Established in 1790, Washington D.C. was almost exactly at the population center at that time (see 1810). Now Fairfield is about 200 miles north of the current center of population. This is a good guideline for where the capitol of a country should be placed. The geographic center being important is a concept that originates in modern times. It is not recognized in the ancient texts (Vastu Shasta).
https://en.m.wikipedia.org/wiki/Mean_center_of_the_United_States_population

Rick Shaddock (Professor of Computer Science at (GraduateSchool.edu ) is working on calculations that consider the relatively small, but important population of Alaska and Hawaii. These 2 states would move the Population Center north and west towards Fairfield, Iowa.

Montgomery City, Missouri is just 176 miles south of Fairfield & Vedic City, Iowa.
Edgar Springs, Missouri was named by the Census Bureau as the population center in 2001.

If we consider the population of Alaska and Hawaii, although relatively small, this would move the centroid north west, and nearer to Fairfield, Iowa.

Population Center of the United States

Montgomery City, Missouri 63361

Dr. David Recheson	Research results reference: The Center of the United States and other Applications of Calculus to Geography (PDF) by David Recheson, PhD Associate Professor Mathematics and Computer Science Dickinson University Carlisle, PA 17013
The center of mass (x, y) for a set of n points in the plan, the ith of which has mass mi at (xi, yi) satisfies Using the centroid formula, the population center would be located in Montgomery City, Missouri, approximately 70 miles west-northwest of St. Louis and 175 miles south of Fairfield, Iowa.