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?
Somehow I think the correct solution will need to involve spherical coordinates, but I want to try something else.
The total degrees of latitude of movement to the North is 57 degrees for the whole trip.
By a fun coincidence, this is close to the number of degrees in a radian.
So the travel will be 360 degrees East and 57 degrees North.
The angle whose tangent is 57/360 is 8.99714342106506 degrees, but ...
But I think this is wrong because the distance between longitude lines varies with latitude. So my idea is to make a series of smaller trips, then recalculate the exact position after each incremental trip. Once that formula is discovered, have a program pick a constant angle and then vary it to get closer to the final destination.
I think I'm back to spherical coordinates.
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Posted by Larry
on 2024-07-30 10:46:29 |
thinking ...
