Survey of Earth-mars trajectories using Lambert's problem and applications

Open Access
Author:
Conte, Davide
Area of Honors:
Aerospace Engineering
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • David Bradley Spencer, Thesis Supervisor
  • George A Lesieutre, Honors Advisor
  • Robert Graham Melton, Faculty Reader
Keywords:
  • astrodynamics
  • lambert's problem
  • Mars
Abstract:
The focus of this thesis is to analyze interplanetary transfer maneuvers from Earth to Mars by solving Lambert’s Problem. Additionally, the orbital parameters of the transfer orbits as well as the relative required ΔVs and times of flights were determined in order to define the optimal departure and arrival windows for a given range of date. The first step in solving Lambert’s Problem consists in finding the positions and velocities of the departure (Earth) and arrival (Mars) planets for a given range of dates. Then, by solving Lambert’s problem for various combinations of departure and arrival dates, porkchop plots can be created and examined. Some of the key parameters that are plotted on porkchop plots and used to investigate possible transfer orbits are the departure characteristic energy, C3, and the arrival v∞. These parameters, in combination with given desired initial and final parking orbital conditions about Earth and Mars, were also used to determine the total ΔV for the various Earth-Mars transfers. Lastly, ΔV results were used to find the necessary amount of propellant needed for the transfer maneuvers as a percentage of total spacecraft mass for a given specific impulse. Moreover, this thesis also considers cases when Lambert’s solution fails to give reasonable results, particularly when the transfer angle between Earth and Mars is close to 0 or 180 degrees. A special case of Lambert’s problem is the Hohmann transfer, which is also discussed in this thesis. The results of the analysis lead to the choice of departure and arrival dates that, given the capabilities of the launch system such as ΔV, makes the mission feasible. Additionally, unless specified otherwise, only time of flight that would be reasonable for an unmanned mission to Mars were considered.