An Analysis of Accuracies of TLE-Based Solar Phase Angles at Satellites

Photometry is one of the most important techniques to analyze physical characteristics of space objects. After-event analyses of photometric light curves of space objects and construction of their physical models all involve the solar phase angle, a parameter defined as the angle between the light incident onto an observed object from the sun and the light reflected from the object. Currently, the position of a space object is usually calculated with a Two-Line-Element (TLE) set. A position so calculated contains a systematic error increasing with the time elapsed from the TLE epoch. This raises the need to analyze the accuracy of the solar phase angle calculated based on the TLE. In this paper, we present comparison for the solar phase angles in the entire year of 2012 calculated using the TLE. The solar phase angles are those of the LAGEOS1, AJISAI, and STELLA, which are SLR (Satellite Laser Ranging) satellites of three representative apogee heights, respectively. For the three satellites we use the highly precise global SLR data as the standard descriptions of the orbits. Our results show that for the two satellites of relatively high orbits, the LAGEOS1 and AJISAI, their B^* values (characterizing apparent resistance forces) were near constant, and their solar phase angle deviations remained on the level of arcminutes or below throughout the year; for the low-orbit STELLA its solar phase angle deviations were much larger, which can be attributed to influences of atmospheric changes. For the STELLA the deviations were particularly severe when B^* values were large and changed rapidly. The deviations for the STELLA also increased dramatically with time from the TLE epoch. The worst-level deviations were about 13' after one day (from the epoch), 50' after 3 days, and 251' after 7 days, which are beyond currently acceptable precision limits. These results suggest that TLE sets within 1 day be used whenever possible in calculating solar phase angles, especially when B^* values are large and in rapid change. We also present an approach to handle UTC leap seconds. The approach is to increase or decrease the time from the TLE epoch by 1 second if the time passes a leap-second moment, with the timestamp-calculation results consequently modified.