A satellite must be brought back from a circular 12hour orbi

A satellite must be brought back from a circular 12-hour orbit to an orbit at a reentry altitude of 75km using a minimum of fuel. What is the altitude of the initial orbit? Calculate the eccentricity of the transfer ellipse Calculate the first velocity increment required. Calculate the second velocity increment to achieve an orbit at re-entry altitude.

Solution

R_a= 12+6378= 6390

R_p = 75+6378= 6450

SMa = R_a+R_p / 2 = 6420

e = R_a-R_p/R_a+R_p   = 0.0046729

T = 2(pi)Sqrt(SM_a^3/GM) = 6178 seconds