Lunar ephemeris at sub microarcsecond accuracy (LESMA) leads to sub-millimeter positional accuracy of the moon
Authors: Biswas Abhijit , Mani Krishnan R. S. 
Published: September 2022

The most accurate LLR (lunar laser ranging) initiative, named APOLLO (apache point observatory lunar laser-ranging operation) demonstrated millimeter-range positional accuracy in 2009, thus improving LLR by one order-of-magnitude.
Since, LLR is a foundational technique in studying gravity, Murphy (principal investigator of APOLLO) stated in 2009, that with this millimeter-range accuracy, the simulation model has been found to be the limiting-factor in extracting the theoretical science results, and hence, we should:
(1) develop the science case and expand our ability to model LLR for a new regime of high precision, (2) develop the theoretical tools for honing the science case for submillimeter LLR, and (3) explore which model/code is worth putting our efforts into. (4) Since millimeter-quality
data are a recent development, the model effort lags. (5) Finally, we will code-in new physics so that we may simulate sensitivities. In connection with simulation model/code, Murphy stated in 2013, that among the four available LLR simulation models: JPL (jet propulsion
laboratory), CfA (the Harvard-Smithsonian center for astrophysics), LU (leibniz University, Hannover, Germany), and IMCCE (Institut de Mecanique celeste et de calcul des Ephemerides, France), the JPL model currently
produces weighted RMS (root-mean-square) residuals at ∼18 mm, which is about half of the other models; so, clearly a gap exists from millimeter ranging-precision of APOLLO. Hence, the CfA, LU, and IMCCE are engaged, since 2013, in a stepwise comparative streamlining effort to identify
the model-differences, errors, and shortcomings. All the four available LLR simulation models can be classified as GR (general relativity)-astronomers model; they are basically similar. Professor Douglas Currie of the University of Maryland, College Park, NASA Lunar Science Institute, stated
in a Conference presentation, in 2012, that Ground stations, that is, the lunar observatories, have improved by a factor of 200, but the agreement between observations and fitted theory has plateaued at ∼2 cm over the past two decades. However, no substantial progress on improving
the fit has been reported in the published literature, till date. Based on about a quarter-century of experience in doing high-precision numerical simulation of celestial orbits, the authors have developed LESMA (lunar Ephemeris at sub Microarcsecond accuracy)
utilizing the methodology of evolved general relativity (EGR) that has incorporated the following two concepts: (1) Relativistic time for integration and (2) methodology of conservation of magnitude of the angular momentum, MΦ , for Φ-rotation
(in addition to the θ-rotation that leads to the rosetting ellipse) of the orbital plane. Incorporation of the two above-mentioned concepts has led to three orders-of-magnitude accuracy-improvement of the computed (1) precession (compared to JPL's DE405) of Lunar orbit,
as verified using three independent methods and (2) radial position (compared to JPL's DE430/431) of the Moon. LESMA will enable scientists to make efficient use of research-funds from NASA, etc., for production of new science results from APOLLO. LESMA will also be useful for getting
better science results (than Folkner reported {in 2014} submeter accurate Position of the Moon) from the GRAIL (gravity recovery and Interior laboratory) mission (costing 500 million USD), by spending a little more for revisiting the computations, utilizing
LESMA data.