Zonal gravity harmonics from long satellite arcs by a seminumeric method

A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites, including two of low (<20°) inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 50 to 660 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, is accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation, atmospheric drag, radiation pressure, and lunisolar gravity are added at 1- to 8-day intervals in the integrated orbits. The results agree well with 1971 and 1972 solutions from other authors using different methods and different satellite and other data sets. These comparisons show the zonal coefficients are now known to better than 0.03 × 10−6 (fully normalized) to at least as high as degree 16.