Page:Theory of the motion of the heavenly bodies moving about the sun in conic sections- a translation of Gauss's "Theoria motus." With an appendix (IA theoryofmotionof00gaus).pdf/27

 FIRST BOOK.

GENERAL RELATIONS BETWEEN THOSE QUANTITIES BY WHICH THE MOTIONS OF HEAVENLY BODIES ABOUT THE SUN ARE DEFINED.

FIRST SECTION.

RELATIONS PERTAINING SIMPLY TO POSITION IN THE ORBIT.

1.

In this work we shall consider the motions of the heavenly bodies so far only as they are controlled by the attractive force of the sun. All the secondary planets are therefore excluded from our plan, the perturbations which the primary planets exert upon each other are excluded, as is also all motion of rotation. We regard the moving bodies themselves as mathematical points, and we assume that all motions are performed in obedience to the following laws, which are to be received as the basis of all discussion in this work.

I. The motion of every heavenly body takes place in the same fixed plane in which the centre of the sun is situated.

II. The path described by a body is a conic section having its focus in the centre of the sun.

III. The motion in this path is such that the areas of the spaces described about the sun in different intervals of time are proportional to those intervals. Accordingly, if the times and spaces are expressed in numbers, any space whatever divided by the time in which it is described gives a constant quotient. 1