Numerical Ephemerides of Planets and the Moon
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NUMERICAL EPHEMERIDES OF PLANETS AND THE MOON EPM AND IMPROVEMENT OF SOME ASTRONOMICAL CONSTANTS EV PITJEVA Institute of Applied Astronomy of RAS Kutuzov quay StPetersburg Russia email evpquasaripanwru ABSTRACT The current state of the last version of the planet part of EPM Ephemerides of Planets and the Mo on ephemerides whose origin dates back to the s is presented Ephemerides of the planets and the Mo on have b een numerically integrated in the PPN metric over a year time interval The dynamical mo del of EPM ephemerides in cludes mutual p erturbations from the nine planets the Sun the ve most massive asteroids the Mo on lunar physical libration p erturbations from other asteroids as well as p erturbations from the solar oblateness and the massive asteroid ring with constant mass distributions in eclip tic plane EPM ephemerides have resulted from a least squares adjustment to observational data totaling more than p osition observations of dierent typ es The set of dierent astronomical constants have b een obtained from accurate radiometic observations The angles of the rotation b etween EPM and the ICRF are in mas x The two versions of EPM ephemerides have b een con y z structed in TDB and TCB time scales as the indep endent variables of the equations DYNAMIC MODELS OF PLANETARY MOTION OF DE AND EPM EPHEMERIDES The current state of the last version of the planet part of EPM Ephemerides of Planets and the Mo on ephemerides whose origin dates back to the s is presented At the same time to ensure space ights the construction of numerical planetary ephemerides was undertaken by several groups in the USA and Russia For comparison Ill further consider our EPM ephemerides created rst at the Institute of theoretical astronomy and later at the Institute of applied astronomy as well as wellknown DE ephemerides of JPL Common to all DELE and EPM ephemerides is a simultaneous numerical integration of the equations of motion of the nine ma jor planets the Sun the Mo on and the lunar physical libration p erformed in the Parameterized PostNewtonian metric for the harmonic co ordinates and General Relativity values The various ephemerides dier slightly in the mo delling of the lunar libration the reference frames the accepted value of the solar oblateness the mo delling of the p erturbations of asteroids up on the planetary orbits the sets of observations to which ephemerides are adjusted Some characteristics of DELE DELE DELE DE LE EPM EPM EPM EPM ephemerides are given in Table The detailed description and comparison of DE and EPM ephemerides are given in the pap er by Pitjeva Table Ephemerides DE and EPM Ephemeris Interval of Ref Mathematical Data integration frame mo del typ e numb er interval DE ! FK Integrating of optical SunMo on planets radar + + p erturbations spacecraft DE dynamic from asteroids LLR frame Keplerian ellipses total EPM ! FK Integrating of optical SunMo on planets radar p erturbations spacecraft from asteroids LLR Keplerian ellipses total DE ! ICRF Integrating of optical SunMo on planets radar + + p erturbations spacecraft DE ! from asteroids LLR mean elements total EPM ! DE Integrating of optical SunMo on planets radar áâ¥à p erturb spacecraft from asteroids LLR mean elements total DE ! ICRF Integrating of optical SunMo on planets radar + p erturbations spacecraft DE ! from asteroids LLR integrated total EPM ! DE Integrating of optical SunMo on radar planets spacecraft asteroids LLR total EPM ! ICRF Integrating of optical SunMo on radar planets spacecraft asteroids LLR asteroid ring total In the past ephemerides have b een aligned onto the FK reference frame then onto the dy namical equator and equinox and now ephemerides are oriented onto the International Celestial Reference Frame ICRF Starting with DE a nonzero value of the solar oblateness 7 J obtained from some astrophysical estimates was accepted for integrating 2 A serious problem in the construction of planetary ephemerides arises due to the necessity to take into account the p erturbations caused by minor planets In DE and our more pre vious versions the p erturbations from only three or ve biggest asteroids were accounted for The exp eriment showed that the tting of these ephemerides to the Viking lander data is p o or The p erturbations from asteroids have b een taken into account in the ephemerides DE DE and EPM ephemerides starting with EPM Masses of many of these asteroids are quite p o orly known and as shown by Standish and Fienga the accuracy of the planetary ephemerides deteriorates due to this factor Masses of few most massive asteroids which more strongly aect Mars and the Earth can b e estimated from observations of martian landers and spacecraft orbiting Mars The ve of asteroids proved to b e double and their masses are known now The masses of Eros and Mathilda have b een derived by p erturbations of the spacecraft during the NEAR yby Unfortunately the classical metho d of determin ing masses of asteroids for which close encounters o ccur is limited by uncertainty in masses of the large asteroids p erturbations by others unmo deled asteroids and a quality of observa tions Perhaps masses of many asteroids will b e obtained by high accuracy observations during the GAIA mission but it will not b e so on So at present masses of the rest of asteroids have b een estimated by the astrophysical metho d The latest published diameters of asteroids based on infrared data of IRAS Infra Red Astronomical Satellite and MSX Midcourse Space Exp eriment as well as observations of o ccultations of stars by minor planets and radar obser vations have b een used in this pap er The mean densities for CSM taxonomy classes have b een estimated while pro cessing the observations At the several meters level of accuracy the orbit of Mars is very sensitive to p erturbations from many minor planets These ob jects are mostly to o small to b e observed from the Earth but their total mass is large enough to aect the orbits of the ma jor planets The ma jor part of these celestial b o dies moves in the asteroid b elt and their instantaneous p ositions may b e considered homogeneously distributed along the b elt Thus it seems reasonable to mo del the p erturbations from the remaining small asteroids for which individual p erturbations are not accounted for by computing additional p erturbations from a massive ring with a constant mass distribution in the ecliptic plane Krasinsky et al Two parameters that characterize the ring its mass and radius are included in the set of solution parameters Thus the dynamical mo del of EPM ephemerides includes the following p erturbations mutual p erturbations from the nine planets the Sun the ve most massive asteroids the Mo on lunar physical libration p erturbations from other asteroids as well as p erturbations from the massive asteroid ring and from the solar oblateness The lunarplanetary integrator emb edded into the program package Krasinsky and Vasilyev ERA ERA Ephemeris Research in Astronomy has b een used Numerical integration of the equations of motion in the barycentric co ordinate frame of J was carried out by the Everhart metho d over a year time interval PROCESSING THE RADAR AND OPTICAL DATA EPM ephemerides have resulted from a least squares adjustment to observational data totaling more than p osition observations of dierent typ es including radio metric observations of planets and spacecraft CCD astrometric observations of the outer planets and their satellites meridian transits and photographic observations Data used for the pro duc tion of ephemerides were taken from databases of the JPL website httpssdjplnasagoviau comm created and kept by Dr Standish the database of optical observations of Dr Svesh nikov and extended to include Russian radar observations of planets on the website of IAA http wwwipanwru PAGEDEPFUNDLEAENGengleahtm Radar observations have b een reduced for relativistic corrections the eects of propagation of electromagnetic signals in the Earth trop osphere and in the solar corona as well as reduction for the top ography for ranging of planet surfaces Sp ecial mention should b e made of the uniqueness of the extremely precise observations of the martian Viking Pathnder landers and MGS Mars Global Surveyor data which are free from uncertainties due to planetary top ography that do remain in radar ranging despite the mo deling of top ography The p ositions of the landers are computed taking into account the precession nutation and estimated seasonal terms of the Mars rotation The part of MGS data obtained during was carried out at sup erior solar conjunction unlike the later MGS data of Although the frequency was high the Xband while the minimum impact parameter p was p R for the date the eect of the solar corona delay was considerable When these data were excluded from the tting the residuals for them were calculated with the obtained ephemerides their rms app eared to b e as large as m which value greatly exceeded the a priory errors These residuals decreased after reduction for the solar corona with dierent values of parameters of the corona mo del for dierent parts of MGS observations A simple mo del of the solar corona was used A B B t N r e 6 2 r r where N r is the electron density e Figure Ranging residuals for Mercury and Venus the scale km Figure Ranging residuals for Mars and Jupiter the scale km Figure Ranging residuals of Viking