Relative Motion Near a Small Gravitational Source
- Paper number
IAC-08.C1.3.5
- Author
Prof. David Spencer, The Pennsylvania State University, United States
- Year
2008
- Abstract
The motion of a spacecraft flying near a small body in the solar system can be modeled as a perturbed linearized relative motion problem. The linearized Clohessy-Wiltshire-Hill (C-W-H) relative motion equations [1] can be used to describe the relative motion of one body with respect to another. One assumption that is made in developing these equations is that the two bodies have no gravitational influence on each other. However, this assumption breaks down when the system being described is one body moving with respect to another with a small gravitational effect. An example of this would be a spacecraft moving relative to a small asteroid. A rotating reference frame is moving in a circular orbit around the central body. The nonlinear relative motion of a massless body relative to the origin of the rotating reference frame is found [2]. Using the same rotating reference frame, but now having a small gravitational source at the origin of the rotating frame, the perturbed relative motion of the massless body relative to the rotating frame is described. The difference between the perturbed and unperturbed solution is found and the solution is linearized about the unperturbed motion. The solution relative to the unperturbed solution is found, and is added to the unperturbed relative motion solution. This analytical solution is compared with results obtained from numerical integration of the motion of the spacecraft in the restricted three-body problem [3]. Various values of representative small gravitational sources are used. Additionally, a parametric study of the resulting behavior of the spacecraft is performed for various initial locations of the spacecraft relative to the small gravitational source. References: 1. Clohessy, W. H., and Wiltshire, R.S., “Terminal Guidance System for Satellite Rendezvous”, Journal of Aerospace Sciences, Vol. 27, No. 9, September 1960, pp. 653-674. 2. Vallado, D.A., Fundamentals of Astrodynamics and Applications. 2nd ed. 2001, El Segundo, CA: Microcosm Press; Kluwer Academic Publishers, pp. 372-395. 3. Wiesel, W.E., Spaceflight Dynamics, 2nd ed., 1997, Boston, MA: McGraw-Hill, pp. 278-296.
- Abstract document
- Manuscript document
IAC-08.C1.3.5.pdf (🔒 authorized access only).
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