Reference no: EM133326041

Question 1. Write a function which solves the two-body problem using the F and G solution or the "Lagrange Coefficient" solution. Verify the answer by comparing it to a numerical integration of the original 2BP differential equations of motion. Perform the propagation and verification for any geocentric circular orbit and any geocentric elliptical orbit. Provide necessary plots and all source codes

Question 2: Consider two spacecraft (A which is a deep-spoce explorer and B which is a refuelling mother-ship) in the same circular orbit of radius a. The mother-ship is initially leading the chasing explorer by 0 radians of true anomaly as shown. It is desired that the deep-space explorer re-fuel in-orbit and therefore rendezvous with the mother-ship. Mission Control has asked you, an astrodynamics engineer to explore options to achieve this by transferring onto a "chase" orbit and then transferring back onto the original circular orbit.

(a) Design an interior "chase' orbit where the transfer orbit is interior to tile circular orbit (find the required velocity impulses). Assume two instantaneous velocity changes which are tangential to the orbit. Assume rendezvous occurs after one orbit of A on the designed "chase" orbit.

(b) Design an exterior "chase" orbit where the transfer orbit is exterior to the circular orbit (find the required velocity impulses). Assume two instantaneous velocity changes which are tangential to the orbit. Assume rendezvous occurs after one orbit of A on the designed "these" orbit.

(c) Discuss the relative advantages/disadvantages of the two options. Is there any circumstance when either option becomes infeasible?