacecraft is in a circular orbit 2000 km above the surface of mars. how much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface? assume the mars radius is 3.4 \times 10^6 m3.4×10 6 m and the mass of mars is  6.4 \times 10^{23}6.4×10 23  kg. (express your answer in the format: 1.23 \times 10^{10} j1.23×10 10 j as "1.23e10 j".)

W = 0.483 x 10^10 J

Explanation:

M = mass of mars = 6.39 x 10^23 kg

m = mass of spacecraft = 5000 kg

R = radius of mars = 3.4 x 10^6 m

hi = initial height = 2000 km = 2 x 10^6 m

hf = final height = 4000 km = 4 x 10^6 m

ri = initial distance from center of mars

ri = R + hi

rf = final distance from center of mars

rf = R + hf

Total energy at an altitude of ''r'' is given as :;

Energy at height ''ri''

Ei = -1.973 x 10^10 J

Energy at height ''rf''

Ef = - 1.439*10^10 J

work done is given as ::

W = (- 1.439*10^10 J) - (-1.973 x 10^10) J

W = 0.483 x 10^10 J