Galactic tide and some properties of the Oort cloud

TL;DR

This paper models the Oort cloud's properties considering galactic tides, revealing its mass is less than Earth's, significantly increasing the estimated number of long-period comets, and establishing new relationships between orbital parameters.

Contribution

It introduces a new physical model of galactic tide effects on the Oort cloud, providing revised estimates of comet populations and orbital dynamics.

Findings

Oort cloud mass is less than 1/2 Earth's mass.

Number of long-period comets with q<5 AU is about 50 times higher than previous estimates.

Orbital period and semi-major axis follow a specific relation a^3 P=1 in natural units.

Abstract

The paper deals with several properties of the Oort cloud of comets. Sun, Galaxy (and Jupiter) gravitationally act on the comets. New physical model of galactic tide is considered. The main results can be summarized as follows: 1. Mass of the Oort cloud of comets is less than 1 mass of the Earth ($M_{E}$), probably not greater than 1/2 $M_{E}$. 2. Theoretical number of long-period comets with perihelion distance $q$ $<$ 5 AU is about 50-times greater than the conventional approach yields. Gravity of Jupiter was taken into account in finding this result. 3. Semi-major axis $a$ and period of oscillations $P$ of eccentricity (and other orbital elements) are related as $a^{3}$ $P$ $=$ 1 in natural units for a moving Solar System in the Galaxy. The natural unit for time is the orbital period of the Solar System revolution around the galactic center and the natural unit for measuring the semi-major axis is its maximum value for the half-radius of the Solar System corresponding to the half-radius of the Oort cloud. The relation holds for the cases when comets approach the inner part of the Solar System, e.g., perihelion distances are less than $\approx$ 100 AU. 4. The minimum value of semi-major axis for the Oort cloud is $a_{min}$ $\ll$ 1 $\times$ 10$^{4}$ AU. This condition was obtained both from the numerical results on cometary evolution under the action of the galactic tides and from the observational distribution of long-period comets. If the density function of semi-major axis is approximated by proportionality $a^{\alpha}$, then $\alpha$ is - 1/2, approximately. 5. The magnitude of the change in perihelion distance per orbit, $\Delta q$, of a comet due to galactic tides is a strong function of semi-major axis $a$, proportional to $a^{8.25}$.