Galactic location from spectrum and red/blue shift

Question

I recently realized that the state of the galaxy as we perceive it from Earth is entirely unique; because of relativity, celestial objects are all viewed with out of date information, but as we observe the sum of them, this information is unique to our position in the Cosmos.

Therefore, would it be possible for a sufficiently advanced civilization (perhaps our own) to calculate the location of the source of observations that included the red/blue shift and spectral output of several celestial objects? I envision a probe that travels at less than relativistic speeds being captured long after its departure, but this might work even for other methods of information transfer.

I think this would merely require that spectral emissions of bodies be sufficiently unique (don't know if that is true) and to be able to calculate the age of the data somehow (half-life? But I think this is usually normalized to the known age of a planet/source of the material that is decaying).

Answer 1

It depends on where and when the probe is captured and read. If it's within a few thousand years and within our own galaxy, photos as suggested by BAR might be enough. Redshift would also work. NASA put a map on the Voyager spacecraft using the position of pulsars.

If the timescale is much longer (millions of years), using a photo of the night sky becomes problematic. The relative position of stars in our galaxy will change a lot. This increases the amount of calculation you'll have to do: basically you'll have to check the view from each star in the galaxy ($10^{11}$) at 1000-year increments. If you have historical records going back that far, good. If not, the calculated positions will become increasingly inaccurate the further back you go.

On these time scales, using redshift from galaxies would be more stable than using individual stars, I suspect.