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A person travelling through a geodesic.

  1. Jan 18, 2007 #1
    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]
     
  2. jcsd
  3. Jan 18, 2007 #2

    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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