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11497958   1422.03     10.864432

11497958   1422.05     34.141890         3.142538              π            3.1415926535     0.0301%

26 April 2015: initial postings used 30-Jan-2015 NASA Exoplanet Archive data.
29 April 2015: updated postings used 28-Apr-2015 NASA Exoplanet Archive data.

19 May 2015: updated text (including the "ROPSETI" acronym).

03 Oct 2015: inserted an example above of a non-adjacent planet pair where the period ratio comparison is between a small planet (1422.05; Rp/R_earth = 1.08) and the only giant one in the system (1422.03; Rp/R_earth = 35.38); coincidentally, 1422.05 gets a very high habitability rating in the following reference:

R. Barnes, V. S. Meadows, N. Evans, arXiv:1509.08922v1, 29 Sep 2015.

                           Potential Evidence of Galactic Intelligence
       Ratio of Orbital Periods - Search for Extra-Terrestrial Intelligence

1. Somewhere in our galaxy there are other technically advanced civilizations.
2. Like us, they have always wondered if there is other advanced intelligence in the galaxy.
3. Some civilizations are many technical-millennia ahead of us.
4. Long ago, the need to learn how to control orbits of rogue objects in their solar system (for their own survival) was recognized and they initiated efforts to do so.
(In 2015, Earth is in the “baby-step-stage” to do this with activities like Dawn, the Minor Planet Center, and ideas involving rocket thrusts, gravitational effects, etc.)

Extending orbital control technology over many millennia, it might be expected that:
5. They could have mastered the ability to alter asteroid and comet orbits at will.
6. They could have extended this to include techniques to move moons.
7. They also could have gone the next even grander step and learned how to move planets for various perceived advantages (e.g.: climate control, etc.).
8. Finally, with such planetary control, it’s possible it occurred to them to also adjust the ratio of adjacent planetary periods to universal constants (such as π, e (Euler’s number), etc.) in an effort to signal their presence to the rest of the galaxy.

The following Table of Kepler candidates and/or confirmed exoplanet pairs, whose period ratios are very close to various universal constants, is either (a) intriguing food for thought, (b) a matter of chance (personal communication: Daniel A. Relles), or (c), in the case of Integers, the outcome of mean motion resonance (MMR) (see Table footnotes).  Going forward, it will be interesting to see if continued improved accuracy in determining exoplanetary periods will move these ratios ever closer to the constants.