Music of the spheres

The or­bital fre­quen­cies of an ex­o­plan­e­tary sys­tem are ar­ranged in near-per­fect fifths.

Cosmos - - Digest -

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.

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