Head of the Laboratory of Ephemeris Astronomy
Pitjeva Elena Vladimirovna Doctor of Science in the field of Physical and Mathematical Sciences |

The main tasks of Laboratory of Ephemeris Astronomy are creation of high-precession ephemerides of the Sun, the Moon, planets and their natural satellites; ephemeris accompaniment of observation programs of Earth satellites, spacecraft and landers; supporting and developing the software for solving the problems of ephemeris and dynamical astronomy.

- Improvement of dynamic models of celestial bodies‘ motion and creation of high-precision ephemerides of the Sun, the Moon, and planets (EPM) and their natural satellites (together with the Astronomical Yearbooks Laboratory); improving parameters of those ephemerides and astronomical constants from radio, laser and optical observations of planets, the Moon, natural and artificial satellites of the major planets. Among the parameters under improvement are, in particular: the masses of satellites and asteroids, planetary rotation parameters, the dynamical oblateness of the Sun and planets, parameters of the relativistic PPN formalism, the secular variations of the gravitational constant and the heliocentric gravitational constant (the solar mass), constraints on dark matter in the Solar System, etc.
- Development of analytical theories of motion and rotation of the Moon and the Earth on the base of the general planetary theory GPT.
- Analysis of impact of planned Russia LLR station on the lunar ephemeris accuracy.
- Ephemeris support of observable programs of Earth satellites, spacecraft and landers at radio antennas «Quasars» of IAA RAS. Analysis and processing obtained measurements for improvement of orbits of observable objects.
- Supporting and developing the software for solving the problems of ephemeris and dynamical astronomy on the basis of the problem-oriented language SLON and the universal program package ERA.

The Laboratory actively collaborates with a number of international organizations: IAU Commissions 4, 7, 8, 15, 16, 19, 20, JPL (Jet Propulsion Laboratory, USA), IMCCE (Institut de Mecanique Celeste et de Calcul des Ephemerides), the Celestial Mechanics sub-faculty of St.-Petersburg State University and takes part in the project of ISLR (International Satellite Laser Ranging Service).

- Construction of numerical ephemerides of the 22 main natural satellites of Mars, Jupiter, Saturn, Uranus, Neptune has been carried out jointly by the Astronomical Yearbooks Laboratory and the Laboratory of Ephemeris Astronomy. Parameters of satellite ephemerides were fit to 70000 astrometrical observations of different types. Dynamical models of satellite motion include the mutual perturbations of the satellites, perturbations from the Sun and the large planets, the gravitation potentials of the central planets, as well as tidal perturbations from Mars to its satellites.

- The semi-analytic theory of the lunar orbital motion has been constructed, and main terms of analytic theory the Earth rotation, including precession and nutation, were determined in the trigonometric form compatible with the general planetary theory GPT, by means of the series in powers of the evolutionary variables with quasi-periodic coefficients without any non-physical secular terms. The trigonometric form of the coordinates is ensured by a special technique of the solution of the lunar equations that enables to separate the short-period and long-period terms. The long-period terms form an autonomous secular system. The solution of the secular system in Laplace-type variables was obtained by using by the normalizing Birkhoff transformation for separating fast and slowly changing variables. The trigonometric solution of the secular system in the semi-analytical form with numerical coefficients was obtained.
- Series of high-precision numerical
**E**phemerides of**P**lanets and the**M**oon – EPM (EPM2004, EPM2008, EPM2011, EPM2013) has been constructed by the simultaneous numerical integration of the equations of motion of planets, the Moon, the Sun, 301 biggest asteroids, 30 trans- neptunian objects (TNO) and the lunar physical libration, with the account of perturbations due to the solar oblateness and the massive rings of small asteroids and TNO. The dynamical models of orbital-rotation motion of the Moon (delayed argument in tidal effects, potential of the Earth is calculated according to recommendations of IERS, interaction between Moon figure and the potential of point mass of Jupiter and Venus) and planets (the two-dimensional ring of small asteroids and the one-dimensional ring of TNO), and the set of constants were renovated; the more accurate and with arbitrary number of bodies integrator with 80-bit floating point, as well as expanded database containing 18700 LLR (1970-2013) and more than 800000 radar and optical planetary observations of different types (1913-2013), including the Russian ranging observations of planets (1962-1995) were used.

Basing on the EPM ephemerides, the following results have been obtained:

- The masses of 21 largest asteroids were determined; estimates of the total mass of the main
asteroid belt

M_{belt}= (12.2±0.2)×10^{-10}M_{Sun}and the total mass of all TNO including Pluto, the 30 largest TNO and the TNO ring of other TNO objects with the 43 au radius

M_{TNO}=592×10^{-10}M_{Sun}were obtained; - The rotation angles for the orientation of the EPM ephemerides into the ICRF2 system were
determined using VLBI data of various spacecraft near planets with background quasars:
ε
_{x}=-0.00±0.04 mas, ε_{y}=0.01±0.04 mas, ε_{z}=0.00±0.03 mas; - The values of relativistic PPN parameters were estimated: β=0.99998±0.00003 and γ=1.00004±0.00006;
- for the first time, it has been found that the heliocentric gravitational constant is decreasing
at the rate:
*GM*= (-6.3±4.3)×10_{Sun}^{-14}(3σ) annually. Using the maximum limits for*M*change, it was obtained that the possible annual change of the gravitational constant_{Sun}*G*must fall within the interval*/G*< +7.8×10^{-14}with a 95% probability; - it was found that the density of dark matter ρ
_{dm}must be less than 1.1×10^{-20}g/cm3at the distance of Saturn‘s orbit, and the mass of dark matter inside Saturn‘s orbit must be less than 7.9×10^{-11}M_{Sun}, even if it is distributed with its density increasing towards the center; - an analysis of the last versions of the lunar part of DE, INPOP and EPM ephemerides shows that differences of geocentric distances for these ephemerides do not exceed 10-15 m that get to differences of the GLONASS satellite less than 1 mm for long time intervals.

Ephemerides of planets and the Moon – EPM (EPM2004, EPM2008, EPM2011, EPM2011/m) along with TT–TDB and ephemerides of Ceres, Pallas, Vesta, Eris, Haumea, Makemake, and Sedna are available from FTP. For the first time lunar libration is available to public for the version EPM2011/m on the same time interval that the entire ephemerides EPM2011/m (1787–2214). The files containing Chebyshev polynomial approximation for access to positions (coordinates and velocities) of objects are provided in IAA‘s binary and ASCII formats, as well as in the unified SPK/PCK formats chosen by the Working Group on Standardizing Access to Ephemerides and File Format Specification as the main format for fundamental ephemerides, and accepted by IAA RAS, NAS JPL (USA), and IMCCE (France).

IV. The software system ERA «Ephemeris Research in Astronomy» that has been powering many products of the IAA during decades has undergone a major rework. The code of ERA-8 has been completely rewritten from Pascal to C (for numerical computations) and Racket (for running SLON programs and managing data). ERA-8 is portable across Windows and Linux, 32-bit and 64-bit. The set of astronomical algorithms was renovated: processing observations, numerical integrations, calculation of partial derivatives of astronomical observables and weighted least squares method for determining the corrections to the parameters, viewer and editor of tables with special support for astronomical data, graph plotter. ERA-8 is portable across Windows/Linux, 32-and 64-bit and provides improved tools for diagnostics, and debugging. Also ERA-8 provides more precise computations, more flexible logic, and more user-friendly interface than past versions. ERA-8 will be freely downloadable to users. Using ERA-8, new results were obtained: improvement of the Pluto orbit from new optical data 1930-2013, and improvement of the Saturn orbit from ranging of Cassini 2004-2014, numerical integration of TT-TDB differences simultaneously with arbitrary number of bodies of solar system. The Russian ephemeris issues since 2016 and preparation ephemerides for the GLONASS space satellite are produced using ERA-8.

V. The demo version of a web site for calculation of planets and satellites ephemerides is provided: http://ephemeris.ipa.nw.ru . Options are provided to select various versions of planetary ephemerides of EPM, DE, and INPOP families. For satellite ephemerides, user can choose between analytical theories and numerical ephemerides designed in IAA RAS. The broad set of options (α and δ in different formats, coordinates in different units. etc.) is allowed. References to respective papers are given in the header of each ephemeris table generated on the site.

1. Krasinsky G.A., Novikov F.A., Scripnichenko V. I. 1987. «Oriented language for ephemeris astronomy and its realization in the system ERA» // Celest. Mech., 45, 219-229.

2. Krasinsky G. A., Pitjeva E.V., Sveshnikov M.L., Chunajeva L.I., 1993. «The motion of major planets from observations 1769-1988 and some astronomical constants».// Celest. Mech., 55, 1-23.

3. Krasinsky G.A., Vasilyev M.V., 1997. «ERA: knowledge base for ephemeris and dynamic astronomy» // IAU Coll. N 165 / Dynamics and Astrometry of Natural and Artificial Celestial Bodies (eds. I.M. Wytrzyszczak, J.H.Lieske, R.A.Feldman), Kluwer Academic Publishers, Dordrecht, 239-244.

4. Krasinsky G. A., 1999 «Tidal effects in the Earth Moon system and the Earth's rotation» // Cel. Mech. Dynam, Astron., v.75, No 1, 39-66.

5. Krasinsky G.A., Pitjeva E.V., Vasilyev M. V., Yagudina E.I., 2002 «Hidden mass in the asteroid belt» // Icarus, 158, 98-105.

6. Pitjeva E. V., 2005 «Relativistic effects and solar oblateness from radar observations of planets and spacecraft». // Astronomy Letters, 31, 5, 340-349, DOI: 10.1134/1.1922533.

7. Pitjeva E.V., 2005. «High-precision ephemerides of planets - EPM and determinations of some astronomical constants». // Solar System Research, 39, 3, 176-186, DOI: 10.1007/s11208-005-0033-2.

8. Krasinsky G. A., 2006 «Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 1: Mathematical model» // Cel. Mech. Dynam, Astron., v.96, No 1, 169-217, DOI: 10.1007/s10569-006-9038-5.

9. Krasinsky G. A., Vasilyev M. V., 2006 «Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 2: Fitting to VLBI data» // Cel. Mech. Dynam, Astron., v.96, No 1, 219-237, DOI: 10.1007/s10569-006-9033-x.

10. Pitjeva E.V., Standish E.M., 2009. «Proposals for the masses of the three largest asteroids, the Moon-Earth mass ratio and the Astronomical Unit». // Celest. Mech. Dynam. Astr., 103, 4, p. 365-372, DOI: 10.1007/s10569-009-9203-8.

11. Pitjeva E.V., 2010 «EPM ephemerides and relativity.» // Proc. IAU Symp. No. 261 / Relativity in fundamental astronomy: dynamics, reference frame, and data analysis // S.Klioner, P.K. Seidelmann, M.Soffel (eds.), Cambridge University Press, 170-178, DOI: 10.1017/S1743921309990342.

12. Brumberg V. A., Ivanova T. V., 2011 «On constructing the general Earth's rotation theory» // Celest. Mech. Dyn. Astr., 109, 4, 385-408.

13. Luzum B., Capitaine N., Fienga A., Folkner W, Fukushima T., Hilton J., Hohenkerk C., Krasinsky G., Petit G, Pitjeva E, Soffel M, Wallace P, 2011. «The IAU 2009 system of astronomical constants: the report of the IAU working group on numerical standards for Fundamental Astronomy». // Celest. Mech. Dyn. Astr., 110, 4, 293-304, DOI: 10.1007/s10569-011-9352-4.

14. Pitjeva E.V., Pitjev N.P., 2012. «Changes in the Sun's mass and gravitational constant estimated using modern observations of planets and spacecraft». // Solar System Research, 46, 1, 78-87, DOI: 10.1134/S0038094612010054.

15. Poroshina A., Kosmodamianskiy G., Zamarashkina M., 2012, «Construction of the numerical motion theories for the main satellites of Mars, Jupiter, Saturn and Uranus in IAA RAS» // IAA RAS Transaction - St. Petersburg: Nauka, 26. 75-87.

16. Pitjev N.P., Pitjeva E.V., 2013. «Constraints on dark matter in the solar system.» // Astronomy Letters, 39, 3, 141-149, DOI: 10.1134/S1063773713020060.)

17. Brumberg V.A. 2013 «Celestial mechanics: past, present, future» // Solar System Research, 47, 5, 347-358, DOI: 10.1134/S0038094613040011.

18. Ivanova T.V., 2013 «Generation of a secular system in the analytical theory for the motion of the moon» // Solar System Research, 47, 5, 359-362, DOI: 10.1134/S0038094613040023.

19. Pitjeva E. V., Pitjev N. P., 2013. «Relativistic effects and dark matter in the Solar system from observations of planets and spacecraft». // Monthly Notices of the Royal Astronomical Society, 432, 4, 3431-3437, DOI: 10.1093/mnras/stt695.

20. Pitjeva E.V., 2013. «Updated IAA RAS planetary ephemerides - EPM2011 and their use in scientific research»// Solar System Research, 47, 5, 386-402, DOI: 10.1134/S0038094613040059.

21. Vasilyev M.V., Yagudina E.I. «Russian lunar ephemeris EPM-ERA 2012» // Solar System Research, 48, 2, 158-165, DOI: 10.1134/S0038094614020075.

22. Poroshina, A. L., 2013 «Numerical theories of motion of Triton and Nereid» // Astronomy Letters, 39, 876-881, DOI: 10.1134/S1063773713110066.

23. Pavlov D.A., Skripnichenko V.I., 2014 « Preliminary results in implementation of a cross-platform version of the ERA software system» // IAA RAS Transaction - St. Petersburg: Nauka, 30. 32-40. In Russian.

24. Pitjeva E. V., Pitjev N. P., 2014. «Development of planetary ephemerides EPM and their applications» // Celest. Mech. & Dyn. Astr., 119, 237-256, DOI 10.1007/s10569-014-9569-0.