Beam into space digitally coded information that would be useful to extraterrestrial astronomers searching for planets around our sun, assuming they are using the same techniques we currently use to search for exoplanets.
Mass and orbital period of Jupiter and other planets. Eccentricity and orientation of orbits. Diameters of sun and planets for transit (eclipsing) measurements. Albedo for direct imaging.
Although many of these parameters will change over time, especially over the very long time scales of interstellar communication, any current measurements will elegantly be correct for any observations aliens make contemporaneously with receiving the message: the information and the observations travel at exactly the same speed.
Reverse this idea and listen for such digitally coded information from stars around which we have discovered some planets.
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