Tanner Campbell, University of Arizona; Adam Battle, University of Arizona; Bill Gray, University of Arizona; Neil Pearson, University of Arizona; Grace Halferty, University of Arizona; Roberto Furfaro, University of Arizona; Vishnu Reddy, University of Arizona;
Keywords: Characterization, Machine Learning, Cislunar SSA
Abstract:
On March 4th, 2022, the third stage of the first-ever Long March 3C/E rocket, used to launch the Change 5-T1 spacecraft, crashed into the Moon after being in orbit for seven and a half years. During the month leading up to the lunar impact, the Change 5-T1 rocket bodys solar elongation was too low for it to be observed with ground-based optical telescopes. The only chance for observations needed for characterization and to constrain the impact location had to be collected during the preceding two Earth close approaches (Jan. 20th and Feb. 8th, 2022). In this paper, we present analysis of observations taken of the Change 5-T1 rocket body on two nights corresponding with the two sequential close Earth fly-bys (32,600 km and 46,900 km, respectively) leading up to the lunar impact. Using a four parameter Fourier fit and least squares minimization, we find a period of 185.221 ± 6.540 s at a 1? confidence level in the light curve of the Change 5-T1 rocket body just before the first close Earth fly-by on Jan. 20th and a period of 177.754 ± 0.779 s at a 1? confidence level just before the second close Earth fly-by on Feb. 8th. Using Markov Chain Monte Carlo sampling and predictive light curve simulation based on an anisotropic Phong reflection model, we estimate both physical and dynamical properties of the Change 5-T1 rocket body at the start of an observation epoch. Leveraging Bayes theorem in this way, we can recover the 95% Highest Posterior Density (HPD) region and Maximum A Posteriori (MAP) estimates of the nine estimated parameters: primary body axis orientation (2), angular velocity vector (3), diffusive/specular reflectivity parameters (2), surface anisotropic/roughness parameters (2).
The MCMC light curve inversion is accomplished by specifying some initial distributions for each estimated parameter based on any a priori knowledge. If any a priori knowledge is lacking, then a uniform distribution over an appropriate interval is chosen and, in this case, we use a partially uninformative prior in the form of truncated uniform distributions that are in keeping with plausible ranges for each estimated parameter. By sampling from these parameter distributions many times and using the predictive model to evaluate goodness of fit with the observed data, a posterior estimate of each of the true parameter distributions can be formed. This posterior estimate is used to inform on future samplings to bias the sampling towards areas of the parameter space with a higher likelihood. Scaled randomness is added to each iteration of the parameter sampling, so a high number of iterations is required (tens to hundreds of thousands) to sufficiently sample the parameter space. The end results are posterior estimates of the likelihood of each chosen parameter conditioned by the observed data and any a priori information.
Date of Conference: September 19-22, 2023
Track: Satellite Characterization