A rapid method for calculating a minor planet trajectory using the Chebyshev approximation, and its fitting to observations

Details A rapid method for calculating a minor planet trajectory using the Chebyshev approximation, and its fitting to observations A rapid method for calculating a minor planet trajectory using the Chebyshev approximation, and its fitting to observations

Jul 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..22...73c&link_type=abstract

(Symposium on Star Catalogues, Positional Astronomy and Celestial Mechanics, Washington, D.C., Nov. 30, 1978.) Celestial Mechani

Astronomy and Astrophysics

Astronomy

Asteroids, Chebyshev Approximation, Orbit Calculation, Planet Ephemerides, Solar Orbits, Trajectory Analysis, Euler-Lagrange Equation, Least Squares Method, Polynomials, Asteroids, Techniques, Trajectories, Observations, Parameters, Orbits, Mathematical Models

Scientific paper

An accurate, simple method for the determination of the trajectory of a minor planet over a relatively short time interval is presented which is based on the use of the Chebyshev approximation. The trajectory is calculated by the numerical integration of the Lagrange equations based on an approximation of the second members of the equations by series of Chebyshev polynomials. The additive constants of integration are determined from observations using the classical least squares method, with the derivative of the variables with respect to the constants obtained by the numerical integration of Chebyshev polynomial series representations of the second members of the Lagrange equations. Calculations of the orbit of Ceres performed by a program using this method are presented and shown to be in good agreement with the APAE ephemerides. Applications of the method of Chebyshev polynomials include the calculation of condensed ephemerides, parameters usually obtainable by the interpolation of classical ephemerides and minor planet orbits from short duration observations.

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