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*From*: Bowman_David/tiger_mpc@tiger.gtc.georgetown.ky.us*Date*: Wed, 17 Apr 96 18:19:20 -0400

Well, I took Jack U's advice and and went to the library and looked up the

topic of latitude for myself in various references and learned a few things.

(Thanks Jack for the reminder about proper research procedure.) The results

follow below.

Def. #1: tilt angle of the local horizontal w.r.t. analogous plane on equator

Def. #2: central angle at Earth's center between the location and the equator

Lerner & Trigg, _Encyclopedia_of _Physics_, VCH, (1991): No entry for latitude

_A_Concise_Dictionary_of_Physics_, Oxford Paperback, (1992): latitude= def. #2

_The_MacMillan_Dictionary_of_Measurement_, (1994): latitude= def. #2

_International_Dictionary_of_Geophysics_Vol._2_, (1967): The jackpot! 4 defs.

given

1. geographic latitude= def. #1

2. geocentric latitude= def. #2

(Apparently seismologists used geographic latitude in calculating

epicentral distances until 1936 at which time they switched to geocentric

latitude.)

3. astronomical latitude= a particular refined version of def. #2 such that

the angular momentum vector of the Earth's rotation (rather than its

angular velocity vector) defines the polar axis and the equator is defined

such that the local geoid (local horizontal plane) is parallel to this

axis. The astronomical latitude is the tilt angle of the geoid w.r.t. the

rotational angular momentum vector.

4. geodetic latitude= same as astronomical latitude except that the Earth's

best fit spheriodal surface is used rather than the local geoid to

determine the local horizontal. Essentially, the geodetic latitude throws

away perturbations in the Earth's gravitational field due to all mass

multipole moments beyond the quadrupole.

Definition 3 above is called "astronomical" because it defines the direction

of the celestial poles and the celestial equator on the celestial sphere as

well as the Declination coordinate of each of the heavenly bodies on the

celestial sphere. The angular momentum vector defines the celestial polar

direction as it is less subject to the wobbling that accompanies the angular

velocity vector omega as the earth rotates due to the Earth's inertia tensor

being ansiotropic and the angular momentum not being exactly along one of the

principal axis directions. Over time the North Pole defined by the angular

velocity vector (NPAV) wanders around w.r.t. and near the North Pole defined

by the angular momentum vector (NPAM). This wandering has components with two

different periods. There is the part with a 14 month period which is a

precession coming from the solution of Euler's equations for a freely rotating

rigid body whose angular momentum is not along a principal axis of its inertia

tensor. There is also a part with a seasonal 12 month period due to seasonal

changes in the Earth's inertia tensor caused by redistributions of air, ice,

and snow through out the year. The combined effect of these two components

causes the NPAV to wander around w.r.t. the NPAM with a typical displacement

of about 10 m between them. The NPAM itself also wanders around w.r.t.

perpendicular to the Earth's orbital plane (ecliptic) with a precession period

of about 25 kyr, and on top of this precession is a nutation whose period is

about 41 kyr due to gravitational couplings between the Earth's mass

quadrupole moment and the Sun and the Moon.

Unfortunately, none of all this interesting information has answered my

original question which was which definition of latitude is used by

cartographers in making detailed maps. Also I would like to know which

definition is used by surveyors in determining geopolitical boundaries. (It

seems obvious that the cartographers would use whichever definition that the

surveyors use.) The DMZ between North and South Korea is bisected by the 38th

parallel according to which definition? The 38th parallel of geocentric

latitude should differ by about 18 km from the geographic/astronomical/

geodetic version. A bigger discrepancy would occur between the two versions

of the 49th parallel which separates Canada from the United States along most

of the border.

David Bowman

Georgetown College

dbowman@gtc.georgetown.ky.us

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