Re: A weighty subject

[brian whatcott <inet@INTELLISYS.NET>]

At 17:10 10/12/99 -0500, you wrote:
> Suddenly I'm worrying about the definition of g!  Is it the rate at which
> objects fall, or GM/R?  It can't be both!
>
> Using the best data I could find,
>    M  = 5.9736 x 10^24
>    R  = 6371.0   (this is the average (volumetric) radius)
>    G  = 6.6726 x 10-11
>
> So g = GM/R = 9.8201 m/s^2.  I'll grant you that this assumes a spherical
> earth, so 9.81 could be the correction due to oblateness.
>
> However, this ignors the rotation of the earth.  At the equator this
> amounts to a centripetal acceleration of
>   a(c) = (464 m/s)^2 / 6378000 m = 0.034 m/s^2
>
> So the rate at which objects dropped at the equator would fall is
> determined by
>   a = g - a(c)  =  9.81 - 0.03 = 9.78 m/s^2
>
> > From these calculations it looks like g = GM/R, but g is not the
> acceleration of falling objects.  (The other possibility is that GM/R would
> really be closer to 9.84 and the spinning of the earth makes objects fall
> at 9.81 m/s^2)
>
> Thus our freshmen labs should apparently aim for 9.78 m/s^2, not 9.81
> m/s^2!  Indeed, the NASA website I checked for the mass and size of the
> earth listed the "surface gravity" as 9.78 m/s^2.  Only if you are moving
> westward at several hundred km/hr would a dropped object fall at 9.81 m/s^2
>
>
> Tim Folkerts

Absolute values for g are established with reversible pendulums.
Large scale differences can be identified from satellite orbits.
Local differences are noted from spring scales
(fused quartz spring gravimeters)

The value for g at Potsdam Geodetic Institute is thought to be
 well established at 9.81274 m s^-2    Even so in 1957 an
international commission recommended that values based on this
criterion be reduced by about one part in ten thousand.

The equation used to predict g given below is provided with
latitude (lambda) and height above sea level in meters (h)
 as parameters.

g in m s^-2 =
9.80616 - 0.025928cos(2 lambda) + 0.000069cos^2(2 lambda) - 0.000003 h

Base stations are situated world wide for harmonizing values of g
Here are some base determinations:
Greenwich   9.81188
Washington  9.80080
Dehra Dun (Asia)  9.79065
Tokyo       9.79801
Paris       9.80943
Potsdam     9.81262

(derived)
North Pole  9.83216
Equator     9.78030

(Sources: Science Data Book R.M Tennent Oliver & Boyd, Edinburgh
          Physical & Mathematical Tables G R Noakes Macmillan)


brian whatcott <inet@intellisys.net>
Altus OK