Trajectory design and propulsion system comparison for a near Earth asteroid rendezvous mission

If the cost of space flight were drastically reduced, mining operations on metal rich asteroids could be profitable. The objective of this thesis is to design an asteroid rendezvous mission and to compare possible propulsion system options. The two propulsion systems studied in detail are a solar sail hybrid system and a liquid chemical system. The asteroid selected is the near Earth asteroid, Eros.

In order to compare these propulsion schemes, two programs were written for use with desktop computers to model the optimal interplanetary trajectories of these propulsion systems. The impulsive thrust program uses Battin's modified Gauss algorithm to solve for the three-dimensional space trajectory based on the two-body problem. The low-thrust program utilizes Pontryagin's maximization principle to optimize the solar sail trajectory generated by a fourth order Runge-Kutta integration algorithm and the method of steepest descent, and Newton's method to solve the resulting two point boundary value problem. Both of these programs contain animated graphics illustrating the spacecraft's trajectory, the Earth's orbit, and Eros's orbit.

Utilizing these tools, optimal mission profiles for each propulsion scheme were selected based upon the lowest required total energy. If the total mission energy was the same for multiple missions, minimum time of flight became the basis for selection. The minimum energy impulsive mission has a launch date of January 30, 2005, and a flight time of 291 days. The total C3 for this mission is 25.391 (km/s)², which requires a total delta V of 6.6393 km/s. Since the delta V required by the chemical booster is the same for all of the solar sail hybrid missions (3.1532 km/s), the minimum flight time missions were selected. The primary mission for the low acceleration (1 mm/s² characteristic acceleration) sail has a launch date of June 6, 2002 and a flight time of 397 days. The primary mission for a 2 mm/s² characteristic acceleration sail has a launch date of July 25, 2002 and a flight time of 286 days.

The figures of merit used to compare the three propulsion systems were the initial mass in low Earth orbit (IMLEO), and the Earth to Eros flight time. The IMLEO for the January 30, 2005 mission chemical system is 2730 kg. The 2mm/s² characteristic acceleration solar sail hybrid system has a mission flight time comparable to the chemical system, but the IMLEO is much greater at 6240 kg. The smaller 1 mm/s² characteristic acceleration solar sail hybrid requires an addition 106 days of flight time, but at a significant IMLEO mass savings. The IMLEO of the 1 mm/s² characteristic acceleration solar sail hybrid is equal to 1590 kg. Since the flight time is not as critical as the mission cost for the unmanned asteroid rendezvous mission, the 1 mm/s² sail hybrid vehicle is the best propulsion system option. The small solar sail has an additional benefit in that it is reusable.