An extension of Herschel's method for dense and extensive catalogues - Application to the determination of solar motion

We present a way of handling and interpreting stellar proper motions, in which the idea of substituting them by great circles, proposed by Herschel in 1783, allows us to take the entire celestial sphere as a field of application, making possible the study of dense and extensive stellar zones. A suitable mathematical processing of data together with Herschel's method make up a good tool in order to search for and detect associations, clusters, systematic patterns of motion and to go deeper in the local galactic kinematic. In this paper, we explain our vision of Herschel's method, illustrating it with some practical examples. The particular case of solar motion is developed in a specific and complete way, using the whole Hipparcos catalogue, Herschel's method and our own mathematical tool, originally designed to determine systematic trends in plates or between catalogues. The solar apex and velocity obtained here are expressed as a continuous function, depending on the distribution of the stellar spectral types.