Lunar Reference Systems

Led by:  Prof. Dr.-Ing. habil. Jürgen Müller
Team:  Dr.-Ing Franz Hofmann
Year:  2014
Funding:  DFG - FOR 1503
Duration:  2014-2019
Is Finished:  yes

Partner and Goals of the project

The project PN3  "Lunar Reference Systems" is a part of the DFG Research Unit FOR1503 "Space-Time Reference Systems for Monitoring Global Change and for Precise Navigation in Space". With the Institute of Geodesy and Geoinformation of the Universität Bonn and the Department for Geodesy and Geoinformation Science of the TU Berlin, two further institutions are involved in this project. 

The goal of the project is to refine the realization of lunar reference systems with an accuracy meeting all requirements of modern geodesy, astronomy and future exploration. Furthermore, lunar reference systems are an indispensable element in the combination of terrestrial and terrestrial reference systems. These are a necessary basis for the further exploration of the Moon and for the exploration of space.   

Sub-project LLR

The LLR sub-project of PN3 is carried out at the Institute of Geodesy at Leibniz Universität Hannover, where the LLR analysis software is further enhanced. In the ephemeris computation, the gravitational effects from the Sun and the Planets on the Moon as an extended body, the gravitational interaction between Earth and Moon, the secular rates of the Earth's zonal potential coefficients and the effect of the solid Earth tides on the lunar ephemeris were investigated and updated. The computation of the lunar rotation was changed from homogeneous body model to a two-layer model with solid mantle and fluid core. The effect of the tidal deformation of the lunar body is now included in the ephemeris computation (lunar rotation and translation) as well as in the computation of the reflector coordinates. To study the benefit of new retroreflectors and measurement technologies like laser transponder, an extensive simulation tool for LLR data was developed.

The refined modeling allows a more accurate determination of various parameters in the Earth-Moon system. For the project partners in Bonn and Berlin a precise lunar ephemeris (position, velocity and orientation angles) as well as precise coordinates of the retroreflectors are availabe.These data is used as input data for the PN3 project partner and can serve as basis for an accurate Lunar Reconnaissance Orbiter (LRO) orbit determination and for registration of LRO images. Also the determination of relativistic parameters benefits from the better modeling.

Selected results

Post-fit residuals

The models in the LLR-analysis were significantly improved and the post-fit residuals after the least squares adjustment were reduced for the whole data set. In comparison to the former model, the annual one-way wrms up to 1984 is reduced by approximately 30 % and reaches values between 15 cm and 20 cm. From 1984 to 1987 the wrms is reduced by about 50 % to a value of 5 cm. Between 1993 and 2005 the wrms reaches values from 2.5 cm to 4 cm and from the beginning of the APOLLO-measurements in 2006 the annular wrms is around 2 cm. This is an improvement of about 30 % compared to the former modelling.

Benefit of a new type of corner cubes

In case of the Apollo 11, 14 and 15 mission, each retroreflector panel consists of 100 or 300 small Cube Corner Reflectors (CCRs). Every panel follows the lunar motion, where the librational movement causes a tilt of the panel w.r.t. the Earth. The angular off set becomes 8 degrees in longitude and 7 degrees in latitude and leads to a temporal spread of the returning laser pulse due to the di fferent distance of the single CCRs within the panel to the Earth. Nowadays, this becomes one of the limiting accuracy factors of LLR measurements.
To overcome this, the Lunar Laser Ranging Retroreflector Array for the 21st Century (LLRRA-21) program (Douglas Currie, University of Maryland, College Park in collaboration with INFN-LNF in Frascati, Italy) has developed a large single CCR. The advantage of this kind of CCR is the absence of reflection ambiguities which allows the use of much shorter laser pulses to obtain a much more accurate timing of the received signal. This will improve the accuracy of LLR measurements down to the mm-level of accuracy and improve the science by one to two orders of magnitude.

To show the eff ect of additional lunar reflectors of the LLRRA-21 type, we ran simulations on the basis of our last LLR solution. They include all real LLR data up to the end of 2013 and further 27 years of simulated LLR data up to the end of 2030. Beside the currently operable LLR stations we simulated future observations from Wettzell (Germany) and Hartebeesthoek (South Africa).

On the lunar side, we started the simulated data with the existing five reflectors and added three possible missions which are able to carry a LLRRA21 in the next future. We select possible landing sites for the missions from the Astrobotics team (AS), the Moon Express team (ME) at two different sites in the northern pole region and the SpaceIL team (IL). The number of annual normal points was fixed to the mean level of observations within the last years, about 400 normal points per year. We simulated four different scenarios:

  1. case: just with existing reflectors
  2. case: all three new CCRs were added, IL just operable in lunar night
  3. case: all added CCRs operable in lunar day and night
  4. case: like case 2, ME positioned in libration zone near lunar north pole

For the case of ongoing measurements to the five existing CCRs with an accuracy of some mm, the simulations show an increasing accuracy of the estimated parameters of about one order of magnitude over the next 25 years. Even a relatively small number of additional precise measurements will have a positive influence on the resulting parameter accuracies. A further strong enhancement can be reached by the new type of single-prism CCRs. With the possibility to push the measurement accuracy to the 1 mm level, and under the assumption of a mm-accurate analysis, they will push the accuracy of the resulting parameters by a further factor of 2-3. With the new reflectors, the accuracy level of further 25 years of LLR to 5 CCRs could be reached in a much shorter time, approx. less than 10 years.

Relativistic parameters

One of the major application of LLR is to test elements or predictions of Einstein’s theory of gravity. LLR analysis allows for constraining gravitational physics parameters related to the strong equivalence principle, Yukawa-like perturbations, preferred-frame effects, or the time variability of the gravitational constant. No violation of general relativity has been found so far. The following table gives a summary of the latest results of relativistic parameters.

ParameterIfE resultsvalue in GR
Variation of gravitational constant G´/G(7.1±7.6)x10-14 yr-10 yr-1
Equivalence principle Δ(mg/mi)EarthMoon(-3.0±5.0)x10-140
Equivalence principle, Nordtvedt parameter η(-0.2±1.1)x10-40
Yukawa term αYuk(-3.7±4.5)x10-120
Additional geodetic precession hGP(-5.6±8.5)x10-40
PPN β-1(-8.7±9.0)x10-50
PPN β-1 from η(-4.5±5.6)x10-50
PPN α1(-1.1±1.5)x10-50
PPN α2(-6.0±9.0)x10-60