How do you actually measure distances and speeds in curved spacetime?

Measuring something as simple as the distance to a nearby object or the speed of a passing particle becomes deeply ambiguous in curved spacetime — the answer depends on who's measuring and how. This paper assembles a complete, coordinate-free toolkit: general formulas for angles (including relativistic aberration for any observer orientation), physical distances accounting for spacetime curvature, and a geodesic deviation equation valid even for extreme relative motion. It's a reference framework that anyone doing precision calculations near black holes, neutron stars, or in cosmology can apply directly.