Math Details for Mercury & Suns
( The Curved Spaces of Newton and Einstein )

These pages present the mathematics which was used to create the images on the previous page.

The aim was to illustrate the so-called advance of perihelion of mercury's orbit as predicted by Einstein's general theory of relativity, and to show a calculation for the Newtonian orbit using a curved Riemannian 3-space. The former aim is the reason Mercury was chosen, and the former aim is also the reason that the plural of sun appears in the title: The advance of perihelion will be greatly enhanced if the sun is replaced by a star which is 1,000,000 times more massive. To further exaggerate the effect, the parameters were changed to make the Newtonian orbit more eccentric, but without changing the perihelion.

The pdf Document
Note: Each link is to one pdf file which is one page of the document.
page02, page03, page04, page05, page06, page07, page08, page09, page10, page11, page12, page13, page14, page15, page16