TESSERAL HARMONICS OF THE POTENTIAL OF THE EARTH AS DERIVED FROM SATELLITE MOTIONS
SMITHSONIAN ASTROPHYSICAL OBSERVATORY CAMBRIDGE MASS
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OBSERVATIONS WERE UNDERTAKEN TO DETERMINE THE ACCURATE VALUES OF ZONAL HARMONICS OF THE GRAVITATIONAL POTENTIAL OF THE EARTH AS DETERMINED FROM THE MOTION OF ARTIFICIAL SATELLITES. The constants associated with the tesseral harmonics in the potential of the earth were derived with good accuracy. Analysis of the observations were made by use of the Differential Orbit Improvement program of Veis and Moore Smithsonian Astrophysical Observatory differential orbit improvement program Seminar. Proceedings, Tracking, Programs and Orbit determination, Jet Propulsion Lab., 1960. Each orbital element of the satellite was expressed by the sum of a polynomial and trigonometric and exponential functions of time. The number of functions was restricted to 25, and the parameters to be varied were restricted to 23. Tables are presented to show approximate expressions for the orbital elements of the 3 satellites Satellite 1958 Delta 2, Dec. 5-11, 1958 Satellite 1959 Alpha 1, April 6-26, 1960 and Satellite 1959 Eta, May 1, June 7, 1960. The amplitudes observed and the phase angles of various trigonometric terms for each element are also tabulated.