A synchronous orbit is an orbit about a planet\'s equator that always remains ab

Question

A synchronous orbit is an orbit about a planet's equator that always remains above the same spot of the planet because the synchronous orbit matches the planet's rotational period. The pilot of the Mars spacecraft (which was named Cheetah 1 and had a 8355 kg mass) asked Tarzan to calculate the altitude of a synchronous orbit so they coud remain over a particular geological feature on the Martian equator. Calculate the altitutde above the Martian equator using the data above and Johannes Kepler's genius. _____ m

What is the total orbital energy of Cheetah 1 in the synchronous orbit? _____ J

What is the orbital kinetic energy of Cheetah 1 in the synchronous orbit? ___ J

What is the gravitational potential energy of Cheetah 1 in the synchronous orbit? ____ J

After the geological observation were made, the pilot of Cheetah 1 increased their orbital altitude by 355 km. What was the minimum amount of work done on the spacecraft to attain the new stable orbit? ____ J

Explanation / Answer

a] r = ( T^2GM/(4pi^2))^(1/3)

h = r- R =   ( (88775^2*6.67e-11*6.417e23)/(4pi^2))^(1/3) - 3390000 = 20443715 -3390000 =  17053715 m

b] Total orbital energy = -GMm/2r = -6.67e-11*6.417e23*8355/(2*20443715) = -8746101514 J

c] KE = -TE = 8746101514 J

d] PE = 2*TE = 2*-8746101514 = - 17492203028 J

e] work done = change in KE = 6.67e-11*6.417e23*8355/(2*(20443715+355000)) - 8746101514 = - 149281627 J

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