Remarks on Chebyshev representation of ephemeris

TL;DR

This paper discusses methods for converting Chebyshev coefficients of ephemeris data into velocity and acceleration representations, extending previous techniques for consistent, continuous ephemeris modeling.

Contribution

It introduces an extended approach for generating Chebyshev coefficients that uniformly handles coordinate, velocity, and acceleration representations.

Findings

The extended method produces continuous ephemeris representations.

Advantages of the new approach over direct derivative application are demonstrated.

The approach ensures consistent treatment of position, velocity, and acceleration.

Abstract

Chebyshev coefficients of a coordinate representation can be used to form the corresponding velocity representation. One way is to directly apply them to the derivatives of Chebyshev polynomials, another is to compute from them the Chebyshev coefficients of the velocity representation. The advantages of the latter over the former ways are illustrated. Also, the approach of generating Chebyshev coefficients developed by Newhall (1989) is extended such that coordinate, velocity and acceleration are consistently treated. The resulting representations are all continuous.