Orbital Dynamic Admittance and Earth Shadow

Abstract

The effects of orbital dynamics on a velocity distribution from a point source — for example, a fragmentation — may be studied by Housen’s method. This technique permits the computation of a spatial density due to the velocity distribution as the sum over all routes between the source point and any point in space of the velocity density divided by the absolute value of the Jacobian determinant of the propagation map. The determination of all routes constitute finding all Lambert (orbital two point boundary value problem) solutions for the two points over a given elapsed time. In order to understand the observed density structures better, the dynamic admittance is introduced. It is the sum of the reciprocal absolute Jacobian determinants spanning all possible routes and is independent of the initial velocity distribution. The bands, pinch point and other features seen in the dynamic admittance plots are analyzed. The effects of the earth in reducing the number of routes, thereby casting a dynamic shadow, are demonstrated.