%   JPL Planetary and Lunar Ephemerides, DE405/LE405%%   JPL IOM  312@@@@@%\documentclass[11pt,titlepage]{article} % this is a LATEX file \usepackage[dvips]{epsfig}      % to include PostScript figures%               *** SWITCH BACK TO PLAIN.TeX USAGE ***\renewcommand\smallskip{\vskip\smallskipamount}\renewcommand\medskip{\vskip\medskipamount}\renewcommand\bigskip{\vskip\bigskipamount} \setlength{\oddsidemargin}{8mm} \setlength{\evensidemargin}{8mm} \textheight 9.00 truein         % default textheight here is 532pt=7.36in  \textwidth  6.25 true in       % default textwidth here is 360pt=5in  \topmargin  -1.3true cm \oddsidemargin  .5true cm \evensidemargin .5 true cm % ---------------------- end preamble ------------------------------------\def\temp{\setbox0=\hbox{\tt \char'15}% \rlap . \kern-.2em\copy0\kern-\wd0 \kern.2em\copy0\kern-\wd0 \ } \def\secp{\kern .07em \temp  \kern .07em}\parindent=20pt% ---------------------- end definitions ------------------------------------\begin{document} \noindent {\bf JET PROPULSION LABORATORY} \hfill {\bf INTEROFFICE MEMORANDUM}\vskip0.1 in\hfill {IOM 312.F -- 98 -- 048 }\vskip0.05 in{\hfill August 26, 1998}\vskip0.1 in\halign{# &#\hfil & # \hfil \cr&TO  &: Distribution \cr\noalign{\vskip0.05 in}&FROM  &: E M Standish \cr\noalign{\vskip0.05 in}&SUBJECT   & : JPL Planetary and Lunar Ephemerides, DE405/LE405 \cr}\vskip0.2 in\noindent {\bf I.  INTRODUCTION}\vskip0.1 inThe latest JPL Planetary and Lunar Ephemerides, ``DE405/LE405'' or just ``DE405'',have been released and are now available via the Internet or on CDrom (see below) along with the extended and compressed ephemeris, ``DE406''.DE405 represents an improvement over its predecessor, DE403, describedin detail by Standish {\it et al.} (1995), and hereafter referred to as the ``DE403 Memo".  Many of the data sets, reduction techniques, etc. are the same as those used for DE403;they will not be described at length in this memo.  Instead, this memo concentrates on the differences: additional data, refinements to the reduction techniques, etc.\vskip0.05 inThe memo discusses the improvement in the orientation of the ephemerides onto the (J2000) International Celestial Reference Frame (ICRF).  It showsthe increased observational data set used for DE405 and the associated residuals.There is a description of the improved method for modeling the perturbations of asteroids upon the planetary orbits.  The individual ephemerides in DE405 are compared with those of DE403.  Tables are included of the initial conditions and dynamical constants, resulting from the least squares fitting process andused for the integration.\vskip0.1 in\noindent {\bf II. ORIENTATION OF DE405}\vskip0.1 inAs has been discussed often, the ephemerides of the four innermost planets along with the moon and the sun are all well-known with respect to each other because of the accurate ranging observations to which the ephemerides are adjusted.  In turn, the orientation of this inner system onto the ICRF is also accurately determined, mainly by the VLBI observations of the Magellan Spacecraft orbiting Venus, but also somewhat byVLBI observations of the Phobos Spacecraft approaching Mars, a frame-tie linkage usingground surveys and lunar laser ranging (LLR)data , and the range observations of the Viking Spacecraft on the surface of Mars.  Some of the Magellan VLBI observations are new since DE403.These data are discussed in the next section.It is believed that the orientation of the whole inner planet ephemeris system of DE405 is now accurate to about 0.001 arcseconds.  A verification of this estimate was provided by the arrival ofthe Pathfinder Spacecraft at Mars in July 1997, where the ephemeris errorwas about 0.001 arcseconds, corresponding to 1 km at that distance; it was mostly in the down-track direction.Ephemerides of the outer planets rely almost entirely upon optical observations;these were initially referenced to various stellar catalogues, then transformed onto the FK4 using the formulae of Schwan (1983), then onto the FK5 system byapplying the equinox offset and motion parameters of Fricke (1982), and finallyonto the ICRF using tentative transformation tables supplied by Morrison (1996).\vfill \eject\noindent {\bf III.  OBSERVATIONAL DATA}\vskip0.1 inTable I lists the observational data to which DE405 was adjusted.  Many of the sets of observational data have been described before (Standish {\it et al}., 1976; Standish, 1985, 1990; Standish {\it et al}., 1995).  Since the creation of DE403, some of these have been augmented by newer data.The actual numbers listed in Table I may differ slightly from those in the DE403 Memo, even though the data set may not have changed.  This happens because some of the processing programs automatically eliminate 3-$\sigma$ values; consequently, a few of the marginal observations may be eliminated from one given ephemeris and not from another.The observational data fit by the ephemerides are now available over the Internet, as described in Section VIII.\vskip0.1 in\noindent {\bf Optical Observations}\vskip0.05 inThe basic optical data sets were described in the DE403 Memo.  For DE405, new observations,both photoelectric and CCD,of the five outer planets from La Palma, Bordeaux, and USNO Flagstaff Station have been added.  The means of the optical residuals for each opposition over the past 20 years are plotted in Figures 1-3, along with error bars indicating the rms value of a single observation.Since many of the recent optical observations have been referenced to the FK5 frame, as modified by the corrections to precession and equinox drift, it becomes necessary to solve for a difference between the orientation of this frame and that of the ICRF frame.  This may be expressed by the formula,${\bf{\hat r}}_{ICRF} \approx {\bf{\hat r}}_{FK5} + {\bf A} \times {\bf{\hat r}}_{FK5}$,where the three components of the vector {\bf A} represent small rotations about the x-, y- and z-axes, respectively.However, the determination of the rotation vector ${\bf A}$ should not beconstrued as a significant determination of the FK5-ICRF frame-tie.  It is necessary to have both optical and ICRF-based observations of the same planets in order to determine the frame-tie, but in the presentcase, the optical observations of the inner planets are no longer included in the ephemeris adjustments and there are very few ICRF-based observations of the outer planets.  Eventually, it will be best touse an FK5-ICRF frame-tie as determined by other sources; this will be done when such a frame-tiebecomes established.\vskip0.1 in\noindent {\bf Radar Observations}\vskip0.05 inRadar-ranging observations now exist through 1997 for Mercury, through 1990 for Venus,and through the end of 1994 for Mars.  All of the observations since 1982, used for DE405, were taken by the Goldstone 64-m antennae (DSS-14).\vskip0.1inIn order to account for the topography of Mercury, a set of fully normalized Legendre functions to the second order was adjusted to fit the surface, following Anderson {\it et al.} (1996):$$ \matrix{ R_0 = & + c_{10}\sqrt{3}\sin \phi + (c_{11}\cos \lambda + s_{11}\sin \lambda)\sqrt{3}\cos \phi + c_{20}{\sqrt{5}\over 2}(3{\sin}^2\phi - 1) \hfill \cr & + (c_{21}\cos \lambda + s_{21}\sin \lambda)\sqrt{15}\sin \phi \cos \phi              +(c_{22}\cos 2\lambda + s_{22}\sin 2\lambda){\sqrt{15}\over 2} {\cos}^2 \phi}\  \hfill $$\noindent where $ \lambda $ is the longitude and $\phi$ is the latitude of the echo point on the surface.The least squares adjustment for DE405 yielded\vskip0.10in\halign{\quad $#$ \hfil & \quad $#$ \hfil & \quad $#$ \hfil & \quad $#$ \hfil \cr   R_0 \equiv 2,439,760 m &   c_{10} = +920 \pm 523 m  &   c_{11} = +186 \pm 38 m           &   s_{11} = -245\pm 38 m  \cr	   c_{21} = +79 \pm 157 m  &    s_{21} = +744 \pm 166 m  &    c_{22} = +292 \pm 32 m           &    s_{22} = +345 \pm 34 m \cr}\vskip0.10inIt is better to not convert these coefficients into definitive shape parameters for the surface of Mercury, since the whole set of Mercury radar is presently being re-analyzed.Instead, in this context, they have served merely as a smoothing function for determining the Mercury ephemeris.\vskip0.10inFor Venus, as in DE403, a topographical model of Pettengill {\it et al}., (1980), was used to reference the measurements to a sphere whose radius was determined to be$6052.30\pm 0.05 $ km, in the least squares adjustment.  \vskip0.10inThe residuals for Mercury and Venus are plotted in Figure 4.\vskip0.10inFor Mars, as in the past, the only radar observations used for DE405 were those used in the closure point analysis.  More important for Mars were the spacecraft measurements, described next.\vskip0.1 in\noindent {\bf Mars Spacecraft Data}\nobreak\vskip0.05 inDE405 was fit to 1257 ranging measurements from the Deep Space Network to the Viking Lander Spacecraft on the surface of Mars, 1976-82, and to 629 ranging measurements to the Mariner 9 Spacecraft in orbit around Mars, 1971--72.  These are the same data as thoseused for DE403.Since the creation of DE405, the following data sets have beenreceived and added to the ephemeris data collection: 14789 Viking doppler points, 89 range pointsto the landed Pathfinder Spacecraft, and 7564 Pathfinder doppler points.  The subsequent adjustments to these data are described by Folkner {\it et al.} (1997)whosereport is recommended for values of parameters describing the rotation and orientation of Mars.\vskip0.1 in\noindent {\bf VLBI and Radiometric Observations of Spacecraft}\nobreak\vskip0.05 inEight additional VLBI measurements of the Magellan Spacecraft orbiting Venus, taken between May and August 1994, were added since the creation of DE403; all 18 of the Magellan VLBI measurements are plotted in Figure 5.  These additional observations have further improved the orientation of DE405 onto theInternational Celestial Reference Frame (ICRF).\vskip0.1 in\noindent {\bf Lunar Laser Ranging Data}\nobreak\vskip0.05 inAdditional LLR ranging data have been received from the MacDonald Laser Ranging Station in Fort Davis, Texas and from the Centre d'Etudes en Recherche en Geodesie et Astronomie (CERGA) in Grasse, France.  There are now 11218 normal points from 1970 to 1997; those of the last few years have accuracies of 2-3 cm.\vskip0.1 in\noindent {\bf Jupiter Residuals}\nobreak\vskip0.05 inThe frame-tie for Jupiter is provided by adjustment to the recent VLBI observations of the Galileo Spacecraft orbiting Jupiter, as well as the VLBI observations and orbit determinationof the Ulysses Spacecraft as it flew by Jupiter in 1992, the VLA observations in 1983, theorbit determination adjustments of the Voyager 1 and Galileo Spacecraft, and range determinationsof all spacecraft that have been in the vicinity of Jupiter.The residuals are listed in Table II and plotted in Figure 6.Transit observations from La Palma are included, shown by the stars; those of the Washington 6-inch transit,by open squares.  The large open circles, left-to-right, represent the determinationsfrom Voyager 1 (1979.2), VLA (1983.3), Ulysses (1992.1), and Galileo (1995.9), respectively.  The full set of Galileo VLBI observations is shown in the third plot of Figure 6, where the the Goldstone-Canberra observations are indicated by an ``$\times$'',and the Goldstone-Madrid observations by a ``+''.  These residuals are plotted again in the fourth plot of Figure 6, where both scales have now been expanded.  For DE405, only the first 12 Galileo VLBI measurements were included in the fit.  However, it is apparent that all observations are fit by DE405 with an accuracy of about 0\rlap .{\tt "}01.As seen in Table II, the Voyager and VLA residuals are at least twice their {\it a priori}standard deviation and they remain unexplained.  Since the other accurate measurements, Ulysses and Galileo, are well-fit and cover nearly the same parts of the orbit as do the Voyager and VLA measurements, the problem cannot be corrected by a simple adjustment of Jupiter's orbital plane.There also seem to be signatures in the optical points, some of which are probably attributable to problems in the measurements themselves,as reported by Morrison and Evans (1998 ) and by Stone (1998).  Both noticed that over the past decade, signatures in the Uranus residuals were