Please i need help wih this problem, it\'s about ortbits, chapter 8 of Classical
ID: 2309335 • Letter: P
Question
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?
Explanation / Answer
time period T= 2*pi*r3/2/( 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