The ancient notion of the ‘music of the spheres’ sounds primitive until you learn something about planetary dynamics. Gravity is wondrous and can nudge planets in a given system into orbits that show an obvious mathematical ratio. Two planets in resonance can emerge, for instance, in a 2:1 ratio, where one goes around its star twice in the time it takes the second to orbit it once. Such linkages might seem almost coincidental to the casual observer until the coincidences begin to pile up.
In the exoplanet system at HD 110067, for example, resonance flourishes, so much so that we have six planets moving in a ‘resonance chain.’ No coincidence here, just gravity at work, although an actual coincidence is that just when I finished a post highlighting system dynamics in closely packed environments like TRAPPIST-1 as a ‘brake’ on inbound comets, an international team should reveal HD 110067’s resonance chain. It’s a beauty, for all six planets not only move in harmonic rhythm but also turn out to be transiting worlds. An orbital dance this complex is rare, but even more so is the ability to study such worlds thanks to the happenstance of our viewing angle.
Transits allow us to extract information, and plenty of it, including analysis of planetary atmospheres as light from the central star passes through them. Because complex resonances are in some sense ‘self-correcting,’ they tell us something about the history of the system, for planet migration during the period when the resonance is being established influences the final state of the system. In HD 110067 we have a mother lode of system harmonics around a star that, usefully enough, is fifty times brighter than TRAPPIST-1, where we have seven rocky planets in a resonant chain.
HD 110067 offers up all of this for that highly interesting category of planets called ‘sub-Neptunes,’ about which we’d like to know a lot more. 100 light years away in the constellation Coma Berenices, HD 110067’s resonance chain is obviously complex. The innermost planet makes three orbital revolutions as the second world makes two – a 3:2 resonance. But the chain continues: 3:2, 3:2, 3:2, 4:3, and 4:3, with the innermost planet making six orbits as the outermost planet completes one.
Image: A rare family of six exoplanets has been unlocked with the help of ESA’s Cheops mission. The planets in this family are all smaller than Neptune and revolve around their star HD110067 in a very precise waltz. When the closest planet to the star makes three full revolutions around it, the second one makes exactly two during the same time. This is called a 3:2 resonance. The six planets form a resonant chain in pairs of 3:2, 3:2, 3:2, 4:3, and 4:3, resulting in the closest planet completing six orbits while the outermost planet does one. CHEOPS confirmed the orbital period of the third planet in the system, which was the key to unlocking the rhythm of the entire system. This is the second planetary system in orbital resonance that CHEOPS has helped reveal. The first one is called TOI-178. Credit and copyright: ESA.
Untangling this particular chain was not easy. The astronomers used data from both ESA’s CHEOPS mission and the TESS space observatory to nail down the system architecture. Data from TESS determined the orbital periods of the innermost worlds to be 9 and 14 days. Observations from CHEOPS tagged planet d at 20.5 days and thus demonstrated that while the innermost planet revolves 9 times around the star, the second revolves six, and the third planet four times. The periods of the three outer planets could then be deduced as 31, 41 and 55 days respectively, with further analysis of the TESS data showing that no solution other than the 3:2, 3:2, 3:2, 4:3, 4:3 chain would work. Ground-based observations supplemented the TESS and CHEOPS data.
The analysis was led by Rafael Luque (University of Chicago) and published in Nature. Says Luque:
“This discovery is going to become a benchmark system to study how sub-Neptunes, the most common type of planets outside of the solar system, form, evolve, what are they made of, and if they possess the right conditions to support the existence of liquid water in their surfaces.”
TOI-178 offers a five-planet resonance chain that may include a sixth world in this system of transiting planets in the constellation Sculptor, some 200 light years out. The paper on HD 110067 takes note of the fact that resonant architectures like these imply a situation that has remained unchanged since the birth of the system, making them useful laboratories for planet formation and evolution. The planetary radii at HD 110067 range from 1.94 that of Earth to 2.85 times as large (1.94R⊕ to 2.85R⊕), and the low densities found in the three planets whose mass has been measured point to the likelihood of large atmospheres dominated by hydrogen.
Image: Tracing a link between two neighbor planets at regular time intervals along their orbits creates a pattern unique to each couple. The six planets of the HD110067 system create together a mesmerizing geometric pattern due to their resonance-chain. © CC BY-NC-SA 4.0, Thibaut Roger/NCCR PlanetS.
Ann Egger (a graduate student at the University of Bern and a co-author of the paper on this work) notes what is ahead in the study of this system:
“The sub-Neptune planets of the HD110067 system appear to have low masses, suggesting they may be gas- or water-rich. Future observations, for example with the James Webb Space Telescope (JWST), of these planetary atmospheres could determine whether the planets have rocky or water-rich interior structures.”
The sheer beauty of the HD 110067 system comes across in the animation below:
Image: To-scale animation of the orbits of the six resonant planets in the HD110067 system. The pitch of the notes played when each planet transits matches the resonant change in orbital frequencies between each subsequent planet. The relative sizes of the planets is accurate, although their true size compared to the star is much smaller. Also available at https://www.youtube.com/watch?v=2rrODAG7nmI.
The paper is Luque et al., “A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067,” Nature 623 (November 29, 2023), 932-937 (abstract).
Is there any advantage in having orbital resonance in scheduling interplanetary flight between the worlds? I’m thinking of regular schedules where each planet can have regular flights to other planets with possible planetary rendezvous within a long journey, making the resonance attribute the equivalent of fixed geographical positions we use for connecting transport hubs like cities, shipping ports, and airports.
Given that these resonances are stable, could an advanced ETI create such resonant orbits by gently reconfiguring planetary orbits over time? Would it need to be done almost simultaneously, or one planet at a time?
On a much smaller scale, and doable with our technology, if there is an operational advantage of such resonant orbits, could we position large space habitats to have the equivalent orbital resonances even though gravity would not be a factor, with the habitats needing dynamic positioning to maintain their orbits?
Somewhat similar in broad concept to our local Interplanetary Transport Network and Mars cyclers such as Buzz Aldrin’s Aldrin cycler . . .
https://en.wikipedia.org/wiki/Interplanetary_Transport_Network
https://en.wikipedia.org/wiki/Mars_cycler
And as an additional passing thought, such gently reconfigured resonant planetary orbits might be yet another target for SETI searches. Yes, it wouldn’t necessarily rule in ETI as opposed to natural processes, but it could be an additional data point to consider with others in assessing whether there possibly is (well, “is” relative to our time of observation) or was ETI in a system.
Hi Alex
Moving an inner planet would cause all the planets in the sequence to change to match, since the resonance is more stable than orbital states nearby the resonance.
I’m not sure about the utility of a resonance sequence for regular traffic – the relative angular velocity is what sets the time-table for return trajectories. Sounds like a task for an astro-dynamics post-doc or grad-student to ponder.
Looking at the video, there are cases where several planets like up to allow the shortest travel times with fast ships. The layovers might be a concern, but no different from the days when “the next sailing vessel to Europe will return in 6 months”. Of course, the schedules will depend on spaceship velocities, and as with airline flights today going through hubs, you can go point-to-point with a charter flight to reduce flight times for extra cost.
I cannot imagine this is any harder than the various trajectory calculations to minimize robot probe mission times or the “gravity highways” calculation to minimize energy. What are supercomputers for?
Is it a coincidence that the planetary alignment in Image 2 roughly approximates a Fibonacci spiral or golden spiral? Especially when the curvature is carried on into the star itself.
Wikipedia finally put the data up for HD 110067.
https://en.wikipedia.org/wiki/HD_110067
Interesting that it is a K0V star, so variable. Maybe as old as 12 billion years and a magnitude of 6.5 in the infrared which should make for a good target for the JWST.
A quibble with the “sonification” presented in the video: many of the notes have been shifted by an octave or multiple octaves, to produce a scale-like collection of pitches instead of a spread-out chord. Depending on whether you sonify the inner planets as lower pitches and the outer planets as higher ones, or vice-versa, the harmony suggested would be (from bottom to top, transposed arbitrarily to begin on C3):
C3-G3-D4-A4-D5-G5 (a voicing of C6/9(no3))
or
C3-F3-Bb3-F4-C5-G5 (a voicing of Csus7)
Each 3:2 resonance between adjacent planets gives a perfect fifth, and each 4:3 resonance gives a perfect fourth.
Fascinating! Thanks, jonW.
Glad that’s interesting. For comparison’s sake, the Trappist-1 system has the chord:
C3-G3-C4-G4-D5-B5-G6 (a very 80’s G/C voicing)
or
C3-Ab3-F4-C5-F5-C6-G6 (Fm(add9)/C)
again depending on whether the outer orbits are mapped to the low end (the first chord) or the high end (the second chord).
Well, now we know the clockwork Nirvana home of the Dalek hating Mechanoids ;)
Wow
This sure is an interesting system. I’ll be looking forward to more images of the planet sizes and graphics explaining this system. Be interesting too see if the outer ones fall into the habitable zone too.
Thanks Edwin
This is the second 6 resonance chain, after TOI-178:
https://exoplanet.eu/catalog/toi_178_b–6858/
to
https://exoplanet.eu/catalog/toi_178_g–6858/
which is currently observed by JWST:
https://www.stsci.edu/jwst/phase2-public/2319.pdf
The davantage of HD 110067 is that it is brighter and closer.
So to review?
This particular resonant system is much akin to Trappist 1 and the Galilean moons, actually. Significantly as well, though, it involves rather hot near-Neptune sized planets around a K star rather than an M or something like the jovian system. And, both Trappist 1 and HD110067 appear to be very ancient, the latter characterized as “pristine”. Likely there are some more instances as yet undetected, since these local detections are result of transit measurements,
1 in a 100 instances, based on likelihood of the stellar ecliptic alignment with our line of sight.
With such symmetry the observer can’t help wondering if there were an artificial element to these configurations. If I recall correctly, Trappist as a configuration is about 6 billion years by estimate and this HD is billions older. Odds are, this is a fallout of a natural process rather than some sort of intervention. And perhaps as suggested, intrinsic to the processes of circumstellar disks on their way to planet formation. Decades ago, when IR and UV observations were scarce, many astronomers were then skeptical that planets could emerge out of the clearing process at all.
And now we’ve got sets of perfect planets emerging like rabbits out of a magician’s hat.
This beauty is fascinating and must have delighted Pythagoras ;) So, do you think there’s a hidden harmony up there? And if we exist, isn’t it to appreciate it ?
Thank you Paul, for this nice article.
There may be two reason these planets form resonant chains.
First they exist deep in the gravity well of the star.
Second, both HD 110067 and TOI-178 have high mass planets, which may mean they all have large magnetosphere. Since they are also deep in the magnetosphere of the stars, could there be a magnetic connection involved…
The inner two planets pass each other at 2 million miles and the outer two at 5 million miles. That’s a lot of magnets passing very close to each other and a lot of torque…
Giant generators???
HD 110067 is a wide hierarchical triple system.
We report that HD 110067, the recently announced host star of a resonant sextuplet sub-Neptunes, is not a single star as claimed in the discovery paper, but
a wide hierarchical triple. The K0 V planet hosting star (V = 8.4 mag, d = 32 pc) has
a companion at a wide projected separation of 13400 au. This companion, namely
HD 110106, is a slightly fainter (V = 8.8 mag) K3 V type 8-year period double-lined
spectroscopic binary. The secondary in this spectroscopic binary is contributing a
significant amount of flux and has a measured high mass ratio.
https://arxiv.org/abs/2312.04599