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

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.