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[submitted]
U.S. Naval Observatory Ephemerides of the Largest Asteroids (USNO/AE98)

USNO/AE98 contains ephemerides for fifteen of the largest asteroids that The Astronomical Almanac has used since its 2000 edition. These ephemerides are based on the Jet Propulsion Laboratory (JPL) planetary ephemeris DE405 and, thus, aligned to the International Celestial Reference System (ICRS). The data cover the period from 1799 November 16 (JD 2378450.5) through 2100 February 1 (JD 2488100.5). The internal uncertainty in the mean longitude at epoch, 1997 December 18, ranges from 0.05 arcseconds for 7 Iris through 0.22 arcseconds for 65 Cybele, and the uncertainty in the mean motion varies from 0.02 arcseconds per century for 4 Vesta to 0.14 arcseconds per century for 511 Davida.

The Astronomical Almanac has published ephemerides for 1 Ceres, 2 Pallas, 3 Juno, and 4 Vesta since its 1953 edition. Historically, these four asteroids have been observed more than any of the others. Ceres, Pallas, and Vesta deserve such attention because as they are the three most massive asteroids, the source of significant perturbations of the planets, the largest in linear size, and among the brightest main belt asteroids. Studying asteroids may provide clues to the origin and primordial composition of the solar system, data for modeling the chaotic dynamics of small solar system bodies, and assessments of potential collisions. Therefore, USNO/AE98 includes more than the traditional four asteroids.

The following criteria were used to select main belt asteroids for USNO/AE98:

Diameter greater than 300 km, presumably among the most massive asteroids

Excellent observing history and discovered before 1850

Largest in their taxonomic class

The massive asteroids included may be studied for their perturbing effects on the planets while those with detailed observing histories may be used to evaluate the accuracy limits of asteroid ephemerides. The fifteen asteroids that met at least one of these criteria are

1 Ceres (new mass determination)

2 Pallas (new mass determination)

3 Juno

4 Vesta (new mass determination)

6 Hebe

7 Iris

8 Flora

9 Metis

10 Hygiea

15 Eunomia

16 Psyche

52 Europa

65 Cybele

511 Davida

704 Interamnia

The refereed paper by Hilton (1999, Astron. J. 117, 1077) describes the USNO/AE98 asteroid ephemerides in detail. The associated USNO/AA Tech Note 1998-12 includes residual plots for all fifteen asteroids and a comparison between these ephemerides and those used in The Astronomical Almanac through 1999.

Software to compact, read, and interpolate the USNO/AE98 asteroid ephemerides is also available. It is written in C and designed to work with the C edition of the Naval Observatory Vector Astrometry Software (NOVAS). The programs could be used with tabular ephemerides of other asteroids as well. The associated README file provides the details of this system.

[submitted]
Compact Binary Chebyshev Polynomial Representation Ephemeris Kernel

The software used to transform the tabular USNO/AE98 asteroid ephemerides into a Chebyshev polynomial representations, and evaluate them at an arbitrary time is available. The USNO/AE98 consisted of the ephemerides of fifteen of the largest asteroids, and were used in The Astronomical Almanac from 2000 through 2015. These ephemerides are outdated and no longer available, but the software used to store and evaluate them is still available and provides a robust method for storing compact ephemerides of solar system bodies.

The object of the software is to provide a compact binary representation of solar system bodies with eccentric orbits, which can produce the body's position and velocity at an arbitrary instant within the ephemeris' time span. It uses a modification of the Newhall (1989) algorithm to achieve this objective. The Newhall algorithm is used to store both the Jet Propulsion Laboratory DE and the Institut de mécanique céleste et de calcul des éphémérides INPOP high accuracy planetary ephemerides. The Newhall algorithm breaks an ephemeris into a number time contiguous segments, and each segment is stored as a set of Chebyshev polynomial coefficients. The length of the time segments and the maximum degree Chebyshev polynomial coefficient is fixed for each body. This works well for bodies with small eccentricities, but it becomes inefficient for a body in a highly eccentric orbit. The time segment length and maximum order Chebyshev polynomial coefficient must be chosen to accommodate the strong curvature and fast motion near pericenter, while the body spends most of its time either moving slowly near apocenter or in the lower curvature mid-anomaly portions of its orbit. The solution is to vary the time segment length and maximum degree Chebyshev polynomial coefficient with the body's position. The portion of the software that converts tabular ephemerides into a Chebyshev polynomial representation (CPR) performs this compaction automatically, and the portion that evaluates that representation requires only a modest increase in the evaluation time.

The software also allows the user to choose the required tolerance of the CPR. Thus, if less accuracy is required a more compact, somewhat quicker to evaluate CPR can be manufactured and evaluated. Numerical tests show that a fractional precision of 4e-16 may be achieved, only a factor of 4 greater than the 1e-16 precision of a 64-bit IEEE (2019) compliant floating point number.

The software is written in C and designed to work with the C edition of the Naval Observatory Vector Astrometry Software (NOVAS). The programs may be used to convert tabular ephemerides of other solar system bodies as well. The included READ.ME file provides the details of the software and how to use it.

REFERENCES

IEEE Computer Society 2019, IEEE Standard for Floating-Point Arithmetic. IEEE STD 754-2019, IEEE, pp. 1–84

Newhall, X X 1989, 'Numerical Representation of Planetary Ephemerides,' Celest. Mech., 45, 305 - 310