Speaker
Nathan Parrish
(University of Colorado Boulder)
Description
This paper presents a study of transfers between distant retrograde orbits (DRO’s) and L2 halo orbits in the Earth-Moon system that could be flown by a spacecraft with solar electric propulsion (SEP). Pseudo-spectral optimal control is used to optimize these highly non-linear transfers. Similar types of transfers that have been studied in the literature include: from Earth orbit to Moon orbit using low-thrust[1], from Earth orbit to libration point orbits using low-thrust[2], from Earth to DRO using impulsive maneuvers[3], from Earth to DRO using low-thrust[4], and from L1 halo orbit to L2 halo orbit. Transfers between DRO’s and halo orbits using low-thrust propulsion have not been studied previously.
This paper takes advantage of modern advancements in computer hardware and optimization software to perform a study of the trajectories that could be flown by a low-thrust, SEP spacecraft from a DRO to a halo orbit about L2. This includes fleshing out several families of transfers that exist, identifying the minimum thrust-to-weight ratio required to fly on each family, and providing an understanding of the time-of-flight vs. propellant-mass. Topputo[5] showed that many distinct families of ballistic transfers exist between the Earth and Moon in a four-body model, and others have demonstrated that such variations exist for other types of transfers in Earth-Moon space[6], [7]. By exploring the families of transfers that exist between DRO’s and L2 halo orbits, this paper provides deeper insights into the trade space available. The circular restricted 3-body problem (CRTBP) is used throughout the paper so that the results are autonomous and simpler to understand.
DRO’s are a type of orbit that have received increased attention in the past few years because of the unique characteristics they exhibit. DRO’s are a type of repeating orbit that exists only in the 3-body problem[8]. When viewed in a reference frame that rotates with the orbits of the primary and secondary bodies, a DRO is retrograde about the secondary body, at a relatively high altitude such that the orbit is significantly perturbed by both the primary and secondary bodies. DRO’s are unique in that they sit between two-body orbits and libration point orbits in terms of stability. These orbits are often dynamically stable, though it has been shown that perturbations in a high-fidelity model of the solar system may cause a spacecraft to depart an otherwise stable DRO[9]. Parker, Bezrouk, and Davis demonstrated several trajectories that transfer from Earth to a DRO, requiring no maneuvers and remaining on the DRO for thousands of years[3].
Mission concepts that have examined DRO’s include the proposed NASA/JPL ARM (Asteroid Redirect Mission)[10] and the Orion/MoonRise concept[11], [12]. Both of these mission concepts would benefit from the capability to transfer between a DRO and a halo orbit about L2. Ongoing research by Davis and Parker is finding that impulsive transfers between those orbits do exist, but they are costly on the order of 150 m/s and require transfer times on the order of weeks to months. Spacecraft with SEP have the potential to greatly reduce the propellant mass required to make such transfers, without much increase in time of flight.
The open source, pseudo-spectral optimal control package PSOPT[13] is used to optimize transfers in the CRTBP. A variety of families of solutions are discovered by seeding different initial guesses, and by then using the continuation method to discover similar transfers. An example transfer optimized using PSOPT is presented in Fig. 1, below. The new software package Maverick[14], developed at CU Boulder, is also used to compare solutions.
[*See attachment for Figure*]. An example transfer viewed in the Earth-Moon synodic reference frame. Dynamics are the CRTBP. The Moon is plotted to scale on the x-axis at (1-μ), and the Earth would appear at (-μ). This transfer has a thrust-to-mass ratio of 1.3E-4 N/kg and a transfer time of 47 days. Thrust is nearly always on for this example. 1.75% of the initial mass is used as propellant. Thrust vectors are plotted only in the bottom-right plot.
**REFERENCES**
[1] J. T. Betts and S. O. Erb, “Computing optimal low thrust trajectories to the moon,” Eur. Sp. Agency, (Special Publ. ESA SP, vol. 2, no. 516, pp. 143–146, 2003.
[2] M. T. Ozimek and K. C. Howell, “Low-Thrust Transfers in the Earth-Moon System, Including Applications to Libration Point Orbits,” J. Guid. Control. Dyn., vol. 33, no. 2, pp. 533–549, 2010.
[3] J. S. Parker, C. Bezrouk, and K. E. Davis, “Low-Energy Transfers to Distant Retrograde Orbits,” in Advances in the Astronautical Sciences Spaceflight Mechanics 2015, 2015, p. AAS 15–311.
[4] J. F. C. Herman and J. S. Parker, “Low-energy, low-thrust transfers between earth and distant retrograde orbits about the moon,” AAS Guid. Navig. Control Conf., pp. 1–11, 2015.
[5] F. Topputo, “On optimal two-impulse Earth-Moon transfers in a four-body model,” Celest. Mech. Dyn. Astron., vol. 117, no. 3, pp. 279–313, 2013.
[6] J. S. Parker, “Families of low-energy lunar halo transfers,” Adv. Astronaut. Sci., vol. 90, no. JANUARY 2006, p. AAS 06–132, 2006.
[7] K. E. Davis and J. S. Parker, “Prograde Lunar Flyby Trajectories from Distant Retrograde Orbits,” 2015, pp. 1–12.
[8] V. G. Szebehely, Theory of Orbits: The Restricted Problem of Three Bodies. 1967.
[9] C. Bezrouk and J. Parker, “Long Duration Stability of Distant Retrograde Orbits,” no. August, pp. 1–9, 2014.
[10] J. N. Pelton and F. Allahdadi, “Handbook of Cosmic Hazards and Planetary Defense,” pp. 535–542, 2015.
[11] J. Hopkins, “OSCAR : Crew-Assisted Lunar Sample Return with Orion Orion Sample Capture and Return,” 2014.
[12] L. Alkalai, J. Hopkins, and B. L. Jolliff, “Orion/moonrise joint human-robotic lunar sample return mission concept,” 2013.
[13] V. M. Becerra, “Solving complex optimal control problems at no cost with PSOPT,” Proc. IEEE Int. Symp. Comput. Control Syst. Des., pp. 1391–1396, 2010.
[14] J. F. C. Herman, J. S. Parker, B. A. Jones, and G. H. Born, “High-speed, high-fidelity low-thrust trajectory optimization through parallel computing and collocation methods,” in Advances in the Astronautical Sciences Spaceflight Mechanics 2015, 2015, p. AAS 15–298.
| Applicant type | First author |
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Primary author
Nathan Parrish
(University of Colorado Boulder)
Co-author
Dr
Jeffrey S. Parker
(University of Colorado Boulder)
