RE: Site information why elevation..

Phil Rogers (
Thu, 10 Jun 1999 22:30:57 -0400

Kevin Fetter wrote:
>What elevation are we talking about. There is two types of elevation, one
>above sea level, and one above the ellipsoid. One topographical maps it is
>above sea level, but on a gps receiver it is above the ellipsoid. Don't
>satellite tracking program use the centre of the earth for calculations,
>and when the program tells how high a satellite is, the point used for how
>far the satellite is fom the surface of the earth is the ellipsoid.

That is correct, but the site height is also used for more than just
object altitude displays. From time to time the USGS and other world
geodetic agencies do a survey on the earth to determine (among other
things) the parameters which define the geodetic spheroid, an ellipse of
revolution from which all other measurements are made. This is the same
as the ellipsoid referenced by your GPS receiver. The geoid on the other
hand represents the physical surface of the earth and is subject to
constant change by seismic effects and global warming among other
things. When a site survey is made, the parameters are given with
respect to the spheroid and consist of 5 items, Latitude, Longitude,
Height above the spheroid and two terms describing deflections of the
vertical in each of the north and east directions (which for your
pusposes may be essentially ignored unless you are doing some really
precise work). Through a relatively simple calculation, these survey
parameters may be used to generate a precise site EFG position plus a
set of 9 direction cosines which are used respectively to translate and
rotate an EFG vector designating an object's location in 3D space to a
site centered cartesian system and from that to an Az, El and Range to
be used for directing a mount (or to XY angles in the case of an XY
mount). The reverse is also true (although not applicable to visual obs
which are inherently two coordinate data) in that an AER position and
velocities may be transformed directly to an EFG vector through use of
the same transformation matrix in reverse. The point here is that your
location height is used not just for object altitude measurements but
also (and primarily) for the continual process of generating pointing data.

Altitude measurements are another story and various techniques can be used
to generate values of varying accuracy (with varying computational demands
depending on how frequently the data must be updated). I will not bore you
with that however, unless someone happens to be individually interested.

> My height above sea level is 95 m but, above the ellipsoid it is 62.217 m. A
>small difference, but for lunar occulations, your height is very important,
>for that we use the height above sea level. Sea level and other factors in
>surveying / GPS are being always improved.

This error due to site height (or omission of it) is indeed small and is
easily quantified. It is given by:

Error = DeltaH * Cos (Elevation Angle)

where DeltaH is the error in site Height used and
Elevation Angle is the Elevation Angle to the target.
Error will be in the same units as used for DeltaH.

Phil Rogers