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*From*: David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>*Date*: Thu, 19 Aug 2004 12:57:38 -0400

Regarding site checking site that Bob notes:

Regarding:

| As part of your answer find a formula for the heading angle of the

| geodesic connecting 2 arbitrary fixed points (of known latitude

| and longitude) on the earth's surface as measured by an observer

| a one of those points

Use this on-line calculator to test your answer:

http://www.vwlowen.demon.co.uk/java/circle.htm

Bob Sciamanda

I wonder if this calculator calculates things using a spherical

earth approximation (as my problem above assumed), or if it actually

uses the formula for calculating geodesic distances and headings for

a surface which is an oblate spheroid. In the latter case there are

two different versions depending on the definition of the latitude

angle used. The common geographic/astronomical latitude measures

the angle between the tangent plane at some point on the surface and

the plane tangent plane to the equator at the same longitude. But

the geodetic latitude measures the central angle at the center of

the earth between a ray from the center through the surface point of

interest and a second ray from the center to a point on the equator

at the same longitude. If an accuracy of about 1% or so is

required a spherical earth approximation is plenty adequate, but if

an accuracy to within 1/10 of a percent is required on some long

distance paths then the spherical earth approximation is not

sufficient because the earth has an oblateness of about 1/298.

BTW, it is substantially more challenging to do the problem of

finding formulae for heading angles and geodesic distances on an

oblate spheroid of revolution. Regardless of which definition of

latitude is used the geodesic heading/distance formulae can be

relatively simply converted into the corresponding formulae for

the other definition of latitude because there is a relatively

simple formula connecting these two different latitude angles to

each other.

Anybody up for doing some spheroidal geometry problems? Recall

the Cassini spacecraft orbiting Saturn is dealing with a planet

that has a 10% oblateness at the surface of the cloud deck and

has a gravitational field that possesses a significant

quadrupole moment contribution.

David Bowman

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