Spacetime Curvature for a Falling Object near the Earth's Surface
The graphic shows a projection of the path followed by a falling object in four-dimensional spacetime into three-dimensional space. Objects fall because they follow geodesics in this spacetime. They are of maximal length, maximizing proper time. For all trajectories, the initial angle or speed does not matter and the curvature is the same, . Near a very massive object such as a black hole, this value is considerably greater.
"Spacetime Curvature for a Falling Object near the Earth's Surface"
Wolfram Demonstrations Project
Published: October 5 2011