In the Kepler 47 system, however, the two stars' orbits of one another are nearly circular, and the stars are very close together. The length of their orbits is about 7.5 days, and they are only about 13 million kilometers apart. (For perspective, that is about a quarter of the average distance between the sun and Mercury.) The researchers determined these parameters using Doppler spectroscopy, which measures emitted light to determine how a smaller body exerts gravitational force on a larger body.
To model the planetary orbits, the researchers used numerical models to find the orbits that best fit the planetary transit data collected by Kepler. The inner planet takes about 49.5 days to orbit the stars and is only about 44 million kilometers away from them; the outer planet takes about 303 days and is about as far away from the pair as Earth is from the sun. That puts Kepler 47's outer planet in the habitable region, where liquid water could exist. With such a location, the outer planet might call to mind the Star Wars world Tatooine, but the researchers say that this planet is probably a gas giant, which is not a hospitable environment for Earth-like life. But Fabrycky notes that if you were in a hot air balloon looking through the outer planet's atmosphere, the dual sunset might look like something out of Star Wars, with the two suns positioned very close together at the horizon. And if the planet has a moon, there's a tiny chance that it could support life.
Ellipses are good approximations of the planets' paths, but they are not perfect because the gravitational forces acting on the worlds are not coming directly from the two stars' center of mass. Fabrycky says, "They're almost going on an ellipse, but they wiggle around it a little bit due to the stars dancing around each other." Over time these forces will cause the orbits of the planets—and thus the shape of this distant solar system to evolve. Fabrycky says that it will take only about a century for the system to change substantially. (In our solar system, by contrast, those kinds of changes take tens of thousands of years.)
Going forward, astrophysicists are continuing to use the telescope to search for potentially habitable planets, applying Kepler's laws to describe their motion. Fabrycky expects that in the next few years researchers will be announcing many more exoplanetary discoveries in both single- and multiple-star systems. Astronomers hope that Kepler will help them find answers to big questions about our universe. Are all binary star systems planar? What different processes give rise to planets? And of course, is there anyone else out there?
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Reply | Report Abuse | Link to thisGiven 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
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.
Reply | Report Abuse | Link to thisHowever, 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 ?
Dear MR Oldershaw,
Reply | Report Abuse | Link to thisI 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
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!
Reply | Report Abuse | Link to thisrloldershaw: I believe.
Reply | Report Abuse | Link to this
Reply | Report Abuse | Link to thisoldhopalong (Cassidy?),
Thanks, me too.
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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
Reply | Report Abuse | Link to this"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
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.
Reply | Report Abuse | Link to thisCurrent 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
From comment 8
Reply | Report Abuse | Link to thisdissected 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
Reply | Report Abuse | Link to thisVino...,
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
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.
Reply | Report Abuse | Link to thisIn 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?
Reply | Report Abuse | Link to thisFor 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 .