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?
Simple. Because it is April 1.
Clear skies, Alan
April 1 is only hours away now….so funny things are supposed ti happen,,
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.
I wonder how would that affect the precision of the exponent?
Simple. Laplace’s Rule of Succession:
http://en.wikipedia.org/wiki/Rule_of_succession
Positions and velocities, to be more precise.
Matt, thanks, I’ll check that reference.
http://arxiv.org/pdf/0903.5321v1
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…
joye, you’re right, I’ll fix it.
“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/
Sean/joye, I was trying to figure out how they were doing it with just positions. My head was starting to hurt. Much better.
oh… velocities. ok.
Blogs are notoriously untrustworthy.
As long as it’s blogs that are untrustworthy, and not bloggers.
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.
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.
uncle sam – it obviously has something to do with april 1 as the kinematic snapshot in use is from that date 😉
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?
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.
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.
Why do we assume that any phyical laws remain valid from day to day?
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.
But isn’t the solar system actually resonant?
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