Laplacean

Definitions

"The object of this paper is to set forth briefly to what extent the principles proposed by Laplace in his Mécanique Céleste, tome 1, livre 2, may be made available in practice for the derivation of preliminary orbits of comets, minor planets, and satellites. […] Before proceeding to a discussion of the difficulties referred to above as having been encountered by various investigators in attempting to formulate practical orbit methods on the basis of Laplace's principles, and before demonstrating the advantages of the methods which I have termed "Short Methods," it is necessary to state that in emphasizing the practical value of the Laplacean principles I do not intend to detract in the least from their great but astronomically less important theoretical value. I shall therefore first consider in brief the general theoretical value of the Laplacean principles by means of a summary of their essential features. […] The direct solution which has just been outlined corresponds to the so-called first hypothesis of other methods. It is evident that the accuracy of Laplace's direct solution depends upon the accuracy of the fundamental observational data for which we have chosen α, δ; α′, δ′; α″, δ″. If the epoch is chosen to coincide with the date of one of the observations, then α, δ are fixed numbers, and the accuracy of the Laplacean solution depends upon the accuracy of the adopted values of their velocities and accelerations or, which is an equivalent statement, upon the accuracy of their first and second differential coefficients. In practically all other methods the accuracy of the solution depends upon the accuracy of the adopted values of the ratios of the triangles."

Etymology