de405iom.tex

该包是根据DE405提供的国际天球矩形参考框架的基本位置和速度方面的资料

strikingly similar to signatures in the Neptune residuals, and 
it is therefore to be assumed that the signatures are caused either by reduction procedures 
or, since both planets were in the same direction in the sky, zone errors in the catalogues.

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\noindent {\bf IV. MODELING THE ASTEROID PERTURBATIONS}
\nobreak
\vskip0.1 in

The basic part of the equations of motion for numerically integrating the ephemerides is the same as 
that described by Newhall {\it et al}. (1983), and modified as described in the DE403 Memo.
Since that time an improved procedure for modeling the asteroids' perturbations upon the
earth, moon, and Mars has been used, different from that used for DE403.

The perturbations from the 300 chosen asteroids which significantly
affect the planetary and lunar ephemerides are modeled in two different ways:

\medskip

\begin{itemize}

\item { } the orbits of the ``Big3" (Ceres, Pallas and Vesta)
were integrated under the gravitational forces of themselves, the sun, planets,
and the moon

\item these integrated cartesian states of the Big3 were fit with
with chebychev polynomials and stored in a temporary file

\item
 the orbits of {\it non}-Big3 asteroids were integrated under 
the gravitational forces of the sun, planets, moon and the Big3 asteroids.  At each
step, the force vectors of these non-Big3 asteroids upon the earth, moon and Mars are
computed, summed, and stored in a temporary file.  Also stored in the same temporary 
file were the contributions from these non-Big3 asteroids to the 
Solar System's center of mass.

\item  the vectors from this second temporary file were fit with 
chebychev polynomials and stored in a final file to be used for the full 
planetary and lunar integration.

\end{itemize}

\medskip \noindent The initial conditions and radii of the asteroids came from a file maintained by
the Solar System Dynamics Group at JPL.  The mass of each individual asteroid was computed 
from the formula, $ GM = 6.27\times 10^{20} {\rm R}^3 \rho_k $, where R is the radius of the 
asteroid in kilometers and where $\rho_k$ is the density of the k$^{th}$ taxonomic class of 
asteroids (S, C, or M).  

\medskip

\vskip0.05 in
The DE405 masses of Ceres, Pallas, and Vesta, in units of the solar mass, were
$4.7\times 10^{-10}, 1.0\times 10^{-10}, 1.3\times 10^{-10}$, found in the least squares
adjustment of DE405.  These are 
6\%, 29\%,  and 13\% lower, respectively, than those estimated by Standish and 
Hellings (1989), but are not significantly different from the DE403 values of 
$4.64\times 10^{-10}, 1.05\times 10^{-10}, and 1.34\times 10^{-10}$, giving 
mean densities of the C-, S-, and M-class asteroids of 1.8,2.4, and 5.0, 
respectively. 

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\noindent {\bf V.  COMPARISON OF DE405 WITH DE403}
\nobreak
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Figure 7 shows comparisons of geocentric coordinates of the inner planets 
and moon between DE405 and DE403.  Over the full interval of nearly six centuries, 
the mean motion differences for the earth and Venus are apparent and amount 
to about 0\rlap .{\tt "}001/century.  The difference in the tidally induced 
deceleration of the moon is about 0\rlap .{\tt "}06/century$^2$.

For the outer planets, Figure 8 shows that the agreement over the 
present century is within 0\rlap .{\tt "}1.
The differences in mean motions lead to larger differences in other centuries,
indicating the uncertainty of extrapolating those orbits beyond the 
observational data coverage.

Over the time-span of the two ephemerides, 1600 AD to 2200 AD, the heliocentric coordinates
of the Earth-Moon Barycenter in DE403 and DE405 may be related quite closely as
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${\bf{\hat r}}_{\rm DE405} \approx {\bf{\hat r}}_{\rm DE403} + {\bf A}($t$) \times {\bf{\hat r}}_{\rm DE403}$
\quad and \quad
${\bf{\hat h}}_{\rm DE405} \approx {\bf{\hat h}}_{\rm DE403} + {\bf A}($t$) \times {\bf{\hat h}}_{\rm DE403}$
\vskip0.05 in
\noindent where
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${{206265 \ {\bf A}^T} = [\  +\ 0\secp 0003 - 0\secp 0002\ T,
\ \  - 0\secp 0003 + 0\secp 0001\ T, \ \ +\ 0\secp 0032 - 0\secp 0009\ T]}$,
\vskip0.05 in
\noindent and where T is the number of centuries past J2000.  The three components of the vector {\bf A}
represent time-dependent small rotations about the x-, y- and z-axes, respectively.

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\noindent {\bf VI.  CONSTANTS, INITIAL CONDITIONS, ETC.}
\nobreak
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Given in Table III are the dynamical constants used in DE405.  Not all 
of the digits are listed for those constants which are followed by an ellipsis (...).
The constants without ellipses are given exactly as they were used in the integration.  
Their values were found from a preliminary solution, then rounded exactly as shown,
and then intorduced into the final solution.

The initial conditions at the starting epoch of the integration, JED 2440400.5 (28 June 1969), 
are given in Table IV.

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\noindent {\bf VII.  DE406, THE NEW "JPL LONG EPHEMERIS"}
\nobreak
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The full precision numerical integration covered the interval, 3000 BC to 3000 AD.  
However, only the interval, 1600 AD to 2200 AD, has been fit with full precision chebychev
polynomials; this set of polynomials is referred to as DE405. 
DE406, on the other hand, covers the full interval of the integration, but in order to
conserve disk space, lower order chebychev polynomials are used and
both the nutations and the lunar librations have been excluded from the file.  
For DE406, however, the interpolation on the 64-day mesh points remains exact, and for other times,
the interpolating accuracy is no worse than 25 meters for all planets and 
no worse than 1 meter for the moon -- adequate for nearly any application except for the 
processing of the most accurate observations.  The nutations may be computed from the 
formula of the 1980 IAU Nutation Theory, and the librations have been saved on a separate file.
\vskip0.08 in
\noindent The binary version of DE406 occupies only 3.3 megabytes per century 
as opposed to the 9.2 required by DE405.  For the full expanse, 3000 BC to 
3000 AD, DE406 occupies only 200 megabytes.

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\noindent {\bf VIII.  AVAILABILITY OF THE EPHEMERIDES AND THE OBSERVATIONS}
\vskip0.1 in
\noindent {\bf DE200, DE405, AND DE406}
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\noindent DE200, DE405, and DE406 are available to the general public via anonymous FTP over the
Internet or on a CDrom sold by the publisher, Willmann-Bell.

\vskip 0.10in
\noindent A user is advised to get and read the file, ``readme'',
available from 

\begin{itemize}

\item  the website, ``http://ssd.jpl.nasa.gov'' [click on ``Horizons'' and then click on
``DE-200, DE-405, and DE-406'']. , or
\item  anonymous ftp : ``navigator.jpl.nasa.gov'' [cd to the directory, ``ephem/export''].
\end{itemize}

\noindent As explained in the readme, there are two methods of obtaining the ephemerides themselves: 

\begin{itemize}
\item  anonymous ftp :  ``navigator.jpl.nasa.gov" [cd to the directory, ``ephem/export''].
\item  from the publisher ($\approx $ \$25): Willmann-Bell, Inc.; 
\vskip0.01in \hskip 140pt PO Box 35025; Richmond, VA 23235; 
\vskip0.01in \hskip 140pt 804-320-7016; 804-272-5920 (Fax); 
\vskip0.01in \hskip 140pt ``http://www.willbell.com/software/jpl.htm".
\end{itemize}

\vskip0.1 in
\noindent {\bf The Observational Data Fit by the Ephemerides}
\vskip0.05in
\noindent The observations being fit by the ephemerides are now available on the website,

``http://ssd.jpl.nasa.gov/plan-eph-data/".  

\noindent There are also files describing the formats
and giving references to the sources of the data.

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\noindent {\bf IX.  CONCLUSION}
\nobreak
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DE405 represents the most accurate planetary positions available.  Certainly, they are not perfect; 
extrapolation forward or backward in time will always show some amount of deterioration.
Subsequent improvements will continue with further acquisition of observational measurements.



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\noindent {\bf X.  REFERENCES}
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\parindent=0pt
\everypar={\hangindent=16pt \hangafter=1}

Anderson,J.D., Jurgens,R.F., Lau,E.L., Slade,M.A., and Schubert,G.: 1996,``Shape and
 Orientation of Mercury from Radar Ranging Data'', {\it Icarus}, {\bf 124}, 690--697.
 \vskip0.04 in
Folkner, W.M., Yoder, C.F., Yuan, D.N., Standish, E.M., and Preston, R.A.: 1997,
 ``Interior Structure and Seasonal Mass Redistribution of Mars from Radio Tracking 
 of Mars Pathfinder", {\it Science}, {\bf 278}, 1749--52.
 \vskip0.04 in
Fricke,W.: 1982, "Determination of the Equinox and Equator of the FK5", 
 {\it Astron. Astrophys.}, {\bf 107}, L13-L16.
 \vskip0.04 in
Ma, C., Arias, E.F., Eubanks, T.M, Fey, A.L, Gontier, A.-M, Jacobs, C.S., 
 Sovers, O.J., Archinal, B.A., Charlot, P., 1998: ``The International Celestial Reference
 Frame as realized by Very Long Baseline Interferometry", submitted to {\it Astron J}.
 \vskip0.04 in
Morrison, L.V.: 1996, private communication.
 \vskip0.04 in
Morrison, L.V. and Evans, D.W.: 1998, ``Check on JPL DE405 using modern optical observations",
 submitted to {\it Astron Astrophys}.
 \vskip0.04 in
Newhall, X X, Standish, E.M. and Williams, J.G.: 1983, ``DE102: a numerically integrated ephemeris of the
 Moon and planets spanning forty-four centuries", {\it Astron. Astrophys.}, {\bf 125}, 150--167.
 \vskip0.04 in
Pettengill, G.H., Eliason, E., Ford, P.G., Loriot, G.B., Masursky, H., and McGill, G.E.: 1980, 
 ``Pioneer Venus Radar Results: Altimetry and Surface Properties", {\it J. Geophys. Res.}, {\bf 85}, A13, 8261--8270;
 table of values transmitted to the authors via W L Sjogren.
 \vskip0.04 in
Schwan,H. : 1983, ``A Method for the Determination of a System of Positions and Proper Motions of
 Stars with an Application to the Washington 6 Inch TC Observations", Veroffentlichungen \#30,
 Astronomisches Rechen-Institut, Heidelberg.
 \vskip0.04 in
Standish,E.M.: 1985, ``On the Orientation of Ephemeris Reference Frames", {\it Cel. Mech. J.}, {\bf 37}, 239-242.
 \vskip0.04 in
Standish,E.M.: 1990, ``The observational basis for JPL's DE200, the planetary ephemerides of the
 Astronomical Almanac", {\it Astron. Astrophys}, {\bf 233}, 252-271.
 \vskip0.04 in
Standish,E.M., Keesey,M.S.W. and Newhall,X X : 1976, ``JPL Development Ephemeris Number 96", Jet
 Prop Lab Technical Report \#32-1603, Pasadena.
 \vskip0.04 in
Standish, E.M., Newhall, X X, Williams, J.G. and Folkner, W.F.: 1995, ``JPL Planetary and Lunar Ephemerides, 
 DE403/LE403", JPL IOM 314.10-127.
 \vskip0.04 in
Standish, E.M. and Hellings, R.W.: 1989, ``A Determination of the Masses of Ceres, Pallas and Vesta from
 their Perturbations upon the Orbit of Mars", {\it Icarus}, {\bf 80}, 326-333.
 \vskip0.04 in
Stone, R.C.: 1998, ``CCD Positions for the Outer Planets in 1996--1997 Determined
in the Extra-galactic Reference Frame", submitted to {\it Astron J.}.
 \vskip0.04 in
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\vfil \eject
%
%  Table:  Observational data fit by DE405
%

\halign{\indent \quad # \hfil & # \hfil & # \hfil & \hfil # \hfil & \hfil # \hfil & \hfil # & \qquad \hfil #\cr
\noalign {\vskip0.05 in \noindent Table I.  Observational data fit by DE405. The columns contain the source, 
the time coverage, the planets measured, the components measured, the {\it a priori} uncertainties of a 
measurement, the number of observations and the group totals. } 
\noalign {\hrule}
\noalign {\vskip0.10 in \noindent OPTICAL MERIDIAN TRANSITS} 
\noalign {\vskip0.05in}
Washington  & 1911--1994 & Sun, ..., Nep  &   r.a., dec.    &   1$\secp $0/0$\secp $5 & 14242 & \cr
Herstmonceux& 1957--1982 & Sun, ..., Nep  &   r.a., dec.     &  1$\secp $0/0$\secp $5 &  2851 & 17093 \cr
\noalign {\vskip0.10 in \noindent PHOTOELECTRIC MERIDIAN TRANSITS}
\noalign {\vskip0.05in}
La Palma    & 1984--1993    &  Mar, ..., Plu &    r.a., dec.   & 0$\secp $25 &  6410 & \cr
Bordeaux    & 1985--1996    &  Sat, Ura, Nep  &   r.a., dec. &   0$\secp $25  & 854 & \cr
Tokyo   & 1986--1988    &  Mar, ..., Nep   &  r.a., dec.    &   0$\secp $5   &  498 & \cr 
Flagstaff - USNO   & 1995    &  Plu   &  r.a., dec.    &   0$\secp $1   &  20 & 7782 \cr
\noalign {\vskip0.10 in \noindent ASTROLABE }
\noalign {\vskip0.05in}
    Quito   & 1969    &  Sat    &  r.a., dec.  &    0$\secp $3--1$\secp $6 &      1 & \cr
    Algiers & 1969--1973    &  Mar,Sat  & & &  48 & \cr
    SanFernando & 1970--1978    &  Mar,Jup,Sat & &  & 338 \cr
    Besan\c con    & 1971--1973    &  Sat   & & & 44 \cr