How did the scientists predict that Uranus was not following its orbit due to neptune.Calculations And Formula

Answer 1

I have only seen the calculations described as "laborious". Basically, Leverrier and Adams compared Uranus's measured positions to its calculated positions, and calculated the position of the assumed perturbing body. I think it was a sort regression analysis with maybe a bit of trial-and-error. The calculations were actually in considerable error regarding the orbit of Neptune, but by luck the search was done at a time when the predicted direction was close.

You can get software to calculate planetary positions from JPL: http://ssd.jpl.nasa.gov/?ephemerides