EPM2011/m
The numerical integration of the equations of motion of the celestial bodies has
been performed in the Parameterized Post-Newtonian N-body metric for General
Relativity in the TDB time scale. EPM2011 ephemerides [2-4] are computed in the
barycentric coordinate system - BCRS, over more than the 400-year interval
(1787-2214) using the program package ERA-7 [1].
Ephemerides EPM2011 were constructed (2011 - July 2012) before the B2 resolution
of 28 GA IAU which fixes the value of the astronomical units of length (au)
equal 149597870700 m and preposes the determination GM_Sun in SI units. In
EPM2011 the au value was determined: au_EPM2011 = 149597870695.88 m. Although
following the B2 resolurion does not increase the accyracy of constructed
ephemerides, the next EPM ephemeris implementation will be made in accordance
with the B2 resolurion.
During some time the planet and lunar parts of EPM2011 ephemerides were being
improved separately. For EPM2011/m ephemerides, the parameters of the lunar and
planet parts of ephemerides have been in agreement with each other ("m" stands
for "Moon"). The result of this agreement was moderate changing of the lunar
motion, whereas the planet positions of EPM and EPM/m coincide.
We always computed the lunar libration along with positions of planets and the
Moon for EPM ephemerides, however, for the first time, the lunar libtarion has
appeared on our website ftp://quasar.ipa.nw.ru/incoming/EPM/.
EPM2011/m ephemerides contain coordinates and velocities of the Sun, the Moon,
nine major planets, three largest asteroids (Ceres, Pallas, Vesta) and 4 TNO
(Eris, Haumea, Makemake, Sedna) (in au, au/day) as well as lunar libration (in
radians) and TT-TDB (in seconds). Also, in addition to IAA binary and ASCII
formats, a representation of ephemerides in SPK/PCK formats has been added,
which will allow easy access to EPM2011/m for users of CALCEPH and SPICE
libraries.
Dmitry Pavlov is responsible for updating the ephemeris software and
files of EPM ephemerides, in particular for creation of the SPK format and
compuring TT-TDB of EPM2011.
For constructing planetary ephemerides using the best modern observations,
it is necessary to take into account all influencing factors.
The dynamical model of the planetary part of the EPM ephemerides includes:
- mutual perturbations from nine major planets, the Sun, and the Moon;
- perturbations from 301 the most massive asteroids, and the 21 largest
trans-neptunean objects (TNO);
- perturbations from a modeled massive asteroid ring with a uniform mass
distribution, and perturbations from a similar massive ring of TNO's
in the ecliptic plane with a radius of 43 au;
- relativistic perturbations;
- perturbations due to the solar oblateness.
Including into the simultaneous integration the 21 largest and very far TNO
(Eris which surpasses Pluto is one of them) causes the significant change of the
barycenter of the Solar System (without TNO, the barycentric coordinates would
be incorrect, as they incorrectly reflect the real positions in the Solar
system). Thus, the comparison of barycentric coordinates of EPM (EPM2008,
EPM2011) with barycentric coordinates of other ephemerides (DE, INPOOP)
knowingly is reasonlesss giving large differences. Only the comparison of
relative coordinates (heliocentric or geocentric) shows real differences between
ephemerides.
Thereby, as compared with EPM2008, the updated dynamic model of the planet part
of EPM2011 includes:
- the ring of TNO's lying in the ecliptic plane with radius of 43 au,
with estimated mass,
- new values of celestial bodies masses, and of other parameters,
- the expanded database (1913-2011).
The values of planet masses of EPM2011 were adopted by the 27 GA IAU
(except Mercury), and are close to values of DE421.
The EPM2011 ephemerides have been fitted to 677670 observations of different
types, spanning 1913-2011, from classical meridian observations to modern
planetary and spacecraft ranging. The ephemerides of the inner planets are based
fully on radio-technical observations (mostly, measurements of time delays).
The accuracy of observations of ranging has improved from about 6 km to several
meters for today's spacecraft data. The ephemerides of the outer planets are
mainly based on optical measurements taken since 1913, when they become more
accurate (0."5). In addition to optical observations of these planets, for the
construction of ephemerides, positional observations of the satellites of the
outer planets are used, as these observations are more precise and practically
free from the phase effect, which is difficult to take into account. The modern
optical data are CCD observations, and their accuracy reaches 0."05.
Radar observations have been reduced using relativistic corrections - the time
delay of the propagation of radio signals in the gravitational fields of the
Sun, Jupiter, Saturn (the Shapiro effect), and the reduction of observations
from the coordinate time of the ephemerides to the proper time of the observer.
In addition, the radar observations of Mercury, Venus, and Mars are corrected
for their topography and for the extra delay of electromagnetic signals in the
Earth's troposphere and in the solar corona. The main reductions of optical
observations of planets involve the correction to the additional phase effect,
the corrections for referring the observations to the ICRF reference frame, and
the relativistic correction for light bending. For the TT-TDB conversion, the
differential equation from the paper by Klioner [5] has been used, and TT-TDB
was obtained by numerically integrating the EPM2011.
For improvement of the planetary part of EPM2011, about 270 parameters
are determined:
- orbital elements of the planets and the 18 satellites of the outer planets;
- the length of the astronomical unit or the value of the solar mass parameter;
- three angles of orientation with respect to the ICRF frame;
- parameters of the rotation of Mars and topography of the inner planets;
- masses of asteroids, the asteroid belts; and TNO's ring;
- the time delay from the solar corona (the parameters of its model were
determined from observations for different solar conjunctions);
- some post-model parameters (beta, gamma, \dot G/G, \dot {GM_\odot}/GM_\odot,
\dot \pi_i, \dot a_i/a_i, etc.)
EPM2011 has been oriented to the ICRF with an accuracy better than 0.1 mas by
including into the total solution the 213 ICRF-based VLBI measurements of
spacecraft taken from 1989-2010 near Venus, Mars, and Saturn (in mas):
varepsilon_X =-0.000+-0.042, varepsilon_Y =-0.025+-0.048, varepsilon_Z =
0.004+-0.028. The carrent maximum errors of the coordinates of the Earth orbit
determined from a comparison of the EPM2011 heliocentric X, Y, Z coordinates,
velocities, and distances with those of DE424 over the 1950-2050 time interval
are less than 250 m (coordinates), 0.05 mm/s (velocities), 5.3 m (distances).
The dynamic model of the lunar motion was constucred by George Krasinsky to take
into account the tidal perturbation in the lunar rotational motion [6]. The
group of George Krasinsky developed the lunar part of the EPM ephemerides [7-8].
At present, Mikhail Vasiliev and Eleonora Yagudina are responsible for the lunar
part of EPM ephemerides, and particularly for the lunar part of EPM2011. 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) are computed by a model with a delayed argument. The
potential of the Moon is calculated up to 4-th order of the zonal index, the
potential of the Earth includes the 5-th order harmonics. In the lunar part of
EPM2011 ephemerides about 70 parameters are estimated from 17134 1970-2010 LLR
data (including Apache data). Currently, the value of the wrms residuals is 5.8
cm. The detailed discription of the lunar part of EPM2011/m ephemerides will be
published soon in the journal Solar System Research.
Some constants of EPM2011/m ephemerides:
2446000.5 (1984) - date of the starting epoch of the integration
JD 2374000.5 (10.09.1787 12h) - date of the backward integration
JD 2530000.5 (22.10.2214) - date of the forward integration
299792.458 km/s - the speed of light
149597870695.88 m - number of meters per the Astronomical Unit
81.3005676344 - the Earth-Moon mass ratio
2.0*1.0D-7 - the solar oblateness
1.0 - the PPN parameter beta
1.0 - the PPN parameter gamma
0.0 - the variation of the gravitational constant
3.57 au - the radius of the asteroid ring
0.01720209895*0.01720209895 [au^3/day^2] =
132712440031 [km^3/s^2] - GM of the Sun
Masses Gm*1.0D-15 in au^3/day^2 (A) and in Gm*1.0D-10 GM_Sun (B):
(A) (B)
MERCURY 49124.9717 1660.1198
VENUS 724345.2333 24478.3829
EARTH 888769.2400 30034.8960
MARS 95495.4869 3227.1560
JUPITER 282534584.0787 9547919.1520
SATURN 84597060.7310 2858856.7272
URANUS 12920248.2576 436624.3736
NEPTUNE 15243591.0921 515138.9725
PLUTO 2166.8443 73.2259
MOON 10931.8946 369.4303
136199 Eris 2485.2618 83.9865
136472 Makemake 908.8701 30.7142
136108 Haumea 625.0359 21.1223
90372 Sedna 515.5171 17.4213
1 Ceres 139.7203 4.7217
2 Pallas 30.9864 1.0471
3 Juno 4.3415 0.1467
4 Vesta 38.5552 1.3029
6 Hebe 1.1986 0.0405
7 Iris 1.9345 0.0654
8 Flora 0.6072 0.0205
9 Metis 0.4838 0.0163
10 Hygiea 12.3140 0.4161
14 Irene 1.0667 0.0360
15 Eunomia 4.2771 0.1445
16 Psyche 3.7720 0.1275
19 Fortune 1.2914 0.0436
23 Thalia 0.3681 0.0124
29 Amphitrite 1.5941 0.0539
41 Daphne 1.2341 0.0417
52 Europa 2.6820 0.0906
324 Bamberga 1.5084 0.0510
511 Davids 1.8087 0.0611
532 Herculina 2.0906 0.0706
704 Interamnia 3.6148 0.1222
asteroid ring 31.286 1.057 (the asteroid ring additional to 301 asteroids)
TNO ring 14825 501 (TNO ring additional to 21 TNO)
References:
1) Krasinsky G.A., Vasiliev M. V., 1997. ERA: knowledge base for Ephemeris and
dynamical astronomy. - Dynamics and astrometry of natural and artificial
celestial bodies, IAU Coll.165 /EDs. Wytrzyszczak I.M., Lieske J.H., Feldman
R.A. Dortrecht: Kluwer Acad. Publ., p. 239-244.
2) 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, vol.432, issue 4, 3431-3437.
3) Pitjeva E. V., 2012. EPM -- the high-precision planetary ephemerides of IAA
RAS for scientific research, astronavigation on the Earth and space software -
"Space-time reference systems for future research". Presentation on IAU Joint
Discussion 7 at IAU General Assembly-Beijing,
http://referencesystems.info/iau-joint-discussion-7.html, id. 37 (14 p.).
4) Pitjeva E.V., 2013. EPM2011 - updated planetary ephemerides of IAA RAS and
their using for scientific reserches. - Solar System Research, 47, N4, 17p, DOI:
10.7868/S0320930X13040063 (in press).
5) Klioner, S.A., et al., 2010, Relativity in Fundamental Astronomy: Dynamics,
Reference Frames, and Data Analysis. - IAU Symp. 261, Cambridge University
Press, p. 112-123.
6) Krasinsky G.A., 1999. Tidal effects in the Earth-Moon system and the Earth's
rotation. - Celes. Mech. Dynam. Astr., V. 75, Issue 1, p. 39-66.
7) Aleshkina E.Yu., Krasinsky G.À., Vasiliev M.V., 1997. Analysis of LLR data by
the program system ERA. - Dynamics and astrometry of natural and artificial
celestial bodies, IAU Coll.165 /Eds.Wytrzyszczak I.M., Lieske J.H., Feldman
R.A. Dortrecht: Kluwer Acad.Publ, p. 228-232.
8) Krasinsky G.A., Prokhorenko S.O., Yagudina E.I., 2010. New version of EPM-ERA
Lunar theory. - Journees 2010, Paris. /Ed. N. Capitaine, 2010. p.61-64.
Elena Pitjeva, e-mail
10 July, 2013.