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NUMERICAL EPHEMERIDES OF

AND THE EPM AND IMPROVEMENT

OF SOME ASTRONOMICAL CONSTANTS

EV PITJEVA

Institute of Applied of RAS

Kutuzov quay StPetersburg Russia

email evpquasaripanwru

ABSTRACT The current state of the last version of the 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 the ve most massive the

Mo on lunar physical libration p erturbations from other asteroids as well as p erturbations

from the solar oblateness and the massive ring with constant 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

 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 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 and the 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 data of IRAS Infra Red Astronomical Satellite and MSX Midcourse Space

Exp eriment as well as observations of o ccultations of by minor planets and radar obser

vations have b een used in this pap er The mean for CSM taxonomy classes have b een

estimated while pro cessing the observations

At the several meters level of accuracy the 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 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 e

Figure Ranging residuals for and the scale  km

Figure Ranging residuals for Mars and the scale  km

Figure Ranging residuals of Viking Pathnder MGS the scale  m

The result was b etter when apart from the B co ecient its time variation was also included

For the remaining MGS data of the solar corona delay was mo deled with another

value of the B co ecient

The residuals of all radiometric data are shown in Fig The rms residuals of ranging

for the Mercury are km for Venus and Mars are km for Viking and Pathnder are m

MGS are m MGS are less m For the MGS observations even far away

from the solar conjunction there still remains a signature at the a priory errors level The reason

for this is unclear mayb e the removal of the orbit of the MGS spacecraft was insuciently accurate

00

Figure Residuals of the outer planets in cos A and in B the scale 

The observations of satellites of Jupiter and are of great imp ortance for optics as

they are more accurate than the observations of their parent planets and practically free from the

phase eect CCD data obtained at Flagsta observatory whose observational program started

in and is still b eing continued are the most accurate All these p ositions are referenced

to ICRF using reference stars taken from ACT or Tycho catalogues Another group of high

accuracy data is photographic observations of satellites of Jupiter Saturn as well as and

Neptune planets obtained at Nikolaev observatory during They are referenced to the

ICRF system by a sp ecial metho d which has given go o d results for minor planets Combination

of the satellite data from Flagsta and Nikolaev has b een successfully used to improve the

planet ephemerides Residuals of all the observations of the outer planets are shown in Fig

Unfortunately observations of are mainly photographic and have quite p o or accuracy and

their rms are worse

ORIENTATION OF EPM ONTO ICRF

Ephemerides EPM were oriented onto the International Celestial Reference Frame ICRF

The most precise optical data of the outer planets and their satellites obtained at Flagsta

Nikolaev La Palma have already b een referenced to the ICRF The remaining optical obser

vations referenced to dierent catalogues at rst were transformed to the FK systems by

Sveshnikov Then they were referenced to the FK using known formulae see as the example

Standish et al and were nally transformed to the ICRF using the values of the three

angles of the rotation b etween the HIPPARCOS and FK catalogues J in mas Mignard

x y z

Orbits of the four inner planets with the exception of angles of the orientation are de

termined entirely by the ranging observations of planets and spacecraft The system of these

planets was oriented to the ICRF by the including the ICRFbase VLBI measurements of space

craft Magellan in orbit ab out Venus and Phob os on its approach to Mars in the adjustment

in the same way that has b een done by Standish b for DE The angles of the rotation

b etween the EPM ephemerides and the ICRF reference frame were obtained in mas

  

x y z

RESULTS OBTAINED

The formal standard deviations of orbital elements of planets are shown in the Table Note

that the uncertainties given in this pap er are formal standard deviations realistic error b ounds

may b e an order of magnitude larger

Table The formal standard deviations of elements of the planets

planet a sin i cos sin i sin e cos e sin

m mas mas mas mas mas

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

where a the semima jor axis i the inclination of the orbit the ascending no de e the

eccentricity the longitude of p erihelion the mean longitude The value of the astronomical

unit has b een obtained

AU  m

The parameters of Mars rotation masses of Pallas Vesta Iris Bamb erga Juno

densities of CSM classes of asteroids the estimation of the total mass of the main asteroid

b elt the solar quadrup ole moment parameters of PPN formalism and have b een estimated

in the tting pro cess to all the observations Table demonstrates some of these values

Table The parameters of the Mars rotation

o o 00 o 00

V I I year year

q q q q

    

The value of precession constant for Mars is close to the recent value obtained from the data

of the Viking Pathder landers and MGS radio tracking Yo der et al

00 00

 year

q

Table Masses of Ceres Pallas Juno Vesta Iris Bamb erga

10

in GM GM 

i

Ceres Pallas Juno Vesta Iris Bamb erga

     

Table The solar quadrup ole moment the radius and the mass

of the asteroid ring the total mass of the main asteroid b elt

J R M M

2 r ing r ing belt

7 10 10

AU M M

   

Table Progress in the determination of the parameters of PPN formalism and GG

11 1

year GG yr

  

  

  

Along with the planetary ephemerides the improved ephemerides of the orbital and rota

tional motions of the Mo on have b een tted by pro cessing the LLR observations

by Krasinsky where the last version of this theory accounting for a numb er of subtle

seleno dynamical eects is describ ed

For further details regarding the masses of asteroids the full set of used observations and

etc the reader is referred to the pap er Pitjeva

THE CONVERSION FROM THE TDB TO TCB TIME SCALE EPHEMERIDES

For correlation and comparison with the widespread JPL DEs ephemerides the EPMs

ephemerides were created up to now in TDB time scale close to T Standish a used

eph

for the DEs ephemerides To b e consistent with IAU resolutions ICRS should b e treated as

fourdimensional reference frame with TCB time scale in which planetary ephemerides should

b e constructed Although the conversion to TCB time scale could not and did not allow greater

accuracy of ephemerides and adjusted parameters users pro cessing the VLBI and Earth satel

lite observations must have TCB ephemerides so the two versions of EPM ephemerides are

constructed for TDB and TCB time scales

In accordance with the recommendations of literature see for example Brumb erg and

Groten the values of masses GM and initial co ordinates of all celestial b o dies involved in

i

integration for the date JD were multiplied by the factor L for the construction

B

of EPM ephemerides in the TCB time scale Because EPM ephemerides are very close to

8

DE ephemerides the value L  obtained for relationship b etween

B

TCB and TDB of DE ephemerides IERS Conversions has b een used

Thus the following mo dications must b e done for the conversion from the TDB to TCB

time scale ephemerides

 the integration ep o ch

dateTCB dateTDB  L dateTDB

B

 p ositions x TCB x TDB  L

i i B

 masses GM TCB GM TDB  L

i i B

8

L 

B

This version involves the same numerical values in terms of TCB and TDB for the unit

of length AU in km and for any velo cities including the sp eed of light At the XXV IAU

General Assembly Dr Standish prop osed another more complicated version of conversion to

TCB ephemerides retaining the same numerical value in SI units for the helio centric constant

GM in terms of TDB and TCB This situation is rather confusing In any case some ocial

recommendation should b e adopted see Brumb erg and Simon

REFERENCES

Brumb erg V A Groten E Astron Astrophys

Brumb erg V A Simon JL in the same issue

Krasinsky G A Vasilyev M V in Proceedings of the IAU Col l Dynamics and

Astrometry of Natural and Articial Celestial Bodies I M Wytrzyszczak J H Lieske

R A Feldman eds Dordrecht Kluwer

Krasinsky G A Pitjeva E V Vasilyev M V Yagudina E I Icarus

Krasinsky G A Communication of IAA RAN p

Mignard F in Towards models and constants for submicroarcsecond astrometry John

ston K J McCarthy D D Luzum B J Kaplan G H eds US Naval Observatory

Washington DC USA

Pitjeva E V Celest Mech Dyn Astr N

Pitjeva E V Communication of IAA RAN p

Standish E M Newhall XX Williams J G Folkner W M Interoce Memorandum

p

Standish E M a Astron Astrophys

Standish E M b Interoce Memorandum F p

Standish E M Fienga A Astron Astrophys

Yo der C F Konoplev A S Yuan D N Standish E M Folkner W M Science

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