Galactic tide

TL;DR

This paper derives the equations of motion for galactic tides considering a cylindrically symmetric potential, providing formulas applicable to Solar System and Oort cloud studies.

Contribution

It presents a new derivation of galactic tide equations accounting for all components and their interactions, suitable for Solar System modeling.

Findings

Derived equations for galactic tide components.

Provided formulas for accelerations in Solar System context.

Quantified galactic parameters relevant to tide calculations.

Abstract

Equation of motion for the galactic tide is derived under the assumption of cylindrically symmetric gravitational potential of the Galaxy. The paper considers galactic tide both for the galactic plane $x-$ and $y-$ components and also for the normal $z-$ component. The $x-$ and $y-$ components of the acceleration come not only from the $x-$ and $y-$ components of the position of a body, but also from its $z-$component of the position vector. Values of the Oort constants are $A$ $=$ (14.2 $\pm$ 0.5) $km s^{-1} kpc^{-1}$ and $B$ $=$ ($-$ 12.4 $\pm$ 0.5) $km s^{-1} kpc^{-1}$. %(the values hold for the galactocentric distance of the Sun). Mass density in the solar neighborhood, 30 $pc$ above the galactic equatorial plane, equals to (0.117 $\pm$ 0.005) $M_{\odot} pc^{-3}$. The result for the acceleration is written in the form easily applicable to Solar System studies, to the evolution of comets in the Oort cloud.