What was the original purpose of the Laplace Runge Lenz vector? I understand the components (comparing centrifugal force to gravitational force) and, more importantly, that if you multiply the LRL by the reciprical of the geocentric gravitational constant (or helio..., etc), you get a vector that points towards perigee in a magnitude that tells you your eccentricity. But, as is (before you convert to the eccentricity vector), it seems to be incomplete? If it was designed to calculate an orbit's eccentricity, you would think he would have divided out the geo/helio/etc centric constant right off the bat. The only thing I can think of is that a different method, independent of a geocentric gravitational constant, used to be used to find the eccentricity and that, if the eccentricity were already known, the LRL vector might have been used to calculate the geocentric gravitational constant?