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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
EPM2002 and EPM2002C -- two versions of high
accuracy numerical planetary ephemerides
constructed for TDB and TCB time scales
E. V. Pitjeva
Institute of Applied Astronomy, St. Petersburg, Russia
To be consistent with IAU resolutions ICRS should be treated as four--
dimensional reference frame with TCB time scale in which planetary ephemerides
should be constructed. For correlation and comparison with the widespread JPL's
DE ephemerides our EPM ephemerides have been created up to now in TDB time
scale, close to T eph used for the DEs ephemerides. The conversion to TCB time
scale might not and did not allow greater accuracy of ephemerides and adjusted
parameters and has been done for convenience of users treating VLBI and Earth
satellite observations. These new ephemerides (EPM2002C) cannot be used for
ephemeris applications of satellites of major planets, if ephemerides of satellites
have been created in TDB time scale.
The last versions of the EPM ephemerides [1] have been produced by simulta­
neous numerical integration of the equations of motion of nine planets, the Sun,
the Moon, lunar physical libration and 300 asteroids over a 125--year time inter­
val (1886--2011) performed in the Parameterized Post--Newtonian metric for the
harmonic coordinates (ff = 0) and General Relativity values (fi = fl = 1). For the
five biggest minor planets their mutual perturbations are accounted, for other
asteroids such perturbations are neglected. Numerical integration of the equa­
tions of motion in the barycentric coordinate frame of J2000.0 has been carried
out by the Everhart method of nineteenth order. We used the lunar--planetary
integrator embedded to the program package ERA [2]. The masses of planets as
well as the provisional initial conditions correspond to the ephemerides DE405
[3]. The values of GM i and initial coordinates of all celestial bodies involved in
integration have been multiplied by (1 + LB ) for the construction of EPM2002C
ephemerides in TCB time scale in accordance with the IAU resolutions (see, for
example, Brumberg and Groten [4]). Because EPM ephemerides are very close to
DE405 ephemerides the value LB = 1:55051976772 \Delta 10 \Gamma8 , obtained for relation­
ship between TCB and TDB of DE405 ephemerides, has been used.
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As shown by Standish and Fienga [5] the accuracy of the planetary ephemerides
deteriorates due to the the perturbations of many asteroids whose masses are not
well known. So, studies of the estimations of masses of the most relevant 300 as­
teroids have been made. The last published diameters of asteroids based on IRAS
data [6] and observations of occultations of stars by minor planets [7] have been
used, and the mean density for the C, S, M taxonomy class has been estimated in
the process of treating observations. The perturbing effects of remaining asteroids
have been modelled as being caused by a circular ring in the ecliptical plane [8].
Mass M of the ring and its radius R are considered as solved--for parameters. The
estimate M ring = (3:6 \Sigma 1) \Delta 10 \Gamma10 M fi is obtained. Consequently, for the total mass
of the main asteroid belt we have M belt = (16:6 \Sigma 2) \Delta 10 \Gamma10 M fi . Both versions of
EPM2002 and EPM2002C ephemerides have been fitted to data totaling about
150000 observations including different American and Russian radiometric obser­
vations of planets and spacecrafts (1961­2001), CCD astromertic observations of
outer planets, and meridian transits of XXth century. Adjustment of EPM2002
and EPM2002C ephemerides onto the ICRF has been accomplished by inclusion
of VLBI measurements of spacecrafts near Mars and Venus. For EPM2002 and
EPM2002C ephemerides the rms residuals for observations are identical, and the
formal standard deviations of all solution parameters and their values (except
orbital elements of the planets) or corrections to the initial orbital elements of
planets coincide within formal uncertainties as it would be expected.
Along with the planetary ephemerides the improved ephemerides of the or­
bital and rotational motion of the Moon have been fitted by processing LLR
observations 1979­2001. The last version of this theory accounting for a number
of subtle selenodynamical effects is described in [9].
The Fortran program to calculate the rectangular coordinates of Sun, Moon,
and nine major planets with the help of the polynomial approximation by means
of Chebyshev's polynomials will be available from anonymous FTP:
//quasar.ipa.nw.ru/incoming/era .
References
1. Pitjeva E. V. Modern numerical ephemerides of planets and importance of
ranging observations for their creation. Cel.Mech. & Dyn.Astr. 2001, 80, 249--
271.
2. Krasinsky G. A., and Vasilyev M. V. ERA: knowledge base for ephemeris and
dynamical astronomy, IAU Coll., 1997, 165, 239--244.
3. Standish E. M. JPL Planetary and Lunar Ephemerides, DE405/LE405. In­
teroffice Memorandum, 1998, 312.F­98­048, 1--18.
4. Brumberg V. A., Groten E. IAU resolutions on reference systems and time
scales in practice, A&A, 2001, 367, 1070--1077.
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5. Standish E. M., Fienga A. Accuracy limit of modern ephemerides imposed by
the uncertainties in asteroid masses, A&A, 2002, 384, 322--328.
6. Tedesco E. F., Noah P. V., Noah M., Price S. D. The supplemental IRAS
minor planet survey, AJ, 2002, 123, 1056--1085.
7. Dunham D., 2002, private communication.
8. Krasinsky G. A., Pitjeva E. V., Vasilyev M. V., Yagudina E. I. Hidden mass
in the asteroid belt, Icarus, 2002, 158, 98--105.
9. Krasinsky G. A. Selenodynamical parameters from analysis of LLR observa­
tions of 1970--2001, Communications of IAA, 2002, No. 148.
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