Sean Breheny wrote:
>
> Hi all,
>
> Ready for another of my OT questions? :-)
>
> I'm trying to find a map or other data that can tell me the local
> gravitational acceleration if I know the lat/lon of a point on the earth.
> In other words, I need to find out the local gravitational acceleration
> to better than 1 milliG in Ithaca NY. So far in searching the web, I have
> not found anything that gives this information (at least not directly, I
> found maps of height above the Geoid but I don't know everything that I
> need to know in order to convert this to simple local gravitational accel).

The problem you're working is something thats been addressed a lot by
the satellite community. Try searching for things like orbit
perturbation theory, gravitational harmonics, orbit propagation, etc...

In school we learned to think of variations in the grav field as
harmonics superimposed over a uniform 1/r^2 field. That makes the whole
thing real simple because you can work to any given accuracy simply by
adding more terms onto the end of the grav potential equations. Of
course, the down side is that you need the proper coefficients for those
extra terms. Fortunately such coefficients exist and can be obtained
from any decent orbital dynamics book. The first book I just pulled off
my shelf has coeffs up to the 4th harmonic, and all the necessary
equations. Here are 3 books chosen randomly from my bookshelf that
should help:

"Orbital Mechanics 2nd Edition", Chobotov, Vladimir A., AIAA Education
Series, 1996
"Fundamentals of Astrodynamics and Applications", Vallado, David A.,
McGraw Hill, 1997
"Orbital Mechanics", Prussing John E., Conway, Bruce A., Oxford Uni
Press, 1993

The first book is the easiest for learning. The 2nd book is the most
detailed and mind numbing. If you use that one be sure to get the errata
list cause it has a history of gratuitous and severe typos.

IIRC correctly the geoid is a sphere with a radius equal to sea level at
the equator and centered at Earth's center of gravity. Which obviously
makes it above ground at the equator by a few (2?) kilometers. It should
be a few tens to hundreds of meters above ground level in NY I think.

Good luck.

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