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    Re: The magical maths of Google Maps
    From: Frank Reed
    Date: 2015 Oct 7, 19:16 -0700

    Dave Pike, you wrote:
    "The first time I tried it I got 5,559.8km. After breakfast, I tried again and got 5,567.84km, 10km less than my spherical trig value and 19km less than my geodesic value. So what does this tell us apart from the Earth expands after breakfast?"

    Ha ha. Yes, well, it might expand after breakfast, but in whose longitude?!? Heh.

    I tried a numerical experiment in "plain" Google Maps which reveals a fair bit about how that distance tool works. I picked a spot that's famous for its latitude: the "Mitad del Mundo" monument in Ecuador. Rather than use the location of the monument, I selected a spot close by that is exactly on the WGS84 equator and a rounded longitude. The coordinates of this spot, call it Point A, are 0.000° N, 78.456° W. Then I measured the distance to this point A to a location in Canada east of Lake Huron exactly 45 degrees north of point A on the same meridian of longitude. This spot, Point B, is at 45.000° N, 78.456° W. Using the same procedure that you've described, I find that the distance between A and B is 3109.2 statute miles. And then I visited a spot in the Atlantic east of the mouth of the Amazon, Point C, located on the equator but exactly 45 degrees east from Point A at 0.000° N, 33.456° W. The distance in Google Maps between points A and C, as it turns out, is also 3109.2 statute miles. This tells us two things. First, it shows that the distance tool is providing pure great circle distances since a distance with a large separation in latitude is identical to the distance for the corresponding separation in longitude (the separation is 45 degrees in both cases). So that's good, and it means you can use this distance tool for celestial navigation calculations. The separation distance will, in fact, be identical to the true zenith distance. Also this number tells us that this Google Maps distance calculator is using a value of 6080.2 for the length of one nautical mile in feet (take the separation in statute miles, multiply by 5280 to get feet, divide by 6080.2 to get nautical miles, and then divide by 60 to get degrees... you get 45.000 in both directions).

    Incidentally, as a matter of advice for anyone following along: there's no practical benefit to "ellipsoidal geodesics" meaning the generalization of the great circle path on a sphere to the slightly elliptical form of the Earth. It's amusing but of no use. If you really want a "true" distance between points, use the tunnel distance --the distance measured on a straight line through the body of the Earth. And notice that the "tunnel" path and the great circle path are coplanar...

    Frank Reed
    Conanicut Island USA

       
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