A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Frank Reed
Date: 2017 Dec 3, 07:04 -0800
David Pike, You wrote:
"If in doubt, use a tape measure."
Right. Or just use a bit of string pulled taut. You can also do this quickly by visual inspection, and this works on a virtual globe, too. Rotate the globe until the start point, end point, and the apparent center of the globe are all on a straight line. That's a great circle.
But back to your tape measure, try it with the antipodal trick that I described. How about a new pair of points: find the great circle from Miami, Florida USA to Jakarta, Java in Indonesia. You could stretch your tape all the way around the globe, or you could start at the antipodes of Miami. Now mark off a course to Jakarta. Measure the course, C, and distance, D. Then from Miami, the course would be 360-C and the distance is 10800-D (that's 180·60-D). Notice that this works because the point antipodal from Miami is necessarily located on the extension of every great circle track from Miami. That is, if I fly from Miami to Jakarta on a great circle and then keep on going, I will pass over the antipodes of Miami not long after. The short, easily-measured track from the antipodes is the remainder of half of the great circle that contains Miami and Jakarta.