Model of Solar Radiation Pressure and Thermal Re-radiation

Abstract

The non-gravitational force solar radiation pressure is the main source of error in the precise orbit determination of GNSS satellites. All deficiencies in the modeling of solar radiation pressure map into estimated terrestrial reference frame parameters as well as into derived gravity field coefficients and altimetry results when LEO orbits are determined using GPS. Here we introduce a new approach to geometrically map radial orbit perturbations of GNSS satellites, in particular due to solar radiation pressure along the orbit, using high-performing clocks on board the first Galileo satellites. We have seen in Chap. 18 that only a linear model (time offset and time drift) need be removed from the estimated Galileo clock parameters and the remaining clock residuals will map all radial orbit perturbations along the orbit. Agreement between SLR residuals and clock residuals is at the cm-level RMS for an orbit arc of 24 h. Looking at the clock parameters determined along one orbit revolution over a period of one year, we show that the so-called SLR bias in Galileo and GPS orbits can be represented by a translation of the determined orbit in the orbital plane away from the Sun. This orbit translation is due to thermal re-radiation and does not account for the Sun’s elevation above the orbital plane in the parameterization of the estimated solar radiation pressure parameters. SLR ranging to GNSS satellites takes place typically at night, e.g., between 6 p.m. and 6 a.m. local time, when the Sun is in opposition to the satellite. Therefore, SLR mostly observes that part of the GNSS orbit with a radial orbit error that is mapped as an artificial bias into the SLR observables. The Galileo clocks clearly show an orbit translation for all Sun elevations: the radial orbit error is negative when the Sun is in conjunction (orbit noon) and positive when the Sun is in opposition (orbit midnight). The magnitude of this SLR bias depends on the accuracy of the determined orbit and should rather be called “GNSS orbit bias” instead of “SLR bias”. All LEO satellites, such as CHAMP, GRACE and JASON-1/2, need an adjustment of the radial antenna phase center offset. When LEO satellite orbits are estimated using GPS, this GPS orbit bias is mapped into the antenna phase center. GNSS orbit translation away from the Sun in the orbital plane not only propagate into the estimated LEO orbits, but also into derived gravity field and altimetry products. The mapping of orbit perturbations using an onboard GNSS clock is a new technique to monitor orbit perturbations along the orbit and was successfully applied in the modeling of solar radiation pressure. We show that the CODE solar radiation pressure parameterization lacks the dependency on the Sun’s elevation above the orbital plane, i.e., the elongation angle (rotation of solar arrays), especially at low Sun elevations (eclipses). Sun elongation angle is used in the so-called T30 model (ROCK) that includes thermal re-radiation. A preliminary version of a solar radiation pressure model for the first five Galileo and the GPS-36 satellite is based on the orbit/clock solution of 2 × 180 days of the MGEX Campaign. We show that, in addition, Galileo clocks map the Yarkowsky effect along the orbit, i.e., a small time lag between the Sun’s illumination of the satellite and its thermal re-radiation. We present the first geometrical mapping of the anisotropic thermal emission of absorbed sunlight of an illuminated satellite.