- TL;DR Summary
- Spatial curvature around a spherically symmetric mass
Suppose I measure the circumference of a circular orbit round a massive object and find it to be c. Suppose I then move to a slightly higher orbit an extra radial distance δr as measured locally. If space was flat I would expect the new circumference to be c + 2πδr. Will the actual measurement (taking the spatial curvature into account) be greater or less than this? and what would this measurement tell me about the local curvature of space in the region? Is there a simple formula relating the change in c with change in r and how might this formula be related to the Schwarzschild metric?