# NavList:

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

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Re: The magical maths of Google Maps
From: Lu Abel
Date: 2015 Oct 6, 21:46 +0000
Hmmm, that's very interesting that the geodesic distance is greater than the great circle distance.  I'm traveling right now with very limited internet access, so I must ask a question that I might look up for myself were I at home:  What is the pole-to-pole distance of the "spherical" earth as opposed to the oblate spheroid (ie, geodesic) earth.  Or, in a similar vein, where do the two intersect -- at the poles, at the equator, or at some intermediate point??

From: David Pike <NoReply_DavidPike@fer3.com>
To: luabel{at}ymail.com
Sent: Tuesday, October 6, 2015 2:37 PM
Subject: [NavList] Re: The magical maths of Google Maps

Frank you wrote.  The only thing you have to double-check with an earth-based mapping product is that they are not being too clever by including ellipsoidal corrections to the distance calculation. If that happens then it's not quite a great circle but awafully close. I haven't checked, but I assume that Google Maps products use the standard spherical great circle calculation.
Yes, if spherical geometry’s hard, ellipsoidal geometry’s almost impossible (Well for me it is).  I see that in November 2000 (that’s only 15 years ago) I completed an MSc assignment to work out and compare: the bearing from London to New York; the bearing of New York to London; the Great Circle distance; and the longitude for the GC lying E/W using spherical trig c.f. the angles and the geodesic using ellipsoidal geometry.  All I had to do it with was a hand-held Casio fx-992s with sin, cos, tan, and 1/x, and it took ten sides of narrow lined A4.  Between 51° 30’ N 000° 05’W and 40° 43’N 073° 59’W I got the Great Circle distance = 5,577.886km and the Geodesic distance = 5,586.662km (I suppose I could now check it out on Google Maps, but it’s cocoa time).  I see that at the time the assessor was kind enough to give me 100/100, but today I can’t understand a word of it.  DaveP

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