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[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 These ephemerides are outdated and no longer available, but the software used to store and evaluate them is still available and provides a robust method for storing compact ephemerides of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

Code site:
https://jms.l.hilton.gitlab.io/usno-ae-98-update/

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