# Geodesic deviation equation

1. Mar 14, 2008

### ijustlost

I'm a bit stuck with trying to interpret this for acceleration in earths gravity. The question is:

$$D^2 Y^d = R_{abc}^dV^aY^bV^c$$

Let (t, x, y, z ) be the natural coordinates for an observer at a point P just above the
surface of the Earth, i.e. with z measuring height. Explain why at P, $$R_{0101}$$ and $$R_{0202}$$ are approximately −g/RE , and $$R_{0303}$$ is approximately 2g/RE , where RE is the radius of the Earth and g the acceleration due to gravity in non-relativistic theory.

Ok so I assume $$Y = (0, x, y, z)$$ describe the observer and $$X = (1,0)$$
describes the earth. Then we get

$$a_x= g/R_E x a_y= g/R_E y$$

and $$a_z = -2gz/R_E$$

but this doesnt seem to make sense

Last edited: Mar 14, 2008