Orbital elements and relative motion
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:
Keplerian elements, "qsw" local orbital frame:
Keplerian elements, "tnw" local orbital frame:
Circular elements, "qsw" local orbital frame:
Circular elements, "tnw" local orbital frame:
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):