How does one physically measure geodesic deviation?

Question

From wiki:

one begins by setting up a family of closely spaced geodesics indexed by a continuous variable $s$ and parametrized by an affine parameter $\tau$. That is, for each fixed $s$, the curve swept out by $\gamma_s(\tau)$ as $\tau$ varies is a geodesic. When considering the geodesic of a massive object, it is often convenient to choose $\tau$ to be the object's proper time. If $x_\mu(s, \tau)$ are the coordinates of the geodesic $\gamma_s(\tau)$, then the tangent vector of this geodesic is:

$$ T^\mu = \frac{\partial x^\mu(s,\tau)}{\partial \tau} $$

Can or how does one physically measure geodesic deviation?

For example if I am undergoing geodesic motion and see a mirror undergoing motion and shoot a light beam at it. I measure the distance (metric) between the mirror and me and not the deviation vector.

Answer 1

Good question. I am not an expert in GR, but according to this paper, you could e.g. take two satellites orbiting earth which have systems for relative distance measurements built in. You then compare their measurement results to predictions for geodesic deviation in a Schwarzschild background that models earth.