Reconstruction of earth orbit parameters from a miniaturized temperature sensor onboard the Delfi-C3 CubeSat

Abstract

This paper reports on the reconstruction of key orbital elements of the Earth's orbit around the Sun from a miniaturized temperature sensor onboard the Delfi-C³ CubeSat, a novel approach never explored before to the best of our knowledge. Delfi-C³ is a triple-unit CubeSat, developed by Delft University of Technology, which was launched on April 28th 2008. Despite its required lifetime of less than three months, Delfi-C³ is still operational and has been beaconing data for 8.6 years, which makes this CubeSat mission unique in terms of a continuous record of telemetry data. Recent inspections of Delfi-C³ telemetry data over five years from different temperature sensors have revealed that the satellite, which uses a passively controlled temperature system, shows surprisingly systematic patterns of periodic nature with an amplitude of 3.1 K and a period of one synodic year. To test a hypothesis that this behavior could be correlated to the orbit of the Earth around the Sun, an analytical model of the temperature fluctuations has been established. The model associates the amplitude, phase and period of the observed temperature data to the eccentricity, the argument of periapsis, and the period of the Earth's orbit around the Sun, respectively. This analysis represented the first attempt to reconstruct the Earth's orbit from satellite temperature measurements. To quantitatively estimate the Earth orbit parameters from in-flight telemetry data, a numerical least-squares estimator has been developed and applied to Delfi-C³ temperature data over the period 2008-2015. Temperature data from the sensor within the FM430 microcontroller of the On-Board Computer (OBC) have been modeled as a function of semi-major axis, eccentricity, and argument of periapsis of the Earth's orbit and, using advanced filtering, it was demonstrated that the achievable accuracy of the estimation leads to surprisingly accurate results of 0.05%, 2% and 2.5%, respectively. This paper also addresses the sensitivity of the results to initial conditions, filtering schemes and estimator settings. Furthermore, we expect that a refined analytical thermal model, where internal dissipations are accounted for in the thermal paths of the internal stack, will allow a comparable accuracy also for other temperature sensors on the satellite. The research provides an exciting demonstration of the opportunities that a close analysis of housekeeping data of small satellites offers for characterizing the internal and external environment of satellites.