Modelling LARES temperature distribution and thermal drag II: Numerical computation of current-epoch thermal forces

Abstract

The LARES satellite is a laser-ranged space experiment to contribute to geophysics observation, and to measure the general relativistic Lense-Thirring effect. LARES consists of a solid tungsten alloy sphere, into which 92 fused-silica Cube Corner Reflectors (CCRs) are set in colatitude circles (“rows”). During its first four months in orbit it was observed to undergo an anomalous along-track orbital acceleration of approximately $ -0.4$ pm/s2 $(pm: = picometer)$ . The first paper in this series (Eur. Phys. J. Plus 130, 206 (2015) - Paper I) computed the thermally induced along-track “thermal drag” on the LARES satellite during the first 126 days after launch. The results there suggest that the IR absorbance $ \alpha$ and emissivity $ \epsilon$ of the CCRs equal 0.60, a possible value for silica with slight surface contamination subjected to the space environment. Paper I computed an average thermal drag acceleration of $ -0.36$ pm/s2 for a 120-day period starting with the 7th day after launch. The heating and the resultant along-track acceleration depend on the plane of the orbit, the sun position, and in particular on the occurrence of eclipses, all of which are functions of time. Thus we compute the thermal drag for specific days. The satellite is heated from two sources: sunlight and Earth’s infrared (IR) radiation. Paper I worked in the fast-spin regime, where CCRs with the same colatitude can be taken to have the same temperature. Further, since all temperature variations (temporal or spatial) were small in this regime, Paper I linearized the Stefan-Boltzmann law and performed a Fourier series analysis. However, the spin rate of the satellite is expected currently ( $ \approx$ day 1500) to be slow, of order $ \approx 5$ /orbit, so the “fast-spin equal-temperatures in a row” assumption is suspect. In this paper, which considers epochs up to 1580 days after launch, we do not linearize and we use direct numerical integration instead of Fourier methods. In addition to the along-track drag, this code produces all components of the thermally induced force on the satellite as a function of time throughout the orbit. We find that in the slow spin regime, although there are substantial excursions from the Fourier results, the Fourier results do provide good average values for the temperature of the CCRs (constant temperature in rows from the Fourier method), and for the daily along-track average drag. However, we also find that the relatively small average along-track drag (which swings between $ -0.7$ pm/s2 and $ -0.25$ pm/s2 and averages $ -0.50$ pm/s2 over days 1460-1580) arises from instantaneous accelerations that have excursions that are about an order of magnitude larger than the resulting orbit-averaged drag. Note that neither the first paper nor this one addresses the additional particle drag on the satellite.