A determination of the coefficient J of the second harmonic in the Earth's gravitational potential from the orbit of satellite 1958 β₂

Abstract

From the secular changes in the longitude of the node and the argument of the perigee, the coefficient J in the gravitational potential function was determined to be (1.6232±.0005)×10−3. If the bounding equigeopotential surface of the earth is assumed to be an ellipsoid of revolution, this value of J implies a flattening ƒ of 1/298.32±.05.

The Earth's Gravitational Potential, deduced from the Orbits of Artificial Satellites

“…Values of JZ and J4 have also been calculated by a different method, using h and &I from Vanguard I, and ignoring the Jz2 and J6 terms. The first analysis of this type (Lecar, Sorenson & Eckels 1959) gave JZ = I 082 x 10-6 and J4 = -2.4 x 10-6, and in a subsequent study, O'Keefe, Eckels & Squires (1959b) found JZ = (I 082.5 ? 0.1) x 10-6…”

Generation of Orbital Elements for the Telstar® Communications Satellites

“…5. By inspection we write the direction cosines, which are quite similar to (18), (19) and (20), as where A substitution of (21), (22), and (23) into (13), (14), and (15) …”

Geophysical results obtained from satellite orbits

“…If terms with n > 6 are neglected, it is possible to evaluate J2 and .I4 from one satellite using both fi and ci,. This method has been applied to the orbit of Vanguard 1 with the terms in J2, neglected (Lecar, Sorenson andEckels 1959, O'Keefe, Eckels andSquires 1959 b). Zhongolovitch (1960 b) used both this method and the one above to obtain values of J,, J3 and J4.…”