With the use of narrow field-of-view instrumentation on faint comets, the accuracy requirements upon computed ephemerides are increasing. It is not uncommon for instruments with a one arc minute field-of-view to be tracking a faint comet that is not visible without a substantial integration time. As with all ephemerides of solar syste objects, the computed motion and reduction of these observations, the computed motion of a comet is further depenent upon effects related to the comet's activity. Thus, the ephemeris of an active comet is corrupted by both observational errors and errors due to the comet's activity

Yeomans, D. K.

English

NASA Technical Reports Server

COMETARY EPHEMERIDES - NEEDS AND CONCERNS
Donald K. Yeomans*
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena, CA 91109
I. Astrometry and Ephemeris Improvement
With the use of narrow fleld-of-view instrumentation on faint comets, the accuracy
requirements upon computed ephemerides are increasing. Today, it is not uncommon for instruments
with a one arc minute fleld-of-view to be tracking a faint comet that is not visible without a
substantial integration time. As with all ephemerides of solar system objects, the computed
motion of a comet is based upon past observations. As well as being corrupted by errors in the
taking and reduction of these observations, the computed motion of a comet is further dependent
upon effects related to the comet's activity. Thus, the ephemeris of an active comet is corrupted
by both observational errors and errors due to the comet's activity.
A. Errors in Observations
The ideal cometary position observation is generally the shortest exposure possible that s t i l l
shows a (nearly stellar) cometary image. Generally the telescope is guided on the comet's
predicted motion so that the surrounding star images are trailed. The accuracy of the comet's
reduced position depends upon the accuracy of the trailed star positions that are used in the
reduction procedure. Often the only suitable star catalog is the Astrographic Catalog which has
only rectangular star coordinates for most zones. These coordinates can be reduced to right
ascension and declination using the given plate constants but these constants are often
out-of-date or inaccurate. While new constants are being determined for the northern hemisphere
zones, the plate constants of the southern hemisphere zones are not being updated as yet. Because
of these plate constant problems and also because the stars of the Astrographic Catalog do not
have proper motion corrections, the star positions can have errors of up to 1-2" (Roemer, 1976).
Personal mistakes in observation reductions sometimes yield errors of 1-4" and while an occasional
error of 4" can easily be detected and the observation rejected, a run of observations biased by
4" can skew the computed orbit away from the actual orbit.
The cometary orbit determination process, and the ephemeris computations that are based upon
this process, assume that published positions of comets refer to the comet's actual
center_of-mass. However, it is the comet's "center-of-light" that is actually measured. Any
center-of-light/center-of-mass offsets would be particularly damaging to ephemeris accuracy if
they were systematically located on one side of the center of mass. Since the photometric
center_of-light is likely to be the area of highest dust density in the cometary neighborhood,
there is some reason to believe that the center-of-light is systematically offset toward the sun
for a dusty comet like Hal ley.
B. Errors Due to the Comet's Activity
Unlike other solar system bodies, the motions of comets are usually affected by substantial
nongravitational perturbations. These effects are thought to be due to the rocket effect of the
outgassing cometary nucleus (Whipple, 1950). For comet Hal ley, nongravitational effects cause the
comet's period to increase by ~ 4 days per period (Yeomans, 1977). For most comets of the Jupiter
class (Period ~ 5-6 years), the existing model for these nongravitational effects seems to succeed
rather well (Marsden, Sekanina and Yeomans, 1973). However, the nongravitational force model does
not succeed for some comets of intermediate period (Period ~ 70 years). For comet Hal ley, the
*The research described in this paper was carried out at the Jet Propulsion Laboratory, California
Institute of Technology, under NASA contract NAS7-100.
46
https://ntrs.nasa.gov/search.jsp?R=19820006122 2020-03-21T10:13:02+00:00Z
model succeeds better than for most intermediate comets but even so there are systematic residual
trends in the observed minus computed observation residuals. For an extreme example, an orbit
solution based upon observations over the 1759-1835-1910 interval yielded systematic residual
trends to 20" in May 1910 when the comet passed within 0.18 AU of the Earth. This would
correspond to an absolute comet position error of ~ 2600 km. Since observation errors probably do
not account for more than say 4" of this 20" residual trend, one must assume that the model for
the comet's equations of motion is deficient. It may be that the nongravitational acceleration
model is not symmetric with respect to perihelion as is now assumed. There may be significant
(but unmodeled) stochastic nongravitational accelerations acting upon the comet's nucleus.
C. Techniques for Ephemeris Improvement
To reduce the observational errors, the observer should guide on the comet's motion to obtain
faint and nearly stellar images, hence minimizing center-of-light/center-of-mass offsets. Each
observer should take at least two plates per evening to identify weak images and properly identify
the comet by comparing the observed and computed motion of the image. To facilitate plate
reductions, each observer should be equipped with the appropriate star catalogs for each section
of the comet's path through the constellations. At least 5 reference stars should be used in the
reduction procedure.
Errors due to the comet's activity are dependent upon the model used in describing the comet's
motion. One might try to model the center-of-light/center-of-mass offset or try a
nongravitational acceleration model that was asymmetric with respect to perihelion. However the
solution for extra parameters in the least squares orbit determination process is dangerous; while
the solution may be improved, the predictive power of the solution can be destroyed.
Cometary orbit determination and subsequent ephemeris computations can be improved by using
observations over as long a data arc as possible with the observations concentrated when the
comet's apparent motion on the sky is largest. Cometary position measurements made at close
geocentric distances, when the comet's apparent motion is large, are the most powerful
observations for ephemeris improvement.
By carefully observing and reducing their data, and by judiciously choosing their observing
times, observers of cometary positions can provide the accurate observations required for
precision ephemerides. However, if the past is any indication of the future, the precision of
computed ephemerides is not so large a problem as is the confusion over the published ephemerides
themselves.
II. Confusion Over the Use of Published Ephemerides
Along with the increased accuracy requirements that are being placed upon recent ephemeris
computations, the ephemeris users now have the responsibility of understanding what type of
ephemeris they are using. Effects that were once negligible for locating an object in wide field
instruments become important for locating the object in narrow field instruments.
Some confusion has been evident in the generation and use of precision ephemerides because
some of the labels used to describe a celestial position have been used erroneously and/or
interchangeably. Prior to an International Astronomical Union (I.A-U.) Commission 20
recommendation in the Fall of 1979, most comet and minor planet ephemerides were geometric. Today
they are either astrographic or apparent. Geocentric ephemerides for the planet Pluto and various
minor planets published in the American Ephemeris and the Nautical Almanac (A.E.N.A.) are
astrometric. Table I presents the various effects that are included in these four types of
ephemerides. In general, photographic observations using stellar offsets should be made employing
astrographic or astrometric ephemerides. Usually visual observations, radio observations and
radar observations will require apparent ephemeris positions. In practice, many radio antennas or
telescopes used for visual observations input astrographic or astrometric ephemerides and make the
necessary corrections to apparent positions within the computer drive system.
An object's astrometric position is directly comparable with cataloged star positions
provided: 1. the stellar positions have been corrected for proper motion and annual parallax, 2.
the catalog's reference equinox is 1950.0, and 3. the object's observed positions have been
corrected for the effects that depend upon an observer's topocentric location. It should be noted
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48
that the future FK5 standard star catalog and star catalogs that will be tied to it w i l l not
include the elliptic portion of annual aberration. Hence these new catalogs wil l be
astrographic.* Most star catalogs now in use (including the Astrographic catalog) are
astrometric. Details for freeing an object's ,position from the various effects listed in Table I
can be found in the Explanatory Supplement (1961).
Pitfalls to Avoid
A. Unless otherwise stated, it should be assumed that each of the four ephemeris types in Table I
use ephemeris (not universal) time. In 1980, ephemens time is 51 seconds ahead of universal
time.
B. Occasionally someone will try to convert a geometric ephemeris to an astrographic ephemeris by
modifying the printed ephemeris time entries by one light travel time. This procedure is
incorrect because it effectively backs up the object and the earth instead of just the object.
C. Many observers now generate their own ephemendes using a two body (sun-object) formulation
initialized by orbital elements. This is quite acceptable providing that the input elements
were generated with a two body orbit determination technique. If the input elements were
generated using planetary perturbations in the orbit determination process, care must be taken
to use these (osculating) orbital elements only if the given epoch is sufficiently close to
the desired ephemeris interval. Osculating orbital elements will be strictly correct only for
the instant of the given epoch and it is dangerous to use them as input to a two body
ephemeris if the epoch is several weeks from the desired ephemeris interval.
*They w i 1 1 also have a new reference equinox of 2000.0.
References
Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical
Almanac.1961, Her Majesty's Stationery Office, London.
Marsden, B. G., Sekanina, Z. and Yeomans, D. K. 1973, Astron. _J. 78, 211.
Roemer, E. 1976, The Study of Comets. NASA SP-393, p. 396.
Whipple, F. 1950, Astrophys. J_. I l l , 375.
Yeomans, D. K. 1977, Astron. J. 82, 435.
49


Cometary ephemerides - needs and concerns

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