Looking at that little rotating starfield, it reminds me of an idle problem I occasionally think of: "If I was somehow lost in space and found by helpful aliens, what useful information could I provide--from memory--for locating my home planet again?"
The best I can think of offhand are ratios that could help them filter existing records:
1. It's the third planet from the Sun, the majority of it is covered with water, etc.
2. It has a moon 1/6 its mass
3. The largest planet in the system has a little over 70% of all the planetary mass
4. The largest planet in the system is 5.2x further from the Sun than my third-planet
But on a larger scale... Somewhere around the middle distance of an arm in a galaxy? I doubt I would have triangulation distances from major quasars memorized.