Why Do We Need Geodesics?
More Generally, in the Presence of an Affine Connection, a Geodesic Is Defined to Be a Curve Whose Tangent Vectors Remain Parallel If They Are Transported...
More generally, in the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it. ... Geodesics are of particular importance in general relativity. Timelike geodesics in general relativity describe the motion of free falling test particles.
What are geodesics used for?
Geodesics are of great importance with wide applications, e.g. dictating the path followed by aircraft (great-circles), how light travels through space, assist in the process of mapping a 2D image to a 3D surface, and robot motion planning.
What is a geodesic and why is it important in general relativity?
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.
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