On the magnetic damping of rotation of artificial satellites of the Earth

Abstract

The observed decreasing spin rate of Vanguard I (1958β2) has been credited to eddy currents induced by the earth's magnetic field. The degree of validity of this explanation has been tested by Wilson [1959, 1960] for both Vanguard I and II by comparisons between observed values of the earth's mean total magnetic field and the values of this field calculated on the basis of the theory of Bauer [1923]. Basic to the comparisons made by Wilson [1959] is evaluation of integrals of the type ((1))where ρ is an arbitrary real number. In (1), is the exact geocentric distance of the artificial satellite under consideration assumed to be moving about the earth in an elliptic orbit of eccentricity e (0 ≤e<1) and of semimajor axis. a. The symbol M denotes the mean anomaly of the satellite, and the function E (M) represents the real single-valued solution for the satellite's eccentric anomaly, E, in terms of M known [Moulton, 1935] to be implicitly defined by Kepler's familiar equation ((2))We hasten to point out that, for reasons to be made clear in the sequel, we shall have no need to seek an explicit representation of E in terms of M.