# Galactic tide in a noninertial frame of reference

## TL;DR

This paper derives the equations of motion and perturbing forces for galactic tides in a rotating noninertial frame, providing tools to analyze comet dynamics in the Oort cloud with a new integral of motion.

## Contribution

It introduces a novel formulation of galactic tide equations in a rotating frame and derives a new integral of motion for modeling cometary dynamics.

## Key findings

- Derived equations of motion for galactic tide in a noninertial frame.
- Presented relations for calculating osculating orbital elements.
- Introduced a new integral of motion for galactic tide modeling.

## Abstract

Equation of motion and the vector of perturbing acceleration (force) for the galactic tide in a noninertial frame of reference is derived. The noninertial reference frame is rotating with a fixed angular velocity $\vec{\omega}$ $=$ $-$ $\omega_{0}$ $\hat{\vec{z}}$ with respect to the inertial frame of reference of the Galaxy. $\vec{\omega}$ is the angular velocity of the solar rotation (rotation of the Local Standard of Rest) around the galactic center, the unit vector $\hat{\vec{z}}$ is oriented toward the north pole of the Galaxy: the Sun is always situated in the plane $y'$ $=$ 0 ($x' - z'$-plane). The equation of motion can be applied to the dynamics of the Oort cloud of comets. Relations for calculation of the osculating orbital elements are presented and a new integral of motion is derived for the conventional approach in modelling of the effect of the galactic tidal field.