If centrifugal force were the factor for the mentioned variation in
g, then we have the following identities:
gpole = ggrav
gequ = ggrav - acf,
because the centrifugal force is zero on the poles, according to the formula:
acf = ω2*r,
and
r = 0 at the poles. At the Equator,
r =
RE (the radius of the RE) and the centrifugal acceleration is directed out of the Earth's axis, i.e. opposite of the gravitational acceleration. That is why they subtract. Using these equations, one can determine the radius of RE if one knows the period of rotation of the Re. This is taken to be
T = 24 h = 86,400 s and angular speed is connected with period of revolution through the formula:
ω = 2*π/T.
Using the above formulas, we get:
acf = ggrav - gequ = gpole - gequ
RE = acf/ω2 = T2*(gpole - gequ)/(4*π2).
Usually, it is customary to express the length of half a meridian. i.e. the distance from the North Pole to the Equator. This length is just a quarter of the circumference of the great circle (2*
π*
RE), i.e.:
L = 1/4*(2*π*RE) = π*RE/2 = T2*(gpole - gequ)/(8*π).
Why do we calculate
L? Because the meter used to be defined through this quantity as ten millionth part of that distance, or, equivalently, this distance is exactly 10 million meters or 10,000 km. But, using the data you provided (g
pole = 9.83 m/s
2 and g
equ = 9.78 m/s
2), we get the following value:
L = 14,900 km
This is a 48.5% discrepancy from the accepted RE figure. Thus, we see that the data you provided is actually inconsistent with the RE model itself. How do you explain this?