Why Phi? – the three planets of the Kepler-47 circumbinary planet system

Posted: May 16, 2019 by oldbrew in Analysis, Astrophysics, Phi
Tags: , ,

Kepler-47 system [Image Credit: NASA/JPL Caltech/T. Pyle]


Astronomers have discovered a third planet in the Kepler-47 system, securing the system’s title as the most interesting of the binary-star worlds, says NASA’s Exoplanet Exploration team.

Using data from NASA’s Kepler space telescope, a team of researchers, led by astronomers at San Diego State University, detected the new Neptune-to-Saturn-size planet orbiting between two previously known planets.

With its three planets orbiting two suns, Kepler-47 is the only known multi-planet circumbinary system. Circumbinary planets are those that orbit two stars.

Continued here.
– – –
Now at the Talkshop let’s take a quick look at the data.

The first two exoplanets found in this system were named ‘b’ and ‘c’ as usual. But recently ‘d’ was spotted in the middle, so in order of distance from the system centre it’s b,d,c.

Anyway, the point here is that the orbit ratio of d:c is 1:1.6180838 (within very small error margins in the data) or 1:Phi (Phi = 1.6180339~, aka the golden ratio).

Another way of putting it is that for every 2.618 orbits of d there is 1.618 orbit of c and 1 (2.618 – 1.618) synodic conjunction in that time period.

This ratio may offer a maximum of stability to the two planets. It’s believed binary stars often eject planets from their neighbourhood.

These two planets also have a semi-major axis (distance from system centre) ratio of 1:square root of 2 (= 1.414~).

So, a very interesting start to the analysis of multi-planet circumbinary systems – assuming of course that others are found sometime.

Data source: exoplanet.eu [click on ‘3 planets’]

Short NASA animation of the Kepler-47 system can be found here.

[Note: this is a revised version of an earlier post on April 16th, following a data update yesterday].

Comments
  1. oldbrew says:

    Tatooine is a fictional desert planet that appears in the Star Wars space opera franchise. It is beige-coloured and is depicted as a remote, desolate world orbiting a pair of binary stars, and inhabited by human settlers and a variety of other life forms.
    https://en.wikipedia.org/wiki/Tatooine

  2. oldbrew says:

    Circumbinary castaways: Short-period binary systems can eject orbiting worlds

    The shortest-period binary star system around which a circumbinary planet has been discovered was Kepler 47, with a period of about 7.45 days.

    http://www.washington.edu/news/2018/04/12/circumbinary-castaways-short-period-binary-systems-can-eject-orbiting-worlds/
    – – –
    From the paper abstract:
    All of the orbits have low eccentricities and are nearly coplanar, disfavoring violent scattering scenarios and suggesting gentle migration in the protoplanetary disk.

    https://iopscience.iop.org/article/10.3847/1538-3881/ab0ca0

  3. David A says:

    Just curious if any Phi relationships have been observed in the orbital relationships between binary stars?

  4. oldbrew says:

    David A – if there’s some data I’ll have a look.

  5. David A says:

    Thank you!

  6. oldbrew says:

    The Orbital Elements of a Visual Binary Star

    Whilst astronomers regard the brighter component as
    fixed and map the motion of the fainter one around it,
    in reality, both stars in a binary system move in ellipses
    around the common centre of gravity. The size of the
    ellipse is directly proportional to the mass of the star
    ,
    so in the Sirius system, for instance, the primary has a
    mass of 1.5 M, the white dwarf companion 1.0 M and
    so the size of ellipses traced out on the sky are in the
    ratio 1.0 to 1.5 for the primary and secondary (Figure
    7.1). The ratio of the masses is inversely proportional
    to the size of the apparent orbits (see eqn 1.1 in
    Chapter 1), so this gives one relation between the two
    masses.
    [bold added]

    Click to access binary_orbit.pdf

    1.0 to 1.5 = 2:3

    In the example given later, the ratio of ω the argument of periastron to Ω the position angle of the ascending node is: ω = 130°.9, Ω = 80°.9 [see fig. 7.6 in the link].

    130.9 / 80.9 = 1.6180469

    However this looks like a fluke as it’s only an example.
    – – –
    NASA: Deriving Kepler’s Formula for Binary Stars

    https://imagine.gsfc.nasa.gov/features/yba/CygX1_mass/binary/equation_derive.html


    The distance between the center of mass and m1 is a1 and between the center of mass and m2 is a2

    Then it gets a bit tricky 😎

  7. oldbrew says:

    David A: the answer is here…

    The two stars inside the binary system have the same orbital period around the center of mass.
    . . .
    the two stars always stay on opposite sides of the center of mass.

    https://www.astronomynotes.com/starprop/s10.htm

    The orbit sizes and therefore speeds are different, that’s all – depending on the masses of the two stars. Size of ellipse is inversely proportional to mass (larger mass = smaller ellipse, etc.).

  8. David A says:

    Thank you!! And actually makes sense.

  9. oldbrew says:

    Our Sun also has an orbit, but instead of a close binary star it depends mainly on the conjunctions (alignments with the Sun) of Jupiter and Saturn together, which occur every 9.93 years on average.

    When they align on the same side of the Sun, the Sun is in/near the middle of a ~10 year outer arc, and when on opposite sides the Sun is in/near the middle of a ~10 year inner loop. IOW a repeating arc-loop cycle of ~20 years. The arcs and loops can take +/- a year or two from the average to complete.

    The Sun’s orbit can extend as far as 2 solar radii from the solar system barycentre in any direction, mostly depending on where the four giant planets are relative to each other at any given time.

    Green line = solar motion path (arc-loop-arc shown here).

  10. David A says:

    Oldbrew, apparently some of the orbital relationships break down at MoND distances.

    “There has been a great observational study done recently by Hernandez et al. (see: http://arxiv.org/abs/1105.1873). They have looked at wide binary stars and found that when they are separated by 7000AU or more, so that their accelerations decrease below 2*10^-10 m/s^2, then their behaviour becomes non-Newtonian, in that their orbital speeds are so large that the centrifugal (inertial) forces separating them should be greater than the gravitational pull inwards from the mass that we can see, so they should zoom off to infinity. A similar behaviour is seen in galaxy rotation curves, which deviate from Newtonian behaviour below this same acceleration. For these simple binary systems, it is hard to see how dark matter (DM) could kick in at a particular acceleration, and Newton and MoND both predict only about 1/10th of the orbital speeds seen. This provides a experimentum crucis, and so I have recently been testing MiHsC on these data: because of their low acceleration, MiHsC predicts a decrease in the stars’ inertial masses so they manage to orbit each other at the faster speed without inertia separating them. The orbital speed predicted by MiHsC is still only 1/2 of that seen, but this is much better than the 1/10th from Newtonian dynamics and MoND. I have just today submitted an abstract on this to the UK’s …”

  11. oldbrew says:

    MoND is a dud, IMO. Dark matter doesn’t exist, or at least no-one can find it which seems a strong hint. Mass can be detected 😐

  12. David A says:

    Could be, yet not certain how that changes the observations of W.B.?

  13. oldbrew says:

    Here’s the Miles Mathis version FWIW.
    http://milesmathis.com/mond.html

    This is mentioned:

    Click to access 1106.1397v2.pdf