Music of the spheres
The orbital frequencies of an exoplanetary system are arranged in near-perfect fifths.
Exoplanet hunters using the Kepler Space Telescope have made an extraordinary discovery: the orbital frequency of five planets in the K2-138 system displays an almost perfect 3:2 ratio, an interval that musicians call a ‘perfect fifth’. The findings were reported in the Astronomical Journal in January.
The ‘orbital resonances’ of K2-138 would make the original Kepler’s heart sing. His 1619 publication Harmonices Mundi calculated musical resonances in the orbits of our Solar System’s planets. The 3:2 interval of K2-138 echoes the perfect-fifth intervals found in songs such as “Twinkle, Twinkle, Little Star”.
Exoplanet systems with orbital resonances have been discovered before. It has often been seen in compact planetary systems and reflects the way the systems develop. Those planets without synchronised orbits would be unstable and knock each other out of orbit.
But K2-138 is the most dramatic example. The five planets, each between 1.6 and 3.3 times the size of the Earth, are so close to their star that the longest orbit is less than 13 days. Like clockwork the periods are 2.35, 3.56, 5.40, 8.26 and 12.76 days, with one planet completing three orbits in the time the next one makes two.
There is a hint of a sixth planet orbiting at about 42 days, raising the possibility of even more planets in the gap. “If you continue the chain it would be 19, 27 and 42,” says lead author Jessie Christiansen of California Institute of Technology.
It is also intriguing that the orbits of K2138 are almost but not quite perfect fifths.
Musicians tune their instruments so they are not quite perfect-fifth intervals to avoid the irritating ‘beat’ phenomenon that happens when tuning is too precise.
According to Christiansen, it is possible the orbits of the K2-138’s planets are just slightly off to avoid being destabilised by the consequences of perfect synchronisation.
The musical scales of the planets were calculated by Johannes Kepler in 1619.