What is the longest calculation of the value of earths gravity?
Actually Earth’s gravity field g is not… not a constant. The number you cite is just an average and, at that, not a very precise average. When you see someone carry the number out to more than a couple of decimal places, e.g., 9.81 N/kg, the someone either is unaware of the source of that average or willing to overlook how misleading that unwarranted precision is. The gravity field can be found with some precision with Newton’s equation g = GM/R^2, where G is a true constant that holds anywhere in the universe, M is the mass of the gravity source (e.g., Earth), and R is the distance from the center of mass M to where g is determined. As I’m sure you can see g gets weaker with increasing R and stronger with decreasing R. In practical terms, for example, g will be smaller on top of Mt. Everest and larger at the bottom of the Pacific Ocean, if the mass M remains the same. Although the variance in g is small over Earth’s surface, it’s not that small. So it will change from point to point
