Mathematical encoding within multiresonant planetary systems as SETI beacons

Abstract

ABSTRACT How might an advanced alien civilization manipulate the orbits within a planetary system to create a durable signpost that communicates its existence? While it is still debated whether such a purposeful advertisement would be prudent and wise, we propose that mean-motion resonances between neighbouring planets – with orbital periods that form integer ratios – could in principle be used to encode simple sequences that one would not expect to form in nature. In this letter, we build four multiresonant planetary systems and test their long-term orbital stability. The four systems each contain six or seven planets and consist of (i) consecutive integers from 1 to 6; (ii) prime numbers from 2 to 11; (iii) the Fibonacci sequence from 1 to 13; and (iv) the Lazy Caterer sequence from 1 to 16. We built each system using N-body simulations with artificial migration forces. We evaluated the stability of each system over the full 10 Gyr integration of the Sun’s main-sequence phase. We then tested the stability of these systems for an additional 10 Gyr, during and after post-main-sequence evolution of the central stars (assumed to be Sun-like) to their final, white dwarf phase. The only system that was destabilized was the consecutive integer sequence (system i). The other three sequences therefore represent potential Search for Extraterrestrial Intelligence (SETI) beacons.