Earth is not perfectly spherical, so I think agreement to within 0.2766% is pretty good and I wouldn't worry about it.By the way, my own trick for not having to remember mu is to use "natural" units. Take a convenient orbit as a reference, say a circular parking orbit around Earth at an altitude of 400 km. Use the radius and speed of that orbit as your units of distance and velocity, respectively. Take the time unit to be the orbital period divided by 2*pi (in other words, it's the distance unit divided by the velocity unit). In these units, mu = 1.
... hoping to ovoid the need to remember the value of the gravitational parameter, mu.
where gsurface = 9.80665 m/s2 by definition
Quotewhere gsurface = 9.80665 m/s2 by definitionThis is the definition of a standard value for 'g', but it does not necessarily reflect the actual value of 'g' at any particular point on the earth's surface. (Supposed to be value at 45 degree latitude, but it's off a bit, and the earth isn't a perfect spheroid anyway) I don't know if it could be responsible for all of the 0.2% error, but I imagine it's part of it.
g = mu/r2ge = mu/re2 = 398600.4418 km^3/s^2 / (6371 km)2 = 0.00982025 km/s2 = 9.82025m/s2 which is not g0. Mean radius and standard gravity are separate agreements.
A related question: When a payload is launched into a 185 km or 200 km or any designated LEO altitude, what zero altitude reference do they use? Radius of the launch site, Volumetric mean radius (km), 6371.0 or something else?
Quote from: aero on 08/31/2014 07:14 pmA related question: When a payload is launched into a 185 km or 200 km or any designated LEO altitude, what zero altitude reference do they use? Radius of the launch site, Volumetric mean radius (km), 6371.0 or something else?There's no universally-accepted convention, and this can cause confusion. For engineering purposes, usually the issue will by bypassed by using the center of the earth as reference, e.g. with a Cartesian state vector or osculating orbital elements.
What field of study would concern itself with this and related questions about the physical characteristics of earth?