Optimum estimation of satellite trajectories including random fluctuations in drag

length is in the order of several centimeters. The introduction of two-stream functions makes it possible to include the satellite speed in the self-consistent equations. This analysis determines the potential field around a moving satellite, which is shown not to have spherical symmetry. Furthermore, the determined potential field is significantly associated with the calculation of Coulomb drag, as indicted in Eq. (15). Two-stream instability predicts a long wake trail behind the satellite and high frequency of oscillation which agrees with the fact. By using the actual data of Explorer VIII and the data of the upper atmosphere (satellite speed = 7.4 X 10 m/sec), the mean thermal speed of electrons = 2.06 X 10 m/sec at the altitude of 1000 km, the mean thermal speed of ions = 1.20 X 10 m/sec, and the temperature = 1100 °K; Eq. (13) then gives as tagnation potential of — 0.156 v as compared with the actual measurement of —0.15 v. Of course, the agreement of the surface potential with the experimental one is not a test of the potential distribution, but only of Eq. (13) and, to a lesser degree, of the assumption concerning the surface interaction. However, the interpretation of Explorer VIII data supports qualitatively the nonspherical potential field. References