Estimation of the Success Probability for Relay Satellite Laser Ranging Around E-M L₂

To simulate the positional relationship between the Moon and the relay satellite ‘magpie bridge’ in a halo orbit around L₂ of the Earth-Moon system, then to evaluate the laser ranging success probability, in this paper we make a computation on the halo orbit with a request of about 14 days in its period, and establish a model given the tremble of the telescope, of the atmosphere and the transverse deviation from the predicted orbit. A numerical halo orbit is given with the period of 14.78 days, the amplitude is 12493km in X (along the Earth-moon connection direction), 34596km in Y, and 11916km in Z (orthogonal to the Earth-moon orbital plane). The minimum amplitude of the calculated halo orbit goes far beyond the Moon-sheltered critical amplitude which is generally 4000km, thus no shade from the Moon exists on the relay satellite. Based on the model of laser ranging success probability established previously, we make an analysis on the success probability according to the laser ranging system at KUNL station (International ID:7820), and the results indicate that the laser ranging success probability rapidly drops down with the increase of the orbit transverse standard deviation. For the average distance from the station to the relay satellite, the detector produces about 0.151 photoelectrons within a single pulse and the corresponding success probability is 14.07% when there is no deviation from the predicted orbit; the number of photoelectrons drops down to 0.035 and the corresponding success probability down to 3.46% when the relay satellite transversely deviates 2km from the predicted orbit. Comparing between the nearest distance and the furthermost distance, with no deviation, the number of photoelectrons declines to 0.139 from 0.174 and the corresponding success probability shrinks to 13.02% from 16.01%. The results provide a reference for the realization of the relay satellite laser ranging with 1.2m telescope at Yunnan Observatory in the following days.