The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

Extended cusp-like regions and their dependence on the Polar orbit, seasonal variations, and interplanetary conditions

Extended cusp-like regions (ECRs) are surveyed, as observed by the Magnetospheric Ion Composition Sensor (MICS) of the Charge and Mass Magnetospheric Ion Composition Experiment (CAMMICE) instrument aboard Polar between 1996 and 1999. The first of these ECR events was observed on 29 May 1996, an event widely discussed in the literature and initially thought to be caused by tail lobe reconnection due to the coinciding prolonged interval of strong northward IMF. ECRs are characterized here by intense fluxes of magnetosheath-like ions in the energy-per-charge range of _1 to 10 keV e_1. We investigate the concurrence of ECRs with intervals of prolonged (lasting longer than 1 and 3 hours) orientations of the IMF vector and high solar wind dynamic pressure (PSW). Also investigated is the opposite concurrence, i.e., of the IMF and high PSW with ECRs. (Note that these surveys are asking distinctly different questions.) The former survey indicates that ECRs have no overall preference for any orientation of the IMF. However, the latter survey reveals that during northward IMF, particularly when accompanied by high PSW, ECRs are more likely. We also test for orbital and seasonal effects revealing that Polar has to be in a particular region to observe ECRs and that they occur more frequently around late spring. These results indicate that ECRs have three distinct causes and so can relate to extended intervals in (1) the cusp on open field lines, (2) the magnetosheath, and (3) the magnetopause indentation at the cusp, with the latter allowing magnetosheath plasma to approach close to the Earth without entering the magnetosphere.