Third-Body Perturbation Effects on Satellite Formations
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Third-Body Perturbation Effects on Satellite Formations Christopher W. T. Roscoe1 · Srinivas R. Vadali2 · Kyle T. Alfriend2
Published online: 29 September 2015 © American Astronautical Society 2015
Abstract The effects of third-body perturbations on satellite formations are investigated using differential orbital elements to describe the relative motion. Absolute and differential effects of the lunar perturbation on satellite formations are derived analytically based on the simplified model of the circular restricted three-body problem. This analytical description includes averaged long-term effects on the orbital elements, including the full transformation between the osculating elements and the lunar-averaged elements, which is absent from previous research. A simplified EarthMoon system model is used, but the results are applicable to any formation reference orbit about the Earth. Simulations are performed to determine the effects of the lunar perturbation on example formations in upper MEO, highly eccentric orbits by using the formation design criteria of Phases I and II of the NASA Magnetospheric Multiscale mission. The changes in angular differential orbital elements (δω, δ, and δM0 ) and in science return quality due to this perturbation are compared to changes due to J2 . The method is then expanded to include the inclination of the Moon’s orbit and results are compared to simulation using the NASA General Mission Analysis Tool.
Srinivas R. Vadali
[email protected] Christopher W. T. Rosco [email protected] Kyle T. Alfriend [email protected] 1
Applied Defense Solutions, P.O. Box 1102, 10440 Little Patuxent Parkway, Columbia, MD, 21044, USA
2
Department of Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station, TX, 77843-3141, USA
J of Astronaut Sci (2013) 60:408–433
409
Keywords Formation flying · Third-body · Magnetospheric Multiscale · Orbital elements
Introduction Long duration satellite formation flying, a critical element of upcoming science return missions [1], is a key area of current research in astrodynamics. The Keplerian (two-body) relative motion problem has essentially been solved, assuming small separations between the satellites and including arbitrary eccentricity [2–6]. However, long duration formations are impossible to design without taking into account the effect of perturbations to the Keplerian motion. Therefore, modern research is focused on accounting for disturbing forces such as the J2 oblateness perturbation, atmospheric drag, third-body effects, and solar radiation pressure. J2 is the dominant perturbation in low-Earth orbit (LEO) and medium-Earth orbit (MEO), followed by atmospheric drag in LEO and lunisolar effects in MEO. In the upper MEO region and high-Earth orbit (HEO), third-body effects are of the same order of magnitude as J2 . In 2003, Gim and Alfriend [7] derived the state transition matrix of relative motion including arbitrary eccentricity and first-order absolute and differential J2 effects using differential mean orbital element
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