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?
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.
Best sendup of Bayesian nonsense ever.
>>Best sendup of Bayesian nonsense ever.<<
Typical of a pope to deny logic.
>>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.
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.
ask a stupid question… ?