### 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}]^{-α}, 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 language | English (US) |
---|---|

Pages (from-to) | 1157-1167 |

Number of pages | 11 |

Journal | Astrophysical Journal |

Volume | 711 |

Issue number | 2 |

DOIs | |

State | Published - 2010 |

### Fingerprint

### Keywords

- Celestial mechanics
- Ephemerides
- Gravitation
- Methods: statistical

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

*Astrophysical Journal*,

*711*(2), 1157-1167. https://doi.org/10.1088/0004-637X/711/2/1157

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

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 711, no. 2, pp. 1157-1167. https://doi.org/10.1088/0004-637X/711/2/1157

}

TY - JOUR

T1 - Dynamical inference from a kinematic snapshot

T2 - The force law in the solar system

AU - Bovy, Jo

AU - Murray, Iain

AU - Hogg, David W.

PY - 2010

Y1 - 2010

N2 - 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]-α, 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.

AB - 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]-α, 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.

KW - Celestial mechanics

KW - Ephemerides

KW - Gravitation

KW - Methods: statistical

UR - http://www.scopus.com/inward/record.url?scp=77649225547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77649225547&partnerID=8YFLogxK

U2 - 10.1088/0004-637X/711/2/1157

DO - 10.1088/0004-637X/711/2/1157

M3 - Article

AN - SCOPUS:77649225547

VL - 711

SP - 1157

EP - 1167

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

ER -