A method of estimating residuals in orbital theory
National Aeronautics and Space Administration, 1961 - Science - 10 pages
The degree of approximation used in determining the orbits of earth satellites is reflected in the residuals (differences between calculated and observed positions). The least-squares procedure generally used to fit theory to observation tends to obscure the significance of theoretical parameters, so that the physical sources of residuals cease to be apparent. A method is outlined herein for estimating the magnitude of the residuals to be expected from an approximate theory presumed to have one missing or incorrect term.
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approximate theory assumed Brouwer calculated and observed calculated satellite circular orbit compensate considered correct term Define degree of approximation derivative determining the orbits difference distance DRAG earth satellites Equation ERRORS DUE ESTIMATING RESIDUALS estimating the magnitude example f is given fit theory free parameters function gravitational field inclination incorrect integral number Jacchia latitude least-squares procedure longitude mean motion measure METHOD OF ESTIMATING MINIMIZATION OF RESIDUALS minimized with respect missing term neglected node observed positions orbital period ORBITAL THEORY orbits of earth outlined pertinent physical sources position is computed positive axis due POTENTIAL quadratic residuals cease RESIDUALS IN ORBITAL restricted result that Rmin rigorous satellite whose position secular servation significance sinusoidal sources of residuals subsatellite point symmetrized formulation taken term represents theoretical parameters theory presumed true anomaly written zenith