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?
https://www.marksmath.org/classes/common/MapProjection.pdf
This document gives the mathematics behind the Mercator projection and why it preserves angles.
• Mercator: T(ϕ,θ) = (θ,ln(|sec(ϕ) + tan(ϕ)|))
A latitude 16S gives a distance 0.28295 south of the equator on the rectangular map whereas 41N gives 0.78586.
Now that things are flat, the arctangent should work:
arctan((0.28295+0.78586)/(2pi)) = 9.6540 degrees
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Posted by Jer
on 2024-07-31 08:34:41 |
Another possible solution
