Modeling and Analysis of the APOLLO Lunar Laser Ranging Data

TL;DR

This paper discusses the modeling and analysis of high-precision lunar laser ranging data from APOLLO, addressing challenges in extracting scientific results due to complex effects and high condition numbers in the analysis model.

Contribution

It introduces methods to improve the analysis of APOLLO lunar laser ranging data, accounting for complex effects and addressing the high condition number problem.

Findings

APOLLO achieves ~2mm measurement uncertainty per session.

Traditional models face high condition numbers, complicating analysis.

Enhanced modeling approaches are necessary for scientific insights.

Abstract

The Earth-Moon-Sun system has traditionally provided the best laboratory for testing the strong equivalence principle. For a decade, the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has been producing the world's best lunar laser ranging data. At present, a single observing session of about an hour yields a distance measurement with uncertainty of about 2~mm, an order of magnitude advance over the best pre-APOLLO lunar laser ranging data. However, these superb data have not yet yielded scientific results commensurate with their accuracy, number, and temporal distribution. There are two reasons for this. First, even in the relatively clean environment of the Earth-Moon system, a large number of effects modify the measured distance importantly and thus need to be included in the analysis model. The second reason is more complicated. The traditional problem with the analysis of solar-system metric data is that the physical model must be truncated to avoid extra parameters that would increase the condition number of the estimator. Even in a typical APOLLO analysis that does not include parameters of gravity physics, the condition number is very high: $8 \times 10^{10}$.