The Thiele-van den Bos Method

Abstract

The radii vectors to two positions in an orbit subtend an ellipse sector and a triangle, the sector being related to the time interval through the law of areas. Gauss introduced the use of the differences sector minus triangle between three positions into the orbit computation of planets, and Thiele (1883) applied the idea to binary stars. Van den Bos’ merit is not merely a modification of the method (transcribing it for the use with the Innes constants) but chiefly in its pioneeringly successful application. The device, having gone entirely unnoticed before, now became most widely applied.