# How to get from the perturbative acceleration formula to the acceleration on the 3 axis in the case of the oblate Earth, considering j2?

If we start from the pertrubative acceleration formula, how do we get the expression for the acceleration for the 3 axis written under that form. I've used the partial derivative for the gradient function , but don't seem to get under that form. Also,for the acceleration on the z axis , why do we have 3- and not 1-. Does anyone has an article with this transformation? • Are you asking 1) How is Eq. 5.1.11 obtained, and 2) Why is there a "3" in the last expression of Eq. 5.1.12 but not in the first two? – uhoh Sep 9 '18 at 3:47
• Yes, to obtain 5.1.12 from 5.1.11, you just need to calculate partial derivatives. Can you show us how you calculated them, so that we can point out what went wrong? – Litho Sep 9 '18 at 12:01
• @AlexandruLapusneanu if you've made some progress on this and think you have an answer, it's always OK to post an answer to your own question, and to accept it as well. – uhoh Jan 28 '19 at 1:57