An arxiv find, via David Hogg (via Facebook, via the internet).
The gravitational force law in the Solar System
Authors: Jo Bovy (NYU), Iain Murray (Toronto), David W. Hogg (NYU, MPIA)Abstract: If the Solar System is long-lived and non-resonant (that is, if the planets are bound and have evolved independently through many orbital times), and if the system is observed at any non-special time, it is possible to infer the dynamical properties of the Solar System (such as the gravitational force or acceleration law) from a snapshot of the planet positions and velocities at a single moment in time. We consider purely radial acceleration laws of the form ar= -A [r/r0]-α, where r is the distance from the Sun. Using only an instantaneous kinematic snapshot (valid at 2009 April 1.0) for the eight major planets and a Bayesian probabilistic inference technique, we infer 1.989<α<2.052 (95-percent confidence). Our results confirm those of Newton (1687) and contemporaries, who inferred α=2 (with no stated uncertainty) via the comparison of computed and observationally inferred orbit shapes (closed ellipses with the Sun at one focus; Kepler 1609). Generalizations of the methods used here will permit, among other things, inference of Milky-Way dynamics from Gaia-like observations.
So: instead of noting that an inverse-square behavior for the force of gravity fits the data, assume that gravity obeys an inverse power law and fit for the power. (It’s two, to within the errors.) Of course there have been many higher-precision tests of gravity in the Solar System than this one; the new thing here is that the data are simply the positions and velocities of all the planets at one particular moment in time, no direct dynamical measurements. A little bit of Bayesian voodoo magic, and there you go.
What I want to know is, what makes the authors so convinced that their instantaneous kinematic snapshot is valid tomorrow?
March 31st, 2009 at 6:20 pm
Simple. Because it is April 1.
Clear skies, Alan
March 31st, 2009 at 6:24 pm
April 1 is only hours away now….so funny things are supposed ti happen,,
March 31st, 2009 at 6:32 pm
The authors should have also cited Bertrand Russell who was the first one, to my knowledge, to raise the possibility that there might be a teapot somewhere between Jupiter and Saturn.
March 31st, 2009 at 6:33 pm
I wonder how would that affect the precision of the exponent?
March 31st, 2009 at 6:34 pm
Simple. Laplace’s Rule of Succession:
http://en.wikipedia.org/wiki/Rule_of_succession
March 31st, 2009 at 6:43 pm
Positions and velocities, to be more precise.
March 31st, 2009 at 6:45 pm
Matt, thanks, I’ll check that reference.
March 31st, 2009 at 6:50 pm
http://arxiv.org/pdf/0903.5321v1
March 31st, 2009 at 6:58 pm
bjswift, the paper you cite cannot be correct. First of all, the random selection of papers in the references seems to have a kind of bias.
Second, and most important, not too long ago a state legislature (I think Indiana’s) already disposed of that problem. Any variation of pi would be illegal…
March 31st, 2009 at 7:00 pm
joye, you’re right, I’ll fix it.
March 31st, 2009 at 7:44 pm
“what makes the authors so convinced that their instantaneous kinematic snapshot is valid tomorrow?”
mmm… wait till tomorrow and see if the positions you predict based on your estimate are valid, I guess. Unless I’m missing something else here.
I think maybe the debate that this would’ve generated in the authors’ labs and elsewhere would be whether computers and other intelligent systems in the future can rapidly churn out physical laws from sampled data without extensive analysis by humans. This paper here may have resulted from those kinds of discussions, and MAY be a simple proof-of-concept. And what better way to prove this hypothesis than demonstrate its ‘power’ in rediscovering Newton’s g-law.
After some serious archive searching, I remember this old blog post here, written way back in the day:
http://blogs.discovermagazine.com/cosmicvariance/2008/07/01/what-good-is-a-theory/
March 31st, 2009 at 9:06 pm
Sean/joye, I was trying to figure out how they were doing it with just positions. My head was starting to hurt. Much better.
March 31st, 2009 at 9:18 pm
oh… velocities. ok.
March 31st, 2009 at 9:20 pm
Blogs are notoriously untrustworthy.
March 31st, 2009 at 9:27 pm
As long as it’s blogs that are untrustworthy, and not bloggers.
April 1st, 2009 at 6:42 am
umm, if you only look for an instant, how do you measure the velocity? Guess that is a variation on the “valid tomorrow?” question. Perhaps the suggestion that it only works on 4/1 is the kindest answer.
April 1st, 2009 at 6:52 am
The authors’ point is fully valid in principle, and familiar to those who have studied comparitive dimensionality (like, what kinds of orbits with two or four spatial dimensions “D” and hence power laws g = GMr^(1-D). If the solar system looks about what it does right now and has been in existence for a long time, any other power law (within some range) other than 1/r^2 leads to instability. No, you don’t need the velocities to know that the planets couldn’t be arranged as they are now under a different power law. The only thing I could puzzle over is the degree of precision in the expected exponent.
You can get this general point from reading Barrow and Tipler’s classic, The Anthropic Cosmological Principle. Indeed, that point is part of the AD argument that life couldn’t have developed under other laws of gravity.
BTW, so I don’t think it does or should have anything to do with April 1.
April 1st, 2009 at 7:15 am
uncle sam – it obviously has something to do with april 1 as the kinematic snapshot in use is from that date
April 1st, 2009 at 7:50 am
Well – I suppose it’s not a coincidence about April “1.0″, but the general point is still valid “in principle” as I stated: other power laws create instability, check up on it. The planets likely would be thrown out of the solar system or wander around enough that they wouldn’t likely keep a nice Titus-Bode style arrangement (note: a “snapshot” does show the current distances, and if you make the assumption those distances are most likely “typical” …)
Why then these authors would make fun of that, I don’t know. Maybe they follow the questionable temptation to make fun of what sounds cutesy (the way many conservatives like to make fun of liberal ideas that sound “squishy” or wealking-sympathetic.) Just remember one thing: the fact that someone presents a point in jest doesn’t prove it is inherently invalid anyway, it just shows their attitudes. “Ad hominem” works in all directions.
BTW, didn’t Newton say the solar system should be unstable anyway (from planets pulling on each other) even with inverse square? Well “there it is” so what happened with all that?
April 1st, 2009 at 8:56 am
apthorp, you can measure velocities by redshift. Useless for the solar system, but if you want to derive properties of galaxies this approach may be useful. Waiting for Earth to complete a significant fraction of its orbit is one thing, waiting for the sun to do the same around the galaxy, well, you’d need a lot of patience.
April 1st, 2009 at 9:14 am
Not having read the paper, the answer to your last question, “what makes the authors so convinced that their instantaneous kinematic snapshot is valid tomorrow?” is “We’re assuming that today’s snapshot is typical”. Indeed, it would be very unlikely for it to fail to be.
April 1st, 2009 at 10:47 am
Why do we assume that any phyical laws remain valid from day to day?
April 1st, 2009 at 11:10 am
Not being a an expert in any of the fields these authors claim to be, I still strongly suspect this paper is an elaborate hoax: phrases like “Newton’s result is therefore
arguably more impressive than any results we present in this short note.” and
“The first force-law inference in
the Solar System (Newton 1687, and also work by contemporaries, particularly Hooke, who
may have priority)”, seem to be something of a giveaway……
Still it’s clever and funny.
April 1st, 2009 at 12:27 pm
But isn’t the solar system actually resonant?
April 1st, 2009 at 1:16 pm
uncle sam, it’s not about whether the method used is correct or not, it’s more that it’s completely silly to put so much effort into finding the power law of the gravitational interaction using some strange Bayesian analysis.
Now that I’ve completely ruined the joke, I’ll supply a funnier one:
http://www.youtube.com/watch?v=3agYeT-T9co
April 1st, 2009 at 1:42 pm
Okay, I will explain the joke.
Clearly there are better ways to test the power law of gravity, or derive Kepler’s laws, than looking at an instantaneous snapshot of the Solar System and making a Bayesian analysis.
However, there are many astronomical objects that are not Keplerian (because they aren’t point masses) where you might like to derive the power law of the potential. For example, the Milky Way galaxy. Furthermore, for systems on a galactic scale, the timescale is so long that essentially we only observe an instantaneous snapshot; we can’t observe a significant fraction of a Milky Way satellite orbit. The techniques derived in the paper may be useful for applying to problems such as estimating the Milky Way’s mass from observations of objects orbiting it, as the last sentence of the abstract points out.
April 1st, 2009 at 6:30 pm
Best sendup of Bayesian nonsense ever.
April 1st, 2009 at 7:52 pm
>>Best sendup of Bayesian nonsense ever.<<
Typical of a pope to deny logic.
April 1st, 2009 at 7:58 pm
>>Why do we assume that any phyical laws remain valid from day to day?<<
Things that change from day to day aren’t often called physical laws. That is all.
April 2nd, 2009 at 4:07 am
I was wondering: How were the gravitational masses of planets historically measured? If they are inferred from Newton’s law of gravity with observations of planetary motion then isn’t that a circular argument when it comes to disproving Newton in favour of general relativity using observations of planetary motion (the precession of the perihelion of mercury)?
What I mean is if you’re choosing M to give best fit between theory and data then how can you use that same data to show that the theory, calculated with said value of M, doesn’t fit? If you had an independent way of measuring M then I can understand that, but historically I’m still puzzled as to how masses of planets could be calculated and the mercury problem was so accurately known without this circularity.
April 6th, 2009 at 1:51 am
ask a stupid question… ?