A Variable Sampling-Time Method for Elliptical Orbit Motion Prediction in Nanosatellites

Nanosatellite missions may contain payloads for high pointing accuracy such as laser communication systems for crosslinks or astronomical observations. Therefore, the satellite requires a precise orbital position and orientation determination in order to point the scientific instrument to the desired target. In this work, an elliptical rotation method based on quaternion representation is presented. The proposed method allows determining the future position of a satellite around its orbit. Furthermore, in Low Earth Orbits (LEO) with an eccentricity larger than zero, the distance between the satellite and the Earth is changing over the time, increasing the satellite velocity in the perigee region compared to the apogee, due to the gravity forces. The elliptical rotation method and the orbital current position are deduced, considering a variable sampling-time as a function of the eccentricity and the orbital current position. The proposed algorithm can increase the position accuracy four times compared to fixed sampling time along the satellite orbit.