Spacecraft Flying in Formation  The relative orbit between satellites can be described by the Hill–Clohessy–Wiltshire (HCW) equations. In this model, a so-called reference satellite is considered that orbits the Earth in a circular trajectory. The motion of one or more follower satellites is studied from a reference frame fixed at the center of the reference satellite. The orbital radius of the reference satellite is assumed to be much larger than the relative separation between the satellites. This set of coordinate axes is called the Local Vertical Local Horizontal Frame. The HCW equations are as follows: Here,  is the mean motion of the reference satellite and  ,  , and  are the radial, along-track, and cross-track directions, respectively. In general, uncontrolled HCW dynamics lead to unbounded relative motion, causing the formation to disperse. The disintegration of the formation can be avoided by matching the semi-major axes of the orbits of the two satellites around the Earth, giving them equal energies. The initial conditionaccomplishes this. In circular formation, the leader and the follower maintain a constant relative separation, satisfying The motion takes place in a plane ±30° to the  - plane and is achieved by deploying the satellites with the following relative initial conditions: "Spacecraft Flying in Formation" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/SpacecraftFlyingInFormation/ Contributed by: Pradipto Ghosh |
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