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Natural relative motion

Orbital elements and relative motion

Effect of small changes in orbital elements

Gaps in orbital elements translate into gaps in position and (inertial) velocity in the local orbital frame.

Formulas giving the increments in position and (inertial) velocity as function of the increments in orbital elements for any elliptical orbit in the "qsw" local frame are the following:

Simplified (order 0) expressions for nearly circular orbits are:

One can derive the jacobian matrix corresponding to a rotating local frame. The 1st order result for "qsw" and "circular" elements is the following:

  • Circular elements, "qsw" local orbital frame (velocity relative to local frame):


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