Calibration of Empirical Models of Thermospheric Density Using Satellite Laser Ranging Observations to Near-Earth Orbiting Spherical Satellites

The thermosphere causes by far the largest non-gravitational perturbing acceleration of near-Earth orbiting satellites. Especially between 80 km and 1,000 km, the thermospheric density distribution and variations are required to model accurately this acceleration for precise orbit determination (POD), ephemeris computation and re-entry prediction of the Low-Earth Orbiting (LEO) satellites. So far, mostly on-board accelerometers are used to measure the thermospheric density. However, such type of satellite is usually of complex shape and any error or mismodelling in the satellite drag coefficient and satellite effective cross-sectional area will directly propagate into the derived thermospheric density values. At GFZ, an empirical model of the thermospheric mass density denoted as “CH-Therm-2018” has been developed by using 9 years (2001–2009) of CHAMP observations.

A completely different approach for thermospheric density determination is based on using satellite laser ranging (SLR) measurements to LEO satellites equipped with retro-reflectors to determine an accurate satellite orbit. These measurements are sensitive to small perturbations acting on the satellite. In order to minimize the error induced by imprecise satellite macro-models, we use in our investigation SLR observations to satellites with a simple spherical shape and thus, relate estimated scaling factors to the thermospheric density.

In this paper, we use SLR observations to two ANDE-2 satellites – ANDE-Castor and ANDE-Pollux – as well as SpinSat with altitudes between 248 km and 425 km to calibrate the CH-Therm-2018 model, as well as four other empirical models of thermospheric density, namely CIRA86, NRLMSISE00, JB2008 and DTM2013. For our tests, we chose a period from 16 August 2009 to 26 March 2010 of low solar activity and a period from 29 December 2014 to 29 March 2015 of high solar activity. Using data of a few geodetic satellites obtained at the same and different time intervals allows us to investigate the reliability of the scaling factors of the thermospheric densities provided by the models. We have found that CIRA86 and NRLMSISE00 most significantly overestimate the thermospheric density at the period of low solar activity among the models tested. The JB2008 model is the least scaled model and provides reliable values of the thermospheric density for the periods of both low and high solar activity. The GFZ CH-Therm-2018 model, on the contrary, underestimates the thermospheric density at the time interval of low solar activity. Using SLR observations at longer time intervals should allow to investigate temporal evolution of the scaling factors of these models more precisely.