A geocacher departs the equator of a spherical Earth on a true heading of 308.6569° traveling along an arch-shaped great circle segment terminating on the exact opposite side of the Earth from his starting point at an east longitude of 179° 25.901’. In route at the precise apex of the “arch” he passes through the relatively unknown gateway while traveling due west stopping just long enough to grab the cache and sign the log before continuing to his destination.
Two Gateways to the West
The cache coordinates can be determined using a Great Circle Calculator or quite simply through intuition. If you use the great circle calculator method be sure to set the Earth model to “Spherical (1'=1nm)”.
You can check your answers for this puzzle on Geochecker.com.
A special honorable mention on this cache page will go to the first person to log the cache then send me an email detailing how the cache coordinates were determined mathematically without the use of a great circle calculator.
Honorable mention goes to: WalkThisWayWalkThisWay