MEPHEM - generate minor planet ephemeris for Magellan TCS

Stephen M. Slivan
Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology

The purpose of this application is to generate a minor planet ephemeris file in the "observing catalog" format used at the Magellan telescopes, that is of accuracy sufficient to acquire the object field with the telescope.


Accuracy of results

MEPHEM uses a 2-body calculation for the minor planet position with respect to the Sun, for which the orbit is modeled as constant over time with no gravitational perturbations. The orbit elements accurately represent the real orbit at only one particular epoch in time, so calculations of minor planet positions closer in time to the epoch will generally be more accurate than those calculated for times farther from the epoch, but neither the magnitude nor the direction of the error can be expressed as a simple function of time. Since MEPHEM is designed specifically to calculate short-term ephemerides for use during an observing run, aiding observers by formatting the output for use by the Magellan TCS, using the 2-body model with orbit elements for an appropriate epoch should yield positions of sufficient accuracy to acquire the object field with the telescope.

The MEPHEM server will normally retrieve updated minor planets orbit elements from the Minor Planet Center daily.

For accurate positions over a longer span of time than is supported by MEPHEM a perturbed ephemeris is needed instead; two resources to calculate perturbed ephemerides (but not in Magellan TCS format) are:

To check the accuracy of the 2-body calculations, positions calculated by MEPHEM were compared with perturbed calculations from JPL HORIZONS for three objects: (4) Vesta, (4179) Toutatis, and 2003 QP112.

Test Case 1: Main-belt object (4) Vesta

The following two plots show the differences in right ascension (red) and in declination (green) between the 2-body positions of (4) Vesta calculated by MEPHEM and perturbed positions calculated using JPL HORIZONS. On each plot the calculation at the elements epoch 2004 Jul 14 is marked by a black circle, where the positions coincide (differences are 0) as expected. For Vesta the orbit is well-established, and the cumulative effect of gravitational perturbations on the orbit is easily seen in the nonzero differences as the MEPHEM positions are calculated farther from the elements' epoch date. The Earth oppositions of Vesta which bracket the epoch occur on 2003 Mar 31 and 2004 Sep 17.

error less than 0.5 s for about 6 months before and after epoch error less than 3 arcsec for about 6 months before and after epoch

Test Case 2: Earth-approaching object (4179) Toutatis

The next two plots are the same as those above except that the object is Earth-approaching (4179) Toutatis. The 2004 Sep 29 encounter with Earth introduces an abrupt and marked error in the 2-body calculations.

error abruptly greater than 2 s after Earth encounter error abruptly greater than 30 arcsec after Earth encounter

Test Case 3: Centaur object 2003 QP112

The next two plots are the same as those above except that the object is 2003 QP112, a Centaur with a semi-major axis of about 21 AU. Astrometric observations of this object span only 54 days so the orbit isn't well-determined.

error less than 0.2 s for about 6 months before and after epoch error less than 3 arcsec for about 6 months before and after epoch

Additional Information

Earth orbit elements
The heliocentric location of Earth is needed by MEPHEM to calculate the effect of annual parallax on a minor planet position; that is, the transformation from heliocentric to geocentric coordinates. MEPHEM linearly interpolates Earth orbit elements from a server-side text file and then uses those results for a 2-body calculation of Earth position. The file contains heliocentric osculating orbital elements of Earth/Moon barycenter referenced to the mean ecliptic and equinox of J2000.0; these elements have been published annually in the Astronomical Almanac (e.g., AA 2004 edition, page E3).

If an ephemeris calculation is requested for a time that's outside the span of Earth orbit data in the file, an approximate Earth position will be used based on "low precision formulae for the Sun's coordinates" (AA 2004 edition, page C24) instead, the RA and Dec rates won't be output, and a warning message will logged for the user.

magnitude
The predicted mean V magnitude for an object is calculated using the object's H and G coefficients in the orbit elements file and the Lumme-Bowell solar phase model (Bowell et al., 1989, Asteroids II, pp. 549-554), which are valid for phase angles up to about 120 degrees. When MEPHEM calculates a magnitude prediction for a phase angle greater than 120 degrees a warning message is also logged for the user.

object
When requesting an ephemeris for a numbered object, specify the target by its minor planet number, optionally enclosed in parentheses. The name (or as much of it as fits in the input field) may also be included following the number, but any strings after the number are ignored. Here are some sample valid input strings for numbered objects:
         1
         2 Pallas
        (3)
	(4) Vesta
       954 Li
      3360 1981 VA
Note that "954 Li" isn't misinterpreted as a provisional designation because 954 isn't greater than 1800.

When requesting an ephemeris for an unnumbered object, specify the target by its (new-style) provisional designation. No distinction is made between upper-case and lower-case letter characters. Here are some sample valid input strings for unnumbered objects (the year must be greater than 1800):

      1982 YA
      2000 SG344
      2000 SG 344

An interactive converter for permanent, provisional, and temporary minor planet designations ( http://cfa-www.harvard.edu/iau/MPDes.html) is maintained by the IAU Minor Planet Center.

offsets
In certain situations the user might wish to apply a small constant shift to the right ascension and/or declination positions calculated for a particular ephemeris. The "RA fixed offset" (in seconds of RA) and "Dec fixed offset" (in arcseconds) input fields are included to meet this need.

output format
A specification for the ephemeris ("catalog") output format is given at http://www.ociw.edu/lco/magellan/catalog.html.

rates in RA and Dec
The rates in right ascension and declination at time t, both reported in arcseconds per second, are the first differences between the J2000 coordinates calculated for time t and those calculated for time t+(1 second).

warning messages
Warning messages alert the user to abnormal conditions that occurred during calculation of an ephemeris.

A variety of warning messages can appear if there's some problem using the Earth orbit elements file when precise Earth positions are calculated. Any of the "using approx Earth calc" messages mean that the precise calculation was not possible, and an approximate Earth position has been used based on "low precision formulae for the Sun's coordinates" (AA 2004 edition, page C24) instead.


Credits


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