# Post-Newtonian acceleration formula

First of all, I have to say that I know very little about tensors and partial differential equations, as I've never done them at school. I'm developing an application which simulates the motion of bodies that are attracted due to gravitation. For now it uses Newton's law of universal gravitation, but I wanted to add corrections due to general relativity main effects. So, after searching a little on the Internet, I found this link:

http://relativity.livingreviews.org/Articles/lrr-2014-2/articlese7.html

As you can see, there is a sort of huge formula for obtaining the Euclidian acceleration of two particles, and it considers the first orders of Post-Newtonian corrections (3PN). However I have some questions about that.

• My application is supposed to work out every frame the position of N bodies instead of only two. Which modifications should be done in order to make the formula valid for N bodies? (Any help is appreciated!)
• Then I'd like to know what are exactly $r'_1$ and $r'_2$... I mean, in the linked article it explains what they are, but it seems that I couldn't understand very well... they are referred as "gauge constants", but I have no idea how to work out their value.