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
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
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.
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-
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
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).
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
(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)
satellites. When constructing the DE and EPM ephemerides, these asteroids were divided
into the C (Carbonic), S (Sillicum), and M (Metallic) taxonomic types according to their
spectral classes, and the estimates of their densities were derived from radar observations
while improving the ephemerides. Apart from the sufficiently large asteroids, thousands of
small asteroids, many of which are too small to be ever discovered from the Earth, produce
a substantial cumulative effect on the orbits of the inner planets. The majority of these
bodies travel within the main asteroid belt, and the distribution of their instantaneous
positions in the main belt may be considered uniform. Thus, the perturbations from the
small asteroids that were not considered individually in the integration may be modeled by
additional perturbations from a massive ring in the plane of the ecliptic with a uniform mass
distribution. Starting with EPM2004 (Pitjeva, 2005a), the two parameters characterizing the
ring (its mass Mrand radius Rr) are included in the set of parameters that are improved
Hundreds of trans-Neptunian objects (TNOs) that were discovered lately also exert
influence on the motion of planets, especially the outer planets. The updated dynamical
model of the EPM ephemerides includes Eris (a dwarf planet discovered in 2003, which is
more massive than Pluto) and 20 of the largest TNOs into simultaneous integration. The
perturbations from the other TNOs were modeled by a homogeneous TNO ring lying in the
plane of the ecliptic and having a radius of 43 AU and an estimated mass (Pitjeva, 2010a).
Thus, the dynamical model created at the IAA RAS, takes into account (besides
the mutual perturbations of large planets and the Moon) a number of relatively weak
gravitational effects that contribute appreciably while processing modern high-precision
• perturbations from 301 of the most massive asteroids;
• perturbations from other minor planets in the main asteroid belt, modeled by a
• perturbations from the 21 largest TNOs;
• perturbations from the other trans-Neptunian planets, modeled by a homogeneous ring
at a mean distance of 43 AU;
of the EPM ephemerides are more accurate than the DE405 ephemerides, which are adopted
as an international standard. The EPM ephemerides have the following advantages over the
DE ones while using EPM for Russian astronavigation:
• They are constructed using independent and constantly updated software.
• They are promptly updated and improved according to incoming new data.
• The clients (GLONASS programs) may request additional needed data in any format.
Convenient access procedures (Bratseva et al., 2010) for external users were recently
devised at the IAA RAS. The users may access the EPM ephemerides of planets and the
Moon together with the corresponding differences TT−TDB, as well as the ephemerides,
computed simultaneously with the EPM ones, of seven additional objects (Ceres, Pallas,
Vesta, Eris, Haumea, Makemake, and Sedna) that are provisionally called dwarf planets.
The EPM ephemerides are available at ftp://quasar.ipa.nw.ru/incoming/EPM/.
The constructed EPM ephemerides used in practice form the basis of the Astronomical
Yearbook, and are needed to fulfill the GLONASS Federal Program and to carry out space
experiments in the Solar System. They also help us to solve some of the problems of
fundamental astrometry, including the determination of the dynamical structure of the Solar
System and a number of astronomical constants.
This work was supported by a grant from the RAS Presidium Program 22 “Fundamental
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