***** File EPHEM.TXT EPHEMERIS The geocentric ephemeris for 0h UT each day has been calculated by the Astrometry Network from the following set of osculating orbital elements (Astrometry Network orbit no. 61). The orbital solution was fit to 7469 astrometric observations over the interval from 1835 August 21 to 1989 January 9 with a weighted rms residual = 1.2 arcsec. Full planetary and nongravitational perturbations have been taken into account at each time step in the ephemeris computations. The angular elements are referred to the ecliptic plane and the equinox of 1950. Epoch of Osculation 1986 Feb. 19.0 TDT (ET) Time of Perihelion Passage 1986 Feb. 9.45895 TDT (ET) Perihelion Distance 0.5871036 AU Eccentricity 0.9672769 Argument of Perihelion 111.84656 deg. Longitude of Ascending Node 58.14339 deg. Inclination 162.23925 deg. Nongravitational Parameters and center-of-light/center-of-mass offset: Radial component, A1 +3.883 E-10 AU/(day)**2 Transverse component, A2 +1.554 E-10 AU/(day)**2 So (see explanation below) 851 km The nongravitational acceleration model (Style II) is described in the following reference: Marsden, B.G., Sekanina, Z., and Yeomans, D.K. Comets and nongravitational forces. V. In Astronomical journal, v. 78, 1973, p. 211 - 225. Because of rather systematic trends in comet Halley's orbit residuals during March - April 1986, it was necessary to model an observation bias to obtain solutions that fit the observations to the level of the data noise itself. However, it is not entirely clear whether the effect is instrumental or an actual displacement of the comet's photometric center from its center of mass. The comet's center of mass was assumed to be offset a distance (S) radially toward the Sun from the observed center of light. This measurement bias, S, varies as the inverse square of the heliocentric distance (r) and the expression was normalized to a heliocentric distance of one AU (i.e. at r= 1 AU, S = So). S = So/r2 This measurement bias was assumed operative during all three apparitions included in the orbit solution. The value of the parameter So resulting from solution No. 61 is 851 km. The following osculating orbital elements are consistent with orbit No. 61 for comet Halley. Using these orbital elements and the export version of the Astrometry Network's Two-Body Ephemeris Generation program, users can generate their own ephemeris information. If care is taken to use the set of orbital elements with the epoch of osculation closest to the desired ephemeris dates, the Two-Body program can generate ephemeris information that is equivalent to corresponding information in the perturbed ephemeris (to approximately the one arc second level of accuracy). Each set of orbital elements is in the same order as the elements listed above - the only differences being that the epochs of osculation and dates of perihelion passage time are given as Julian dates rather than calendar dates. The second line of each element set contains the calendar date corresponding to the epoch directly above it on the first line. *** P/HALLEY TWO-BODY ELEMENTS *** 2445200.5 2446470.32863 0.5852278 0.9675859 111.82385 58.10886 162.25637 1982 AUG 19.0 2445310.5 2446470.45296 0.5858829 0.9675453 111.80417 58.10083 162.25872 1982 DEC 7.0 2445430.5 2446470.57072 0.5864306 0.9675064 111.79191 58.09832 162.25950 1983 APR 6.0 2445540.5 2446470.69050 0.5869451 0.9674637 111.78220 58.09763 162.25970 1983 JUL 25.0 2445680.5 2446470.79138 0.5872224 0.9674243 111.78673 58.10574 162.25698 1983 DEC 12.0 2445840.5 2446470.88815 0.5874794 0.9673746 111.79348 58.11507 162.25353 1984 MAY 20.0 2445990.5 2446470.94022 0.5874862 0.9673322 111.80837 58.12618 162.24895 1984 OCT 17.0 2446070.5 2446470.95080 0.5873858 0.9673142 111.82000 58.13272 162.24593 1985 JAN 5.0 2446190.5 2446470.96022 0.5872995 0.9672880 111.83062 58.13796 162.24307 1985 MAY 5.0 2446185.5 2446470.95983 0.5873038 0.9672895 111.83011 58.13774 162.24321 1985 APR 30.0 2446275.5 2446470.96216 0.5871911 0.9672652 111.84044 58.14134 162.24063 1985 JUL 29.0 2446330.5 2446470.96064 0.5871307 0.9672605 111.84482 58.14232 162.23958 1985 SEP 22.0 2446375.5 2446470.95982 0.5871094 0.9672624 111.84616 58.14247 162.23925 1985 NOV 6.0 2446420.5 2446470.95925 0.5871015 0.9672710 111.84644 58.14247 162.23920 1985 DEC 21.0 2446515.5 2446470.95901 0.5871055 0.9672780 111.84688 58.14343 162.23928 1986 MAR 26.0 2446625.5 2446470.95965 0.5871410 0.9672928 111.85290 58.14647 162.24019 1986 JUL 14.0 2446730.5 2446470.96823 0.5871630 0.9673312 111.86639 58.15668 162.24171 1986 OCT 27.0 2446820.5 2446470.98321 0.5870762 0.9673555 111.87354 58.16592 162.24268 1987 JAN 25.0 2446935.5 2446471.01007 0.5869611 0.9673842 111.88703 58.18176 162.24389 1987 MAY 20.0 2447040.5 2446471.05245 0.5866979 0.9674136 111.89612 58.19769 162.24481 1987 SEP 2.0 2447145.5 2446471.10491 0.5863577 0.9674421 111.90371 58.21398 162.24552 1987 DEC 16.0 2447220.5 2446471.15008 0.5859881 0.9674632 111.90348 58.22335 162.24584 1988 FEB 29.0 2447325.5 2446471.19641 0.5855362 0.9674834 111.89906 58.23058 162.24603 1988 JUN 13.0 2447435.5 2446471.27010 0.5849150 0.9675144 111.89678 58.24318 162.24627 1988 OCT 1.0 2447525.5 2446471.30900 0.5843262 0.9675342 111.88097 58.24162 162.24626 1988 DEC 30.0 2447640.5 2446471.34163 0.5836317 0.9675556 111.86132 58.23841 162.24624 1989 APR 24.0 2447765.5 2446471.33194 0.5829334 0.9675705 111.83024 58.22380 162.24622 1989 AUG 27.0 D.K. Yeomans Discipline Specialist for Astrometry Jet Propulsion Laboratory 4800 Oak Grove Dr. Pasadena, CA 91109 ------------------------- APPENDIX OBSNTERP Interpolation Program The Fortran source code OBSNTERP.FOR is an interactive, seven-point Lagrange interpolation program that will return ephemeris data for periodic comet Halley over the interval November 26, 1981 through June 23, 1989, when it is run on the table EPHEM.TAB (in the EPHEM directory). VAX/VMS and MS-DOS executables of OBSNTERP are called VAXNTERP.EXE and PCNTERP.EXE, respectively; like OBSNTERP.FOR, they are stored in the \SOFTWARE\OBSNTERP directory of this disc. To run the program, type PCNTERP (or VAXNTERP ) and respond to the prompts. You can speed up the interpolation time by shortening the data table to include only the interval that you require and by requesting output for dates in chronological order. The information in the data table was generated with IHW orbit number 61, which was based upon 7469 astrometric positions over the interval August 21, 1835 through January 9, 1989. (Each line of the table is a fixed width of 110 characters plus .) The definition of each output quantity is given below: Date: Calendar date and Julian date (times in these ephemerides are universal times). RA, DEC: Geocentric right ascension and declination referred to the mean equator and equinox of 1950.0 - light time corrections have been applied. DELTA: Geocentric distance of comet in AU. DELDOT: Geocentric velocity of comet in km/sec. R: Heliocentric distance of comet in AU. RDOT: Heliocentric velocity of comet in km/sec. THETA: Sun-Earth-Comet angle in degrees. BETA: Sun-Comet-Earth angle in degrees. MOON: Comet-Earth-Moon angle in degrees. PSANG: Position angle of extended Sun-Comet vector. PSAMV: Position angle of minus comet velocity vector. (Position angles are measured east from north.) Ravenel N. Wimberly Astrometry Team Member Jet Propulsion Laboratory 4800 Oak Grove Dr. Pasadena, CA 91109 [NOTE: this write-up by R. N. Wimberly was slightly edited to reflect the fact that executable versions of OBSNTERP.FOR were generated at NASA/GSFC and deposited on this disc. -- M. B. Niedner, Jr.]