Shifting eclipses and 3:2 orbital ratio found in giant exoplanets

Posted: May 18, 2015 by oldbrew in Astronomy, Astrophysics

NASA's next exoplanet hunter (TESS)  [image credit: MIT]

NASA’s next exoplanet hunter (TESS)
[image credit: MIT]

Try to imagine Saturn and Uranus orbiting the Sun in 8 and 12 days respectively. Far-fetched? In our solar system, yes, but something very similar has been observed in an exoplanetary star system, as was recently discussed by scientist and blogger Hugh Osborn, one of the co-authors of a study of the surprising 2-planet system.

In his blog post, Osborn notes re the March 2015 solar eclipse:
Calculating something so far ahead seems like an impressive feat but in fact astronomers can precisely work out exactly when and where eclipses will occur for not just the next hundred, but the next million years. Such is the way for most transiting exoplanets too, the calculations for which could probably be valid in thousands of years.

But a new planetary system, discovered by a team that includes Warwick astronomers (including me), doesn’t yet play by these rules. It consists of two planets orbiting their star, a late K star smaller than our sun, in periods of 7.9 and 11.9 days. The pair have radii 7- and 4-larger than Earth, putting them both between the sizes of Uranus and Saturn. They are the 4th and 5th planets to be confirmed in data from K2, the rejuvenated Kepler mission that monitors tens of thousands of stars looking for exoplanetary transits. (36 other planet candidates, including KIC201505350b & c, have been released previously).

But it is their orbits, rather than planetary characteristics, that have astronomers most excited. “The periods are almost exactly in a ratio of 1:1.5” explains Dave Armstrong, lead author of the study. This can be seen directly in how the star’s brightness changes over time. This lightcurve appears to have three dips of different depths, marked here by green, red and purple dips. ”Once every three orbits of the inner planet and two orbits of the outer planet, they transit at the same time”, causing the deep purple transits.

But this doesn’t just make for an interesting lightcurve; the closeness of these periods to a 3/2 ratio also causes other weird effects. “The planets perturb each other and change their period every orbit, so they never quite transit when you expect”, explains Armstrong. These shifts are called Transit Timing Variations (or TTVs).

The size of these TTVs is related to the mass of the planets, and some previous multi-planet systems have been weighed in this way. When the team went back to observe the larger planet less than 9 months later, they found that the transit time had shifted by more than an hour. And their period ratio of 1.5035 means the resulting TTVs are likely to continue increasing over a few years, potentially shifting the system more than a day from its current rhythm.

Full blog post including graphics and animations:
Shifting Eclipses – K2′s Second Multi-planet System | Lost in Transits.

Paper – One of the closest planet pairs to the 3:2 Mean Motion Resonance,
confirmed with K2 observations and Transit Timing Variations: EPIC201505350

Exoplanet discoveries – animation:

  1. oldbrew says:

    ‘their period ratio of 1.5035’

    143 x 1.5035 = 215.0005
    So 143 orbits of the outer planet = 215 orbits of the inner one.
    144:216 (i.e +1 orbit of each planet) would be 2:3 exactly, and 144 is a Fibonacci number.
    215 – 143 (= 72) is the number of conjunctions in the period of 143 outer and/or 215 inner orbits and is half of 144.

    It can be seen from the planetary data that the ratio of the distance from the star (measured in AU) of these planets is very close to 3:4 i.e. 0.077AU : 0.103AU (78:104 = 3:4).

  2. tallbloke says:

    Good find OB. The fact that both the period ratios and orbital distances are close to simple ratios says something about the relationship between the falloff of gravity and orbital resonance too. What would the ratio of distances be if the planets were in a different orbitally resonant relationship such as 2:5?

  3. oldbrew says:

    TB: about 6:11 – like Jupiter:Saturn.

    The orbit ratio is roughly the square root of the cube of the AU ratio.

  4. tallbloke says:

    Nice, so it drops straight out of Keplers 3rd law.

  5. oldbrew says:

    That’s it, and likewise Jupiter’s moons Io, Europa and Ganymede are just inside 8:5 AU ratio (each pair) which gives a 2:1 orbit ratio.

  6. tallbloke says:

    Interesting article on orbital resonance. Very clear explanations

  7. Bob Weber says:

    ren, you’re the gift that keeps on giving! The two proton density spikes (~25/cm^3) showed up on, and hemispheric power also went up to 60GW twice, boosting the Kp index to 5 and 6. That’s a great site with interplanetary shocks listed out. That’ll save me a lot of time going back several years picking them out in evaluating past polar vortex excursions and tectonics.

    If Hans Jelbring’s “Wind Driven Climate” thesis would just show up, life would be grand… 2 months and counting….

    Cool article here guys… it resonates well.

  8. oldbrew says:

    TB: bookmarked that link🙂

    Some of its topics (e.g Resonance in the Asteroid Belt) were discussed here:

  9. oldbrew says:

    Here we have a 3:2 resonance with a conjunction every 24 days, while in our own solar system we have one (Neptune:Pluto = 3:2 orbits) lasting around 495 years.

    Why wouldn’t there also be similar types of resonances at periods between those two? Seems a reasonable bet IMO.