Tesseral harmonics of the Earth's gravitational field from camera tracking of satellites

A total of 7234 Baker-Nunn camera observations of 5 satellites were analyzed to determine simultaneously 44 tesseral harmonic coefficients of the gravitational field, 36 station coordinates, and 511 orbital elements. Supplementary observational data incorporated in the solution included accelerations of 24-hour satellites and directions between tracking stations from simultaneous observations; observation equations were also written for the differences between geometrical and gravitational geoid heights at tracking stations. Several variations in relative weighting of different observational data and a priori variances of parameters were tested. The previous independent solution most closely approached was that by Anderle based on Doppler data, from which the rms discrepancy was ±0.18×10−6 for 38 normalized harmonic coefficients, or ±7 m in total geoid height. An equatorial radius of 6,378,160±5 m was obtained.