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Re: Pear shaped Earth
From: Richard B. Langley
Date: 2002 Oct 3, 09:22 -0300
From: Richard B. Langley
Date: 2002 Oct 3, 09:22 -0300
Here are 3-term expressions for the distance in km for a degree of latitude and longitude that I developed for the Royal Astronomical Society of Canada Handbook a couple of years ago based on the WGS 84 ellipsoid: 1 degree lat = 111.13295 - 0.55982 Cos[2 phi] + 0.00117 Cos[4 phi] 1 degree long = 111.41288 Cos[phi] - 0.09350 Cos[3 phi] + 0.00012 Cos[5 phi] where phi is the latitude. The series were obtained by truncating the relevant series expansions developed from first principles. The 3-term expressions should be accurate to about 1 centimetre or so for distances on the ellipsoid. I spot checked several values with a table in the American Practical Navigator to confirm correctness. -- Richard Langley Professor of Geodesy and Precision Navigation >David Weilacher wrote: > >> My conclusion from this is that a pear shaped earth has a negligible effect on >> the accuracy of sight reduction. It doesn't matter what distance you are from >> the center of the earth (well there is an over-simplification) as long as the >> horizon is also at the same level. Since the horizon is likely to be only 4 >> to 10 nm away, this pear shape notion becomes moot because you and the horizon >> are at the same height. >> > >Agree with this. > >> so, if I've understood correctly, a degree at >> 10d of lat.is 59.71 nm, and a >> degree at 90d of lat. is 60.007 nm. > > >Woke up in the middle of the night, an attack of logic: if the earth bulges out >at the equator and is flattened at the poles, then shouldn't a degree, expressed >as nm, be longer at the equator and shorter at the pole? > =============================================================================== Richard B. Langley E-mail: lang@unb.ca Geodetic Research Laboratory Web: http://www.unb.ca/GGE/ Dept. of Geodesy and Geomatics Engineering Phone: +1 506 453-5142 University of New Brunswick Fax: +1 506 453-4943 Fredericton, N.B., Canada E3B 5A3 Fredericton? Where's that? See: http://www.city.fredericton.nb.ca/ ===============================================================================