Beijing ( , ) and New York City ( , ) lie at nearly the same latitude
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Vector calculus and field geometry · Tensors and differential geometry
Invariance, Ch The metric, the connection and geodesics
Problem
Beijing (39.9∘N, 116.4∘E) and New York City (40.7∘N, 74.0∘W) lie at nearly the same latitude. Model the flight between them as the great-circle route on a perfectly spherical Earth of radius R⊕=6371km, idealising both cities as lying exactly on the parallel λ0=40.0∘N, one at longitude 116.4∘E and the other at 74.0∘W.
((a)) Find the longitude separation between the two cities, measured the short way round.
((b)) Find the length of the great-circle route between them.
((c)) By symmetry the highest point (vertex) of this great circle lies exactly midway in longitude between the two cities. Find the latitude reached there.
((d)) Find the length of the alternative route that follows the parallel λ0=40.0∘N the whole way between the same two longitudes, and compare it with the great-circle length.