Please i need help wih this problem its about ortbits chapte

Please i need help wih this problem, it\'s about ortbits, chapter 8 of Classical Mechanics, Taylor.

Problem :

1-Orbit transfer : Rosetta (3000 kg) is in a circular orbit around the Churyumov–Gerasimenko comet (1013 kg) at a distance of 30 km from its center.

a) Calculate the period of the orbit of 30 km. Calculate also the period of a circular orbit 10 km from the center.

b)  We want to pass the probe of the 30 km orbit to 10 km. Calculate the factors in points P and P \', respectively apoapsis and periapsis of the transfer orbit. Indicate their numerical value.

c) Rosetta has 24 motors each providing 10 kN thrust. Suppose it uses only 6 of them to change velocity at the points P and P \', how many seconds they will operate at each point?

Solution

time period T= 2*pi*r^3/2/( G M) =

here r=30*10³ m, G= 6.67*10^-11 newton m² kg^-2 , M=1013kg

putting these values in the above equation

T= 2*3.14* (30*10³ )^3/2 /6.67*10^-11* 1013 =(32.5806*10⁶) /(67.57*10^-9)=48.22*10¹³sec

the period of circular orbit 10 km from the center is

T=2*3.14*10⁶ /(67.57*10^-9 )=0.093*10¹⁵ =9.3*10¹³ sec