Last month astronomers announced the first discovery of multiple planets orbiting a pair of stars. Binary star systems, which comprise two stars orbiting around a common point, are very common—about half of sun-size stars are thought to be members of binary star systems. But it was only in 2011 that astronomers reported the first confirmed instance of a binary system with even a single planet. The newly discovered system, named Kepler 47, consists of a star about the size of the sun and a smaller companion, orbited by two planets.

The reason it has taken so long to find exoplanets around binary stars isn't because they are rare, but because it is hard for us to see them from an earthly vantage point. The data for the Kepler 47 discovery come from the Kepler space telescope, which orbits the sun, not Earth, so our planet doesn't block its view. The spacecraft's mission is to search for planets in the habitable zones around their suns, hopefully giving scientists a better idea of how many systems have planets that could support life.

Kepler detects exoplanets by measuring the tiny changes in a star's brightness caused by the passage of a body in front of it, à la the transit of Venus last witnessed in June. Thus, Kepler can only find planets whose orbits line up with its line of sight. Otherwise the planet will not alter the star's light from the telescope's point of view. Scientists thereby are limited in how many of these systems they can find; distant stars don't arrange themselves to provide a better view. Daniel Fabrycky, an astrophysicist at University of California, Santa Cruz, and one of the authors of the paper announcing the discovery, says, "the punch line is that there's nothing special about it; planets can form around binary stars, too."

Any description of celestial motion starts with classical physics—specifically, Newton's law of gravitation. This law describes the force exerted on one body by another. It says that the force is proportional to the masses of the bodies and inversely proportional to the square of the distance between them. Because force equals mass times acceleration, one can use these two different descriptions of force to write a system of differential equations that will describe the motions of any number of bodies. The problem of describing their motion is called the n-body problem, where n represents the number of bodies in a system. It is actually not too hard to derive the equations, once given the masses and velocities of a bunch of bodies. But only the 2-body problem yields an explicit answer. The solutions for other values of n have to be found through numerical methods, which lead to arbitrarily accurate approximations, rather than by finding universal solutions to the equations.

A binary star system with two orbiting planets is a 4-body problem. But, Fabrycky says, in the case of Kepler-47 the two planets are so much smaller than the two suns that their masses can be assumed to be zero. Thus, the 4-body problem becomes a 2-body one for the two stars, because the planets don't tug on them very much. The solution to this 2-body problem is for each star to be in an elliptical orbit around the two bodies' center of mass. These orbits are described as Keplerian because Johannes Kepler—the Renaissance astronomer for whom the spacecraft is named—first noticed that the planets in our solar system have elliptical, not circular, orbits.

(At left, a simulation of two similarly sized stars in elliptical orbit around their center of mass, the red cross. Source: Wikimedia Commons/Zhatt)

12 Comments

1. 1. rloldershaw 10:50 AM 9/11/12

   
   Given the masses of the two stars and the morphology of this system, Discrete Scale Relativity proposes that Kepler 47 is a self-similar analogue to a LiH molecule with one of its shared electrons in a highly excited Rydberg state.
   
   Do I expect anybody to believe me?
   Not yet.
   
   But it is a discrete fractal world.
   
   Robert L. Oldershaw
   http://www3.amherst.edu/~rloldershaw
   Discrete Scale Relativity

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2. 2. vinodkumarsehgal 12:35 PM 9/11/12

   Kepler after studying our solar system had come out with Laws of Planetary Motion. One of these Laws states that planets rotate around our Sun in planetary orbits. He did not go into the physical reasons for the planetary orbits. Ideally speaking, for a two part body system, orbits should be circular. But in the case of our solar system having 8 planets, gravitational force acting upon any planet, though arising primarily from Sun, may also arise secondarily from other 7 planets. This secondary gravitation force acting upon in any planet may deviate the orbit from circular to elliptical.
   
   However, in case of Kepler 47, why the binary stars should revolve around common center of mass in elliptical orbit? Further why the two planets should have elliptical orbits ?

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3. 3. vinodkumarsehgal in reply to rloldershaw 01:10 PM 9/11/12

   Dear MR Oldershaw,
   
   I have got some ideas of DSR after reading some articles from your website. However, one thing I can not appreciate is : At cosmological scales at atomic level, at what level to fix the bench mark for the purpose of comparing the analogues? At nucleus? At H or He atom? At molecular level? Then, there are all sort of sub atomic particles -- electrons, protons, neutrons, quarks etc. So from where to start for the purpose of comparing the analogue?
   
   If Kepler 47 is an analogue of LiH molecule, our solar system should also be analogue of some molecule. Astronomers knowledge about Kepler 47 system may be quite rudimentary but they have knowledge of our solar system with fair degree of certainty. So it will be prudent to first find atomic scale analogue in case of our own solar system rather to speak of Kepler 47 system.
   
   Further, in your site you have spoken of DSS at three discrete scales -- atomic, stellar and galactic. In your comment , you are speaking of DSS at planetary level
   
   In case, DSR is ubiquitously true for planetary systems, there should be similarity on various parameters viz mass, distance, intrinsic angular momentum ( spin), speed etc. It implies similarity should hold good for following parameters within molecular and planetary system :
   
   i) Mass of nucleus and mass of planetary stars
   ii) Distance between nucleus and electron in Rydberg or non-Rydberg states Vs distance between star and planets
   iii) Nos of planets and nos. of electron
   iv) Rotational Speed of electron and orbital speeds of planets
   v) Spin of electron and spin of planets
   
   Vinod Kumar Sehgal
   vinodsehgal1957@yahoo.com
   
   

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4. 4. CliffClark 04:49 PM 9/11/12

   Sorry, I may have missed this in the body of the text. This seems to me to be a nice classical description of the movements of the two masses in space. But assuming an Einsteinian system (ie. "gravity wells" - and yes, I am an interested member of the public, not someone who really knows) would the different distances between the two stars at different times in their orbit around the common point contribute to instability of the system as well, similar to the planets? If this is stable, for how long? Why? Second, the scale comparison between the stellar system and the LiH molecule is intriguing. But does that not assume a point-like local mass for the electron - eg. collapsed waveform - and ignore the quantum (non-localized) nature of the electron? Really interesting stuff!

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5. 5. oldhopalong 05:03 PM 9/11/12

   rloldershaw: I believe.
   

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6. 6. rloldershaw 08:45 PM 9/11/12

   
   oldhopalong (Cassidy?),
   
   Thanks, me too.
   ----------------------------
   
   Vino...,
   
   The discrete self-similar scaling equations (determined from observations of fundamental systems at subatomic, atomic, stellar and galactic scales) allow one to relate analogues on different scales. When you are dealing with an infinite self-similar hierarchy there is no "bottom level" or "most fundamental level". All cosmological scales are equally fundamental. You can, however, relate things on different scales, and determine appropriate analogues from different scales, if you have the correct discrete self-similar scaling equations.
   
   According to Discrete Scale Relativity, the Solar System is a self-similar analogue to a Li atom with its outermost electron in a very high Rydberg state with n = 168. If l = 160 there will be 8 peaks in the Schrodinger radial wavefunction. The middle electron has n = 5 and is the surprisingly spherical (S state) outer envelope of the Sun. Presumably the innermost electron is in the groundstate.
   
   All of your questions and many more are answered in full at http://www3.amherst.edu/~rloldershaw . Start with Papers #1 and #2 of "Selected Papers" to get a basic understanding.
   
   RLO
   Fractal Cosmology

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7. 7. vinodkumarsehgal in reply to rloldershaw 02:01 AM 9/12/12

   
   "If l = 160 there will be 8 peaks in the Schrodinger radial wave function."
   
   Are the 8 peaks in the Schrodinger wave function analogues to 8 planets in Solar system? Are the distance between peaks have some DSS with distance between planets? Do energy levels at 8 peaks have some scale similarity with masses of planets?
   
   Why I am posing these questions? Since if DSR is a truly ubiquitous principle of Nature, similarity should be exhibited in all facets of Nature, at least with our Solar system about which we have fair amount of knowledge
   
   There are trillion of stars and and there may be billion of multi planetary star systems. Kepler has started functioning in 2009 only and since than it has discovered about 2000 exoplanets. If DSR is an all pervading fundamental principle, every star and every star system with multi planets should have some analogue.
   
   In fact, fundamental nature of DSR ( if it is really there, I don't know) demands that when stars, planets and galaxies are formed from some nebula, DSR as encoded in the atomic level should govern the formation of stars, planets and galaxies

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8. 8. vinodkumarsehgal 02:26 AM 9/12/12

   I understand and appreciate your quote that in infinite DSR, there is no fundamental or bottom level. One may start with any scale and there may be self similar analogues over as well as below that scale.
   
   Current Physics considers quarks, electrons and neutrinos as the most elementary matter particles. That is another issue if these elementary particles turn our to be some composite particles in future. If the contention as given in the above para is really true, it implies nutrino, electron and quarks ( in the increasing order of mass) in one generation only should have some self similar analogues at above scales at i) atomic/molecular level ii) Stellar/planetary level iii) galactic level. Since matter particles below sub atomic scales ( electron, quarks ) are not yet known, I ignore self similar analogues below the sub atomic scales though this shall violate your principle of infinite scale DSR
   
   From your site, I do not find any examination with such issues.
   
   You will appreciate that for DSR to be a fundamental principle of Nature, it should be

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9. 9. vinodkumarsehgal 02:30 AM 9/12/12

   From comment 8
   
   dissected and examined in detail at all fundamental levels of Nature. If DSR turns out to be applicable at some levels and at other levels it fails then it will prove to be some ad-hoc principle of Nature

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10. 10. rloldershaw 10:43 AM 9/12/12

    
    Vino...,
    
    At http://www3.amherst.edu/~rloldershaw there is a prominent list of 40 "Successful Predictions and Retrodictions". These are all discussed on the website.
    
    Discrete Scale Relativity predicted, in a published paper, that planets would be found orbiting ultracompact stellar-mass objects. Several years later, pulsar-planets were discovered, much to the surprise of the astrophysical community.
    
    In 1987 {Astrophysical Journal 322, 34-36] I predicted that our galaxy would contain a vast population of unbound planetary-mass objects far outnumbering the stars. Sumi et al [Nature 19 May 2011] reported that microlensing research had discovered at least 100 billion unbound planetary-mass objects within our galaxy. Again, much to the surprise of astrophysicists.
    
    In 2000 I posted a paper to arxiv.org (later published) predicting that the lowest mass M dwarf stars would have a highly anomalous and quite diagnostic under-abundance of planetary companions. Observational evidence has increasingly supported this prediction and a paper published in Astronomy and Astrophysics in 2011 (Bonfils et al) has now virtually confirmed this prediction. Again, much to the surprise of astrophysicists.
    
    Discrete Scale Relativity's most crucial prediction (dark matter = primordial Kerr-Newman ultracompacts; 8 x 10^-5, 0.145 and 0.580 solar masses are the primary peaks in the predicted mass spectrum) awaits adequate observational data for a definitive verdict. A related prediction is that the dark matter cannot be "WIMPs", and that prediction has withstood a 30-year onslaught of false-positives and a near-religious faith in the first coming of a "WIMP".
    
    Discrete Scale Relativity has passed every retrodictive test that observations allow and that I have been able to do so far.
    
    Robert L. Oldershaw
    Discrete Fractal Cosmology

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11. 11. vinodkumarsehgal in reply to rloldershaw 12:34 PM 9/12/12

    I had not raised questions on the validity of DSR. I had read these examples of DSR's retrodictive and predictive powers in your web site also.
    
    In comments 7,8 and 9, I had raised some fundamental issues of DSR which somehow your web site does not deals with. Do you find issues as raised by me as irrelevant?
    
    

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12. 12. rloldershaw 06:24 PM 9/12/12

    
    For anyone who might think that Discrete Scale Relativity is worth looking into, here are a couple more motivators.
    
    - Natural Planck mass ( ~ 0.7 times the proton mass); Planck scale M, L and T are all closely associated with the proton
    
    - Resolution of the vacuum energy density crisis
    
    - Explains enigmatic physical meaning of the fine structure constant
    
    - Explains physical meaning of Planck’s constant – its numerical value and physics.
    
    - Definitive predictions for the dark matter mass spectrum of stellar-mass black holes
    
    - Offers a promising path to the unification of GR and QM
    
    - Retrodicts masses of baryons, leptons and mesons at the >99% level
    
    Papers discussing these topics are available 24/7 FOR FREE at: http://arxiv.org/a/oldershaw_r_1 .

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