  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 $a^{8.25}$.
