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EPM-ERA2012 Lunar Ephemeris and selenodynamical parameters from LLR data(1970-2012)

M.V. Vasilyev, E.I.Yagudina

IAA RAS, St-Petersburg, Russia


Reflector at the Moon

The reflector 's positions at the Moon surface

3.5 m telescope at Apache station


INTRODUCTION
MODERN EPHEMERIDES: 1. JPL, USA: DE403, DE405, DE421;... 2. IMCCE, Observatoire de Paris INPOP10-Integrateur Numerique Planetaire de l"Observatoire de Paris"); 3. IAA RAS, Russia-EPM-ERA2012

The present analysis of (17580) LLR observations, (time interval 1970, March - 2012, February)


Model

( brief description).

The dynamical model EPM-ERA has been developed by G.A. Krasinsky. The model is constructed by simultaneous numerical integration of the equations of orbital and rotational motion of the Moon, major planets, asteroids; The potential of the Moon is calculated up to 5-th order of harmonics; The potential of the Earth includes the 4-th order harmonics ; The tidal perturbation in the lunar orbital motion (due to tidal dissipation on the Earth's body) as well as in rotational Lunar motion (due to tidal dissipation on the Moon's body) is computed by a model with a constant lag. Method of integration : Everhart's method of the 23 order with the constant step of integration. Partials of lunar ranging respective to dynamical parameters of the orbital and rotational model of the Moon are mostly computed by integrating variational equations; in some cases, they were obtained by integration of a rigorous system of equations with slightly varied values of the parameter under study (for example, k2 Moon). During the fitting process LLR observations are reduced with a model according to IERS Conventions. All the calculations were made by ERA system, IAA RAS, Russia .


Station McDonald MLRS1 MLRS2 HALEAKALA CERGA APACHE Total

Time interval 1970 March -1985 June 1985 January- 1988 January 1988 August-2012 February 1988 August-1990 August 1985 Jan - 2012 February 2006 July - 2010 November 1970 March -2012 February

NumberLLR observations 3440 275 3114 694 9113 944 17580

Table1:

Distribution of LLR observations


Reflectors: 1. 2. 3. 4. 5.

number of ranging: Apollo-11 1788; Apollo-14 1769; Apollo-15 13492; Lunochod2 504; Lunokhod1 29.

Observations obtained using FTP servers: ccdisa.gcfc.nasa.gov/pub /slr, Oca.eu/gemini/donnes/las_lune, (Partly from private correspondence , thank to Dominique Feraudy)


N
1-6 7-12

Parameters estimated Lunar orbital state vector for the epoch JD 2446000.5 Euler's angles and their time derivatives for the same epoch

13-18, 22-24 Coordinates of reflectors A11, A14, L2, L1 45-47 20 25-42 44 48-51 55 56-58 64-65 X coordinate for reflector Apollo 15 (A15) Coordinates of 6 observational stations Lag of the Earth's body tides Secular trends in siderial angles of the Earth and Moon Lag of the Moon's body tides
33

52-54, 59-63 Harmonics of lunar potential from C20 to S Lunar Love numbers k2, h2, l2

Secular trends of the corrections to the parameters of Earth's equator

,


wrms (m) O- C postfit residuals 2 7 .7 1 3 .3 1 8 .8 7 .5 4 .6 11.3 6 .4 6 .5 4 .4
5.9

Number of Observational observations stations

Interval of observations

2 7 .9 1 3 .0 1 8 .7 7 .4 4 .5 11.3 6 .3 6 .4 4 .4 5 .8

3143 253 1135 2969 4870 538 1002 2203 944 16658

McDonald MLRS1 CERGA CERGA CERGA Haleakala MLRS2 MLRS2 Apache (All stations)

19700415.0 - 19850630.0 19850301.0 - 19880127.1 19840407.2- 19860612.2 19871012.2-19941213.2 19950107.2-20120202.2 19841113.1 - 19900830.1 19880229.0 ­ 19951228.0 19950113.0 -20120201.0 20060407.1 - 20101030.1 19700415.0 -20120202.2

EPM-ERA2012 ephemeris, statistics of residuals


EPM-ERA2012 ephemeris, residuals (laser ranging )


Residuals for DE and INPOP10 ephemerides compared with EPM-ERA2011
Ephemeris DE403 DE405 DE421 INPOP10
EPM-ERA 2012
Residuals Wrms (cm) Number of observations Number of deleted observations

5 5 5 5

.1 .3 .2 .1

1 1 1 1

7 7 7 7

1 1 1 1

3 3 3 3

4 4 4 4

5 5 5 5

7 4 0 7

9 3 0 8

5.8

17580

890


EPM-ERA2010

EPM-RA2012

Interval of 19700315.0observations 20100404.1 Number of observations Wmrs (cm) Postfit res.

19700315.020120202.0 17580

17134

6.8

5.8


INPOP10 DE403
INPOP10

DE405

EPM-ERA 2012 Residuals (laser ranging) for DE, INPOP10 EPM-ERA 2012ephemerides

DE421


Conclusion
· The investigation has shown that the inner accuracy of DE ephemerides (5.1-5.3cm) and INPOP10 French one (5.1 cm) (in the case the derivatives from EPM-ERA are used ) is slightly better than that of EPM-ERA2012 (5.8 cm). · The re-weighting LLR observations was a main factor for result improvement. · It is shown that the inner accuracy of EPM-ERA model does not practically depend on the use of either 19 or 15 significant decimal digits in floating point calculations. · The processing of LLR observations of Haleakala station was modified. · The improvement of dynamical model (tidal perturbations in Moon's rotation) is still required.


Future work:

· The model of tidal perturbations in Moon's rotation will be adjusted and tested. · The observations of Matera station will be added in common solution. · To put at site IAA RAS the value of selenodynamical parameters from EPM-ERA 2012 version.

· Thank you very much for your attention!


· 1)Krasimsky edge base for Ephemeris and dynamical astronomy // Proceedings of IAU Colloquium 165, 1996, Poznan, Poland, P.239-244. · 2)Aleshkina E.Yu., Krasinsky G.A., Vasiliev M.V . Analysis of LLR data by the program ERA // Proceedings of IAU Colloquium 165, 1996, Poznan, Poland, P.228-232. · 3)rasinsky G. . Selenodynamical parameters from analysis of LLR observations of 1970-2001.// Comminications of the IAA RAS, 2002, N 148. P 1-27. · 4)Yagudina E.I. Numerical Lunar Theory EPM2008 from Analysis of LLR data.// Book of abstracts Journees2008, Dresden, 22-24 September 2008. P 11. · Referenses at Krasinsky' papers on orbital and rotational model of the Moon. · "Tidal Effects in the Earth-Moon System and Earth's Rotation." , Celestial Mechanics 75/1, 39-66,1999. · "Dynamical history of the Earth-Moon system. " Celestial mechanics 84, 27-55,2002

REFlERE.NRAEknowl S: S G.A., Vasi iev M.V E