Dynamical inference from a kinematic snapshot: The force law in the solar system

Jo Bovy, Iain Murray, David W. Hogg

    Research output: Contribution to journalArticle

    Abstract

    If a dynamical system is long-lived and non-resonant (that is, if there is a set of tracers that 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 system (such as the gravitational force or acceleration law) from a snapshot of the positions and velocities of the tracer population at a single moment in time. In this paper, we describe a general inference technique that solves this problem while allowing (1) the unknown distribution function of the tracer population to be simultaneously inferred and marginalized over, and (2) prior information about the gravitational field and distribution function to be taken into account. As an example, we consider the simplest problem of this kind: we infer the force law in the solar system using only an instantaneous kinematic snapshot (valid at 2009 April 1.0) for the eight major planets. We consider purely radial acceleration laws of the form a r = -A [r/r 0], where r is the distance from the Sun. Using a probabilistic inference technique, we infer 1.989 < α < 2.052 (95% interval), largely independent of any assumptions about the distribution of energies and eccentricities in the system beyond the assumption that the system is phase-mixed. Generalizations of the methods used here will permit, among other things, inference of Milky Way dynamics from Gaia-like observations.

    Original languageEnglish (US)
    Pages (from-to)1157-1167
    Number of pages11
    JournalAstrophysical Journal
    Volume711
    Issue number2
    DOIs
    StatePublished - 2010

    Fingerprint

    inference
    solar system
    tracers
    kinematics
    tracer
    distribution functions
    eccentricity
    dynamical systems
    gravitational fields
    planets
    planet
    intervals
    moments
    orbitals
    energy
    distribution

    Keywords

    • Celestial mechanics
    • Ephemerides
    • Gravitation
    • Methods: statistical

    ASJC Scopus subject areas

    • Space and Planetary Science
    • Astronomy and Astrophysics

    Cite this

    Dynamical inference from a kinematic snapshot : The force law in the solar system. / Bovy, Jo; Murray, Iain; Hogg, David W.

    In: Astrophysical Journal, Vol. 711, No. 2, 2010, p. 1157-1167.

    Research output: Contribution to journalArticle

    Bovy, Jo ; Murray, Iain ; Hogg, David W. / Dynamical inference from a kinematic snapshot : The force law in the solar system. In: Astrophysical Journal. 2010 ; Vol. 711, No. 2. pp. 1157-1167.
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