A geodesic (great-circle-sided) triangle is surveyed on the Earth's surface
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Tensors and differential geometry · Tensors and differential geometry
Invariance, Ch Curvature
Problem
A geodesic (great-circle-sided) triangle is surveyed on the Earth's surface, treated as a sphere of radius R⊕=6371km. The triangle's area is measured to be A=500km2.
((a)) Use the Gauss-Bonnet theorem to find the angle excess ∑αi−π in radians.
((b)) Convert the excess to arcseconds (1rad=206265′′).