### geodesic

(equivalent to a straight line in curved space)

A **geodesic** is a generalization of a straight line,
a "shortest possible path", which in flat Euclidean space
is indeed straight, but in curved spaces (or surfaces)
that is less clear.
The concept is used for the shortest paths
on the surface of the Earth
and for such paths within the curved space of general relativity.
In the former case, the fact that the Earth is not
a perfect sphere adds complication and using
an oblate spheroid as the shape of the surface
allows for more accuracy.

In GR, the path of a particle (or electromagnetic radiation)
when no accelerating force other than gravity is present
is a *geodesic*.
GR treats gravity by conceiving space and time as a
**spacetime** such that the effects of gravity are due to geometry,
i.e., an object affected by gravity and otherwise uninfluenced
is following a geodesic.

Two points in spacetime (i.e., each an instantaneous event, each at
some point in space) can be separated in a **time-like** manner,
i.e., a geodesic exists that could be traveled, or in
a **space-like** manner, i.e., too far apart to be reached
in the given time difference since it would require
superluminal motion (faster-than-light travel).

(*mathematics,geometry*)
**Further reading:**

http://en.wikipedia.org/wiki/Geodesic

http://en.wikipedia.org/wiki/Geodesics_in_general_relativity

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