Phileas Fogg III wants to commemorate his grandfather's circumnavigation by going around the world in 80 hours. This will be by airplane, and he wants to start out at 16° South, travel somwhat north of east maintaining a constant direction bearing, and end up at the same longitude at latitude 41° North. This sort of path (constant direction bearing) is called a loxodrome, which maps as a straight line on a Mercator projection.
What should that constant direction bearing be?
If I understand correctly, a Mercator projection is the mapping of a sphere onto a cylinder of the same equator. The cylinder is then unrolled.
We can let the Earth have a radius of 1 unit. The start is tan(16) below the equator. The finish is tan(41) above the equator. The distance parallel to the equator is the length of the equator: 2pi.
The angle is then arctan((tan(16)+tan(41))/(2pi)) = 10.425 degrees N of E.
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Posted by Jer
on 2024-07-30 09:22:26 |
Possible solution
