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

- Constructing a numerical theory of motion of the major planets and the Moon, improving its parameters by making use of radiometrical, 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 the major planets and of their largest satellites, the masses of the perturbing asteroids, parameters of planet rotations, 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), etc.
- Construction and practical application of numerical ephemerides of natural satellites of the major planets.
- 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).

- Developing the astronomical part of the unified Windows/Linux
version of the program package ERA and supporting the DOS version
available via anonymous FTP.

The program package ERA includes:- Translator from the problem-oriented language SLON in which any tasks of ephemeris and dynamical astronomy may be described.
- Integrated Development Environment (IDE) for performing the SLON programs. The IDE includes en editor for editing the SLON programs, en editor of the ERA-tables which are the structural units of the ERA database, and the online Help service.

- In the ERA system the new version of the integrator has been implemented. The floating point operations use 80 bits of the arithmetical unit (extended precision), while in the past only 64 bits (double precision) were used. This integrator ensures significant better integration accuracy. Round-off errors have dropped two orders of magnitude. Comparison of results of simultaneous integration of the Moon, major and minor planets and trans-neptunian objects forward and backwards over 434 years has shown that the discrepancies of positions of the Moon and planets are kept less than 1 cm. The discrepancies of positions for some bodies were meters and tens of meters for the previous version of the integrator.
- Uniform access facilities in the ERA system have been developed for different versions of native (EPM2004, EPM2008) and foreign (American — DE403/LE403, DE405/LE405, DE406/LE406, DE421, DE423 and French — INPOP06, INPOP08, INPOP10a) numerical ephemeris of the main bodies in the Solar System.
- The new program package containing IAA Planetary and Moon Ephemeris
(EPM2004, EPM2008) along with associated reading and interpolating routines
has been created recently.

Package features are:- support of the polynomial approximation for both binary and ASCII ephemeris files;
- user is allowed to obtain the rectangular coordinates of the Sun, Moon, and nine major planets with respect to different centers (barycentric, geocentric, heliocentric, and planetocentric);
- support of wide-known languages: Fortran, C, Pascal, Java;
- source code available to public via FTP;
- easy to use, accompanied by user manual in English.

Moreover, the Fortran implementation of this package gives a possibility to obtain access to differences between the TT and TDB time scales (for EPM2004 and EPM2008) and ephemeris of the other seven dwarf planets: Ceres, Pallas, Vesta, Eris, Haumea, Makemake, and Sedna, obtained simultaneously with the main EPM2008 ephemeris. - Supporting and supplementing the database of optical and radiometrical
observations of the major planets, their satellites, and
spacecraft (currently, the database includes about 680000
observations of 1913-2010). Supporting the ERA-system database of
observations and orbital elements of asteroids and comets,
updating the LLR database (1970-2011) for measurements of six stations
including high-precise data of Apache Observatory ("APOLLO").

The following updated data are available:

The Russian ranging observations of planets (1962-1995).

Normal places of ranging to Mars Global Surveyor - MGS (1998-2006) and Odyssey (2002-2007) spacecraft , representing observations in a compressed form. - Developing the high-precision planet ephemerides EPM2004 constructed over
the 1880-2020 year interval by the simultaneous numerical integration of the
equations of motion of planets, the Moon, the Sun, 301 biggest asteroids and
the lunar physical libration, with the account of perturbations due to the
solar oblateness and the massive ring of small asteroids. The version of
the EPM2004 theory was adopted as the ephemeris basis of Russian Astronomical
Yearbook since 2006 and is available to outside users via FTP.

The renovation of the planet part of the EPM2008 ephemerides includes the new values of masses of planets and other bodies of the Solar System determined by different authors from spacecraft or satellite data and other improved constants, the updated dynamic model with the 21 largest trans-Neptunian objects (TNO) added in a simultaneous numerical integration, as well as the updated database 1913-2008. For the first time influence of TNO was taken account of while constructing the EPM2008 ephemeris and the total mass of TNO was estimated.

The total mass of the main belt asteroids represented by the sum masses of 301 asteroids and the asteroid ring was determined:M The total mass of all TNO including Pluto, the 21 largest TNO and the TNO ring of other TNO objects with the 43_{belt}= (13 ± 2 )·10^{-10}M_{Sun}(≈ 3 Ceres mass).*au*radius was defined:M For the transition from the time of observations (UTC) to Barycentric Dynamical Time (TDB), time for construction of modern planet ephemerides, it is necessity to have transition between Terrestrial Time (TT) and TDB._{TNO}= 775·10^{-10}M_{Sun}(≈ 164 Ceres mass or 2 lunar mass).

The TT-TDB time differences for EPM2004 and EPM2008 was obtained by numerical integrating.

Ephemerides EPM2008 is available to outside users via FTP.

The current version of the EPM2011 ephemeris has been developed. In comparison with EPM2008 it includes following:- the additional TNO ring in the ecliptic plane with the radius of 43 au;
- the updated value of the Mercury mass obtained recently by data of the tree encounters of the Messenger spacecraft with Mercury;
- the improved reduction of data due to the Jupiter and Saturn relativistic effect of Shapiro;
- the refined values of masses and coordinates of asteroids and TNO;
- values of parameters improved from 680000 position observations 1913-2010.

*GM*and its time change, the restriction on the change of the gravitation constant_{Sun}*G*.

The direct value of the geliocentric gravitation constant was obtained first the change of the geliocentric gravitation constant (the solar mass) was estimated*GM*= 2712440033(1) [Í_{Sun}^{3}/s^{-2}], Taking into account the maximal limits of the possible M*M*= (-5.0±4.1)·10_{Sun}/GM_{Sun}^{-14}per year (3σ)._{Sun}change it was found from the*GM*change obtained that the gravitation constant_{Sun}*/G*falls within the interval

-4.2·10 ^{-14}<*/G*< +7.5·10^{-14}per year with 95% probability. - Improving the model and the parameters of the numerical theory of orbital and rotational motion of the Moon accounts for the effects of elasticity of the lunar body, tidal dissipation in the Moon, and friction coupling between the lunar mantle and its fluid core for processing the current LLR observations. The analysis of 17742 LLR data 1970-2011 was carried out applying the five different numerical theories DE403, DE405, DE421 (JPL.USA), INPOP10a (IMCCE, France) and theory EPM-ERA developed in IAA RAS. The investigation is shown that numerical theories give close results, although the inner accuracy of DE and INPOP10a ephemerides (5.4 cm) (in that case the derivatives from EPM-ERA are used) is slightly better than that of EPM-ERA2011 (6.1 cm).
- The theories of the satellites of Mars (Phobos, Deimos) were constructed by numerical integrating equations of satellites motion using the Everhart method of order 19. The dynamical model takes into account the expansion of the Mars gravity field up to degree and order 12, the mutual perturbations of the satellites, perturbations of the Sun, Jupiter, Saturn, and the Earth-Moon system, moreover, the tidal perturbations from Mars on Phobos. The database of the Mars satellites contains about 20000 absolute and differential astrometric observations 1877— 2007 obtained at Earth-based observatories and at "Mariner-9", "Viking-1,-2","Phobos-2", "Mars Express" spacecraft. The orbital elements of Phobos and Deimos were improved by the weighted least squares method (WLSM) using the astrometric observations, and initial values of the areocentric coordinates and velocities of the satellites were obtained. The comparison of the Phobos and Deimos ephemerides constructed with other numerical ephemerides of Mars satellites (R.Jacobson, JPL and V. Lainey, IMCCE) was shown that the discrepancies of satellite positions were up to 30 km for Phobos and up to 20 km for Deimos. The construction of ephemerides was carried out within the framework of the universal program package ERA (Ephemeris Research in Astronomy).
- Construction of numerical ephemerides of main natural satellites of
the outer planets is carried out jointly Laboratory of Astronomical Yearbooks
and Laboratory of Ephemeris Astronomy. The ephemerides of the Galilean
satellites of Jupiter (Io, Europa, Ganymede, Callisto), Saturn's satellites
(Mimas, Enceladus, Tethys, Dione, Rhea, Titan, Hyperion, Iapetus),
Uranus's satellites (Ariel, Umbriel, Titania, Oberon, Miranda),
and the Neptune's satellites (Triton, Nereid) were constructed on the time
interval 1960-2020 by numerical integration of the equations of motion
for satellites systems of the outer planets using the Everhart method
of order 19. The motion models include the oblateness of the central planets
(J
_{2}, J_{4}for Saturn and Uranus, up to J_{6}for Jupiter), the mutual perturbations of the satellites, perturbations of the Sun, and the large planets. The database contains differential observations, Voyager-2 date for the Uranus satellites, observations of mutual events for some of the Saturn satellites addition to Earth-base astrometric position observations. 5921 observations of the satellites of Jupiter, 29529 ones of the Saturn satellites, 13802 — the Uranus satellites, 2483 — the Neptune satellites (1962-2010) were used. The orbital elements have been improved and other parameters of satellite ephemerides have been determined. In particular, the eccentricities of the orbits of Triton and Nereid were determined:

e_{Triton}= 0.00223±0.00010, e_{Nereid}= 0.75367+0.00008, at that, for the first time, the eccentricity of the Triton orbit was obtained.

The coefficients of the second zonal harmonics of Neptune J_{2}= 0.003711±0.000015 and Uranus J_{2}= 0.001449±0.000001 were estimated.

The comparison of the satellite ephemerides constructed with theories of other authors (theories of V. Lainey for the satellites of Jupiter, theories of TASS1.7 for the satellites of Saturn, and the JPL numerical ephemerides for the satellites of Uranus and Neptune) was carried out. The comparison showed that the results were in agreement on the whole. The significant discrepancies were only for some satellites, that is explained by the lack of accurate observational data and features of their structure and motion. The constructed theories of the Jupiter and Saturn satellites have already been used for the calculation of the satellite ephemerides, which are available at the IAA RAS website. - The consistent secular system of equations for the general theory of
the Earth's rotation and equations for forward motion of planets and the
Moon has been constructed (in the framework of the problem of construction
of a long-term analytic theory of the Earth's rotation).

The three-axial rigid-body Earth's rotation problem is treated in the form compatible with the General Planetary Theory GPT. The equations of the orbital motion of the major planets and the Moon and the equations of the Earth's rotation in Euler parameters are reduced to the autonomous secular system describing the evolution of the planetary and lunar orbits (independent of the Earth's rotation) and the evolution of the Earth's rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth's rotation is presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients without any non-physical secular terms. The solution of the secular system was obtained by the method of the variation of the arbitrary constants within the linear theory with respect to small parameters depending on the dynamical flattening. - The analytical Moon's theory is treated in the trigonometric form compatible with the general planetary theory GPT. The Moon is considered to be an additional planet in the field of eight major planets. All the analytical calculations are performed by the echeloned Poisson series processor EPSP.

The results are following:- The intermediary was constructed up to 14th order relative to small parameters depending on the masses, mean motions and the semi-major axes of the principal planets and the Moon.
- The indirect planetary perturbations were obtained within the frames of the main problem. They are expressed in the classical theories of the Moon by the secular terms.
- The secular system was constructed in the analytical form to find the direct and indirect planetary perturbations within the frames of the general problem (8 planets + the Moon).