The determination and analysis of the orbit of NIMBUS 1 rocket, 1964-52B: Variations in orbital inclination

The influence of aerodynamic drag and the geopotential on the motion of the satellite 1964-52B is considered. A model of the atmosphere is adopted that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation. A differential equation governing the variation of the orbital inclination combining the effects of air drag with those of the Earth's gravitational field is given.The 310 observed values of inclination are modified by the removal of perturbations due to luni-solar attraction, solid Earth and ocean tides, solar radiation pressure, low-order long-periodic tesseral harmonic perturbations and changes due to precession. The method of removal of these effects is given in some detail.The variations in inclination due to drag are analysed to give four values of the average atmospheric rotation rate at heights of 296–476 km at latitude 0–54°. These values are as expected from previous analyses.The analysis of the change in inclination due to solar radiation pressure shows that this rapidly tumbling cylindrical satellite may be considered as equivalent to a spherical satellite of a given area-to-mass ratio.Analysis of the inclination near 15:1 resonance with the geopotential yields values of lumped geopotential harmonics of order 15 and 30, namely, $\text{10}{}^9\text{C}\text{?}{}^{0.1}{}_{15}\text{= ?31.2 ± 2.3 10}{}^9\text{S}\text{?}{}^{0.1}{}_{15}\text{= ?4.4 ± 3.2 10}{}^9\text{C}\text{?}{}^{0.2}{}_{30}\text{= 39.0 ± 10.7 10}{}^9\text{S}\text{?}{}^{0.2}{}_{30}\text{= 51.8 ± 10.0}$