A person travelling through a geodesic.

Main Question or Discussion Point

A person travelling through a geodesic. Does experiment some kind of acceleration?, since the geodesic equation analogue to Newton one is:

[tex] \Delta _{u} u =0 [/tex] and in an Euclidean space there's no acceleration for a particle line [tex] X(u)=au+b [/tex]
 

Answers and Replies

pervect
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Someone following a geodesic will be in "free fall". They won't feel any acceleration - if they have an accelerometer, it will also read zero. If you set up a global coordinate system, however, the second time derivatives of the position coordinates will in general be nonzero.

Think, for example, of an object orbiting a central mass in a circular orbit. Such an object is locally in free fall, and could set up a local coordinate system that is nearly inertial over small distances.

In a global coordinate system anchored to the central mass, the second time derivative of the spatial postion coordinates will be nonzero, however.
 

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