### 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 that is not so clear cut.
The concept is used in determining shortest paths
on the surface of the Earth (a 2d curved "space")
and for 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, a geodesic is the path of a particle (or electromagnetic radiation)
when no accelerating force other than gravity is present.
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 unimpeded or otherwise
affected is following a geodesic.

Two points in spacetime (i.e., each an instantaneous event 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, or requiring
"faster-than-light travel".

(*mathematics,geometry*)
http://en.wikipedia.org/wiki/Geodesic

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

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