Formation Pattern Analysis of Follower Spacecraft for Elliptic Reference Orbits
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Formation Pattern Analysis of Follower Spacecraft for Elliptic Reference Orbits Jonghee Bae1 · Youdan Kim2
Published online: 14 July 2015 © American Astronautical Society 2015
Abstract Formation analysis is performed for the periodic relative motion between two spacecraft in Keplerian elliptic orbits. For a leader spacecraft moving in a circular orbit around the Earth, the relative motion of a follower spacecraft has an ellipse in the radial/along-track plane. On the other hand, when a leader spacecraft flies in an elliptical orbit, the follower spacecraft does not have an ellipse of fixed eccentricity in the relative motion plane due to the eccentricity of the reference orbit. In this study, the spacecraft formation flying is analyzed to describe the natural periodic relative motion. The instantaneous eccentricity of the relative motion is derived in the radial/along-track (R/AT) plane (x − y plane) formation and the along-track/crosstrack (AT/CT) plane (y − z plane) formation. Numerical simulations are performed to yield the periodic relative motion and the formation trajectories in the elliptical reference orbit. The variation of the formation radius according to the eccentricity of the reference orbit is analyzed for R/AT plane and AT/CT plane formations. In addition, the range of the angle difference between two follower spacecraft is described with respect to the eccentricity of the leader spacecraft. Using these results, the desired constraints can be provided for a designer to choose the formation pattern in accordance with the mission requirements. Keywords Spacecraft formation flying · Formation pattern · Relative motion dynamics · Periodic relative motion · Keplerian elliptic orbit Jonghee Bae
[email protected] Youdan Kim [email protected] 1
Convergence Technology Research Head Office, Korea Aerospace Research Institute, Daejeon, South Korea
2
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, Korea
168
J of Astronaut Sci (2013) 60:167–185
Introduction Spacecraft formation flying has been studied by many researchers since multiple satellites in a formation provide reliability, financial benefits, and high resolution images compared to a single large spacecraft [1–3]. To describe the relative motion of the formation flight, Hill-Clohessy-Wilshire (HCW) equations are widely used [4], which are a simple model based on the linearized dynamics in circular reference orbits. However, the HCW equations have a limitation on expressing the relative motion in Keplerian elliptic orbits due to the underlying assumptions about nonlinearity and eccentricity. The nonlinearity problem of the HCW equations has been improved by considering higher-order terms, and the eccentricity problem has been studied by using time or true anomaly as a free variable. Vaddi et al. described the initial condition of the HCW equations considering the nonlinearity as well as the eccentricity of the relative motion in the elliptical orbit [5]. Through the TschaunerHempel (TH) equation, which uses the true
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