# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Pear shaped Earth
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?  Where's that?  See: http://www.city.fredericton.nb.ca/
===============================================================================

```
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