Abstract
In the numerical integrations of the outer planets, when the inner planets are not considered, the initial conditions are determined by least square adjustment with a complete ephemeris. In the present work, we compute the resulting uncertainty on the initial conditions by the analysis of the very simple problem which consists in fitting by least squares a straight line to a sine curve. Explicit formulae for the computation of the error due to the fitting process are given. In particular, fitting over an integer number of periods is very close to the worst case. The determination of the initial conditions in the LONGSTOP project (Milani,et al., 1987) is analysed as an example. It is shown that the uncertainty on the main frequencies of the secular system due to the determination of the initial conditions is of the order of 0.01 arcsec/year.
Similar content being viewed by others
References
Applegate, J.H., Douglas, M.R., Gursel, Y., Sussman, G.J., Wisdom, J.: 1986, ‘The outer solar system for 200 million years’,Astron. J. 92(1), 176
Bretagnon, P.: 1982, ‘Théorie du mouvement de l'ensemble des planètes,’Astron. Astrophys. 114, 278
Carpino, M., Milani, A., Nobili, A.M.: 1987, ‘Long term numerical integrations and synthetic theories for the motion of the outer planets,’Astron. Astrophys. 181, 182
Laskar, J.: 1987, Secular evolution of the solar system over 10 millions years,Astron. and Astrophys., (in press)
Milani, A., Nobili, A.M., Carpino, M.: 1987, ‘Secular variations of the semimajor axes: theory and experiment,’Astron. Astrophys. 172, 265
Simon, J.L.: 1983, ‘Théorie du mouvement des quatre grosses planètes. Solution TOP82’,Astron. Astrophys. 120, 197
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Laskar, J., Simon, J.L. Fitting a line to a sine. Celestial Mechanics 43, 37–45 (1987). https://doi.org/10.1007/BF01234552
Issue Date:
DOI: https://doi.org/10.1007/BF01234552