5.1b: When is it NOT okay to assume the Earth is a sphere?
Description
This article is from the Geographic Information Systems FAQ, by Lisa Nyman lnyman@census.gov with numerous contributions by others.
5.1b: When is it NOT okay to assume the Earth is a sphere?
A quick test is: Compute the values of R produced by the equation with the
WARNING when you use the highest and lowest latitudes that occur in your
analysis. Compare the results produced by using these two values in your
analysis. If the different results are different enough to cause you to
change your action (or your recommendation, or your interpretation of the
implication of the results, etc.), then assuming the Earth is spherical is
NOT okay.
For most purposes, it is quite satisfactory to treat the Earth as a sphere.
If necessary, an ellipsoid can provide a better approximation. Some
standard textbooks that may be helpful follow (reviews are by Steve
Robertson of Tangent Survey Systems in Canada: stever@mindlink.bc.ca):
Bomford, Guy 1980 _Geodesy_ Clarendon Press, Oxford
ISBN 0-19-851946-X
Review: For geodetic computations, this is pretty well
the standard in English. It's a cookbook and offers no
development, however.
Vanicek, Petr, and Krakiwsky, Edward 1986 _Geodesy, the Concepts_
North-Holland, Amsterdam
ISBN 0-444-87775-4
Review: This offers a great, but quite involved, discussion
of the concepts behind geometrical (and all other) geodesy.
Torge, Wolfgang 1980 _Geodesy_ de Gruyter, Berlin
(translated to English by C. Jekeli)
ISBN 3-11-007232-7
Review: This concentrates mostly on gravimetric geodesy, but
has some geometrical stuff, well explained without too much
mathematics.
Software for solving distance and azimuth problems on the ellipsoid can be
obtained (as of 10/10/96) by anonymous ftp from several sources, two of
which are listed below:
The URL of the National Geodetic Survey (of the National Oceanic and
Atmospheric Administration in the US Department of Commerce) is:
ftp://www.ngs.noaa.gov/pub/pcsoft/for_inv.3d/
Review (by Ronald C. McConnell of Bellcore:
rcmcc@cc.bellcore.com): They have Fortran source and PC
executable versions of both the normal "inverse" great circle
calculations (two lat/long pairs to distance and bearing), and
the less used "forward" calculation (one lat/long pair plus
bearing and distance to the second lat/long pair). They have
both 2-dimensional and 3-dimensional versions of each. The
inverse program works to within a few seconds or a few
minutes, depending on the fortran compiler, of the antipodal
points. The forward program seems immune to any and all
problem locations and pairs of locations. You can choose
among a couple of dozen ellipsoids.
See the read.me file for explanations. The NGS software directory may
contain other listing of interest. Its URL is:
http://www.ngs.noaa.gov/PC_PROD/pc_prod.html/
Case is relevant in many URLs - eg: this one.
Another anonymous ftp source for ellipsoid software is the US Geological
Survey (of the US Department of the Interior), at:
http://kai.er.usgs.gov/ftp/PROJ.4/proj.html
Again, see the README file for explanations. The URLs for the USGS
directory and home page are:
http://kai.er.usgs.gov/ftp/index.html
http://kai.er.usgs.gov/homepage.html
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