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arXiv:1308.6416v1 [astro-ph.EP] 29 Aug 2013

ISSN 0038-0946, Solar System Research, 2013, Vol. 47, No. 5, pp. 386-402. c Pleiades

Publishing, Inc., 2013. Original Russian Text c E.V. Pitjeva, 2013, published in Astronomicheskii

Vestnik, 2013, Vol. 47, No. 5, pp. 419-435

UDK 521.172:523.2

Updated IAA RAS Planetary Ephemerides-EPM2011

and Their Use in Scientific Research

c ?2013 г. E. V. Pitjeva

Institute of Applied Astronomy, Russian Academy of Sciences,

nab. Kutuzova 10, St. Petersburg, 191187 Russia

Received December 20, 2012

Abstract -The EPM (Ephemerides of Planets and the Moon) numerical ephemerides

were first created in the 1970s in support of Russian space flight missions and since then

have been constantly improved at IAA RAS. In the following work, the latest version of

the planetary part of the EPM2011 numerical ephemerides is presented. The EPM2011

ephemerides are computed using an updated dynamical model, new values of the parameters,

and an extended observation database that contains about 680 000 positional measurements

of various types obtained from 1913 to 2011. The dynamical model takes into account mutual

perturbations of the major planets, the Sun, the Moon, 301 massive asteroids, and 21 of the

largest trans-Neptunian objects (TNOs), as well as perturbations from the other main-belt

asteroids and other TNOs. The EPM ephemerides are computed by numerical integration

of the equations of motion of celestial bodies in the parameterized post-Newtonian n-body

metric in the BCRS coordinate system for the TDB time scale over a 400-year interval. The

ephemerides were oriented to the ICRF system using 213 VLBI observations (taken from

1989 to 2010) of spacecraft near planets with background quasars, the coordinates of which

are given in the ICRF system. The accuracy of the constructed ephemerides was verified by

comparison with observations and JPL independent ephemerides DE424.

The EPM ephemerides are used in astronavigation (they form the basis of the

Astronomical Yearbook and are planned to be utilized in GLONASS and LUNA-RESURS

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programs) and various research, including the estimation of the solar oblateness, the

parameters of the rotation of Mars, and the total mass of the asteroid main belt and TNOs,

as well as the verification of general relativity, the secular variations of the Sun’s mass and

the gravitational constant, and the limits on the dark matter density in the Solar System.

The EPM ephemerides, together with the corresponding time differences TT - TDB and

the coordinates of seven additional objects (Ceres, Pallas, Vesta, Eris, Haumea, Makemake,

and Sedna), are available at ftp://quasar.ipa.nw.ru/incoming/EPM.

DOI: 10.1134/S0038094613040059

HISTORICAL INTRODUCTION

Until the coming of the space age in the 1960s, the classic analytical theories of planetary

motion developed by Le Verrier, Hill, Newcomb, and Clemens, which were fully consistent

with optical observations in terms of accuracy, were being constantly refined in accordance

with the development of astronomical practice.

However, the launch of the first satellites exposed the demand for a more accurate

calculation of the coordinates and the speeds of planets. Deep-space experiments and

the introduction of new observational techniques (lunar and planetary ranging, trajectory

measurements, etc.) required the development of planetary ephemerides that would be far

more accurate than the classical ones. On the other hand, it was the new observational

facilities that made it possible to develop ephemerides of the new generation.

The errors of the current best ranging observations do not exceed several meters, which

makes it necessary to compute the ranging correctly up to the 12th significant digit. An

appropriate model of the motion of celestial bodies is required to achieve such high precision.

The construction of a proper model that would take into account all the significant factors

is a serious problem, and the current most feasible way to solve it is to perform numerical

integration of the equations of motion of the planets and the Moon on a computer.

In the late 1960s several research groups in the United States and Russia developed

numerical theories to support space flights. American groups worked at the California

Institute of Technology and the Massachusetts Institute of Technology. Russian high-

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precision numerical ephemerides of planets (Akim et al., 1986) were created as a result of

the research carried out at the Institute of Applied Mathematics, the Institute of Radio

Engineering and Electronics and the Space Flight Control Center, and the Institute of

Theoretical Astronomy, where N. I. Glebova, G. I. Eroshkin, and a group led by G. A.

Krasinsky developed theories independently. This work was continued at the Institute of

Applied Astronomy (IAA), where a series of EPM (Ephemerides of Planets and the Moon)

ephemerides was produced. In order to provide technological support for such research, a

large group of developers working at the IAA under the direction of G. A. Krasinsky created

a unique software system called ERA (Ephemeris Research in Astronomy) that uses a high-

level language targeted at astronomical and geodynamical applications. This ensures the

flexibility of the system, which is being constantly upgraded, and considerably simplifies the

development of various applications. The two dynamical models of planetary motion that are

being developed in the series of DE (Development Ephemeris, JPL) (Standish, 1998; 2004;

Folkner, 2010; Konopliv et al., 2011) and EPM (Krasinsky et al., 1993; Pitjeva, 2001; 2005a;

2012) ephemerides are currently the most complete, have the same precision, and are faithful

to modern radio observations. For the reasons of technological independence, researchers at

the Institut de Mecanique Celeste et de Calcul des Ephemerides (IMCCE) have started

constructing their own numerical planetary ephemerides INPOP (Fienga et al., 2008; 2011)

in 2006. The history of the creation of planetary ephemerides, the EPM2004 ephemeris and

the differences between the DE and EPM ephemerides are discussed in greater detail in

a paper by Pitjeva (2005a). In the present work the planetary part of the latest, updated

version of the EPM ephemerides (EPM2011) and its use in various scientific investigations

are discussed.

EPM DYNAMICAL MODEL OF PLANETARY MOTION

Construction of high-precision planetary ephemerides that are needed for space

experiments, and would guarantee the meter-level accuracy of modern observations, requires

creating a proper mathematical and dynamical model of the motion of planets, which takes

into account all the significant perturbing factors on the basis of general relativity (GR).

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The motion of the barycenter of the Earth-Moon system is appreciably perturbed by

the Moon itself. The Moon’s orbit is subject to perturbations from the asphericity of the

gravitational potentials of the Earth and the Moon, which makes it necessary to characterize

the positions of the equators of the Earth and the Moon with respect to an inertial coordinate

system (i.e., take into account the impact of precession, nutation, and physical libration) with

sufficient accuracy. The resonant behavior of the coupling between orbital and rotational

motions of the Moon makes it essential to reconcile various theories in a unified dynamical

model. As a consequence, modern numerical theories are built by simultaneous numerical

integration of the equations of motion of all planets and the Moon’s physical libration, while

also taking into account the perturbations on the figure of the Earth due to the Moon

and the Sun and the perturbations on the figure of the Moon due to the Earth and the Sun.

Construction of the theory of the Moon’s orbital and rotational motions and its improvement

using lunar laser ranging (LLR) observations are the most difficult tasks in creating modern

ephemerides of planets and the Moon. This work was carried out at the IAA under the

direction of G. A. Krasinsky and is described in a series of papers (Aleshkina et al., 1997;

Krasinsky, 2002; Yagudina et al., 2012). The lunar theory takes into account the effects

associated with elasticity, tidal dissipation of energy, and the frictional interaction between

the Moon’s liquid core and its mantle, and cites selenodynamical parameters obtained

through the analysis of LLR observations made from 1970 to 2010.

The influence of solar oblateness on planetary motion was established theoretically a

long time ago, and some researchers even tried to attribute to it the anomalous motion of

Mercury’s perihelion which was discovered by Le Verrier in the late 19th century. The solar

oblateness causes secular variations of the orbital elements of planets, with the exception

of semimajor axes and eccentricities, and has to be taken into account when constructing

the model of planetary motion. The problem lies in the fact that the solar oblateness is

determined indirectly from some complex astrophysical measurements that are subject to

various systematic errors caused by equipment imperfection and the solar atmosphere and

activity. The use of modern equipment made it possible to give a more reliable estimate

J2= 2 · 10−7. This value is used for the construction of ephemerides starting with DE 405

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(Standish, 1998) and EPM2000 (Pitjeva, 2001). Recently, it became possible to determine

the dynamical solar oblateness while processing of high-precision radar observations when

constructing planetary ephemerides (see Pitjeva, 2005b).

A serious problem arises in the construction of modern high-precision planetary

ephemerides due to the necessity of taking into account the perturbations caused by asteroids.

The DE200 and EPM87 ephemerides considered the perturbations only from the 3-5 largest

asteroids; the experiments revealed that this was impossible to attane a proper representation

of high-precision observations of the Viking 1 and Viking 2 landers, i.e., a representation

which would match the a priori errors (6-12 meters) of these observations. Amplitudes of the

perturbations from asteroids were determined analytically by Williams (1984) considering

commensurability between the orbital periods of the asteroids and Mars. The perturbations

from 300 asteroids that were selected by Williams due to the significant perturbations of

the orbit of Mars caused by them (Williams, 1989) are taken into account starting with

the DE 403 (Standish et al., 1995) and EPM98 (Pitjeva, 1998) ephemerides. However, the

masses of the majority of these asteroids are either unknown or known with insufficient

accuracy, and Standish and Fienga (2002) showed that the accuracy of planetary ephemerides

deteriorated substantially with time due to this factor. Direct dynamical estimates of the

masses of asteroids may be obtained by analyzing their perturbations to other celestial

bodies caused by them. This technique may be applied when examining spacecraft near

asteroids, binary asteroids or asteroids with satellites, perturbations on the Mars and the

Earth caused by asteroids and revealed through the processing of radar observations of

Martian spacecraft and landers, and close encounters of asteroids. Applying the latter

(classical) method requires great caution, since optical observations may produce large errors

(Krasinsky et al., 2002). These techniques were used to measure the masses of several dozen

asteroids, but the construction of high-precision planetary ephemerides demands taking

into account the perturbations from about 300 large asteroids. If the estimates of the

diameters and densities of these asteroids are available, one may also estimate their masses.

The diameters of hundreds of asteroids were determined by processing the infrared data

from the Infrared Astronomical Satellite (IRAS) and Midcourse Space Experiment (MSX)

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