Analysis of Satellite Motion from Radio Reception

This paper presents an analysis of a radio signal originating from a tumbling and rotating earth satellite. An equation is derived for the relative motion of the unit position vector pointing from the observer to the satellite with respect to the satellite coordinate system. From this, the amplitude variation of the ground received radio signal is calculated. It is further shown how a recording of this amplitude variation can be used to calculate the tumbling angle of the satellite in space. A simple example is given in which this angle between the normal of the plane of a satellite turnstile antenna system and a fixed axis in space is determined with the help of AGC recording. These recordings can be made either with linear or circular polarized receiving antenna. For future stabilized satellites, these derived equations can be used as an easy check of the operational condition of the stablization system itself.