An Investigation into Establishing a Formation of Small Satellites in a Lunar Flower Constellation

Lunar science missions such as LADEE and GRAIL achieved unprecedented measurements of the Lunar exosphere and gravity field. These missions were performed with one (LADEE) or two (GRAIL) traditional satellites. The global coverage achieved by these missions could have been greatly enhanced with the use of a constellation of satellites. A constellation of communication satellites at the Moon would also be necessary if a Lunar human base were to be established. Constellations with many satellites are expensive with traditional technology, but have become feasible through the technological advancements and affordability of cubesats. Cubesat constellations allow for full surface coverage in science or communication missions at a reasonable mission cost. Repeat ground track orbits offer interesting options for science or communication constellations, since they provide repeat coverage of the surface at a fixed time between sequential visits. Flower constellations are a family of constellations being studied primarily by Daniele Mortari at Texas A\u26M University that make use of repeat ground tracks. Orbital parameters are selected such that the nodal period of the orbit matches the nodal period of the primary body by a factor dependent on the number of days and the number of revolutions to repeat the ground track. All orbits in a flower constellation have identical orbital elements, with the exception of the right ascension of the ascending node (RAAN) and the initial mean anomaly, which are determined based on the desired phasing scheme desired. Flower constellations have thus far primarily been studied at Earth. A flower constellation at the Moon could be quite useful for science or communication purposes. In this scenario, the flower constellation satellites would be small satellites, which introduces many unique challenges. The cubesats would have limited propulsion capability and would need to be deployed from a mothercraft. Orbital maintenance would then be required after deployment to retain the repeat ground track nature of flower constellations. The limited fuel on the cubesats and the maneuvers required determine the lifetime of the constellation. The communications range of the cubesats will also be limited; following a successful deployment, the mothercraft must move into a long-term communications orbit where it can see both the children craft and Earth, to act as a communications relay. This work investigates the differences in flower constellations at the Moon versus at Earth. It is found that due to the longer rotation period of the Moon, the number of petals in the flower constellation must be quite large in order to produce reasonable orbit sizes. Two types of flower constellations are investigated: a single-petal and multi-petal constellation. The single-petal constellation consists of a string-of-pearls formation within one inertial flower constellation orbit. The multi-petal configuration has one satellite per inertial orbit, with the orbits spaced symmetrically within a 360° RAAN distribution. Optimal methods for deployment are explored for both configurations. Phasing orbits are used to deploy the single-petal constellation. This is found to be a simple and low-cost deployment scheme. The multi-petal configuration requires larger plane change maneuvers, and three-burn transfer orbit solutions that are optimal over single impulsive burn maneuvers are found. The mothercraft maneuver into the long-term communications orbit is also investigated. This maneuver is once again just a phase orbit maneuver for the single-petal constellation and is low cost. A polar mothercraft orbit is desired for the multi-petal configuration, again requiring a large and expensive plane change maneuver. As was the case with the deployment maneuver, a three-burn transfer orbit series is found to be cost optimal over a series of impulsive burns for this maneuver. Finally, once the constellation is established, orbit maintenance maneuvers are calculated. A 4 kg cubesat with 1 kg of fuel is assumed, and various thruster types are used to correlate required maintenance ΔVs to propellant mass required. It is found that the flower constellations at the Moon can be maintained for between 100 and 800 days, depending on the efficiency of the thruster system used. Ultimately, a small satellite constellation at the Moon is found to be feasible to establish and maintain for a science or communication mission