# Geodesic deviation

1. Apr 9, 2010

### Isa1

Hi there,

I'm trying to understand the derivation of geodesic deviation given here:

http://wps.aw.com/wps/media/objects/500/512494/supplements/Ch21.pdf

but I can't figure out why x(t)+\chi(t) obeys the geodesic equation (eq.(7)). Of course x(t) does, since it is per definition a geodesic. Could it be that \chi(t) is so small that it is negligible and doesn't change the geodesic character of x(t)?

I'd really appreciate some help. Thanks!

2. Apr 9, 2010

### Altabeh

It is because the point $$x(\tau)+\chi(\tau)$$ is in the beginning of the paper said to be on a nearby geodesic at the same proper time so no matter if $$\chi(\tau)$$ is small!

AB