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\Large {Dynamical screening of interactions in gravitating\\
systems and the ephemeris time.}\\
\large {A.V.Vityazev, A.G.Bashkirov }\\
Institute of Planetary Geophysics, Moscow, Russia.\\
e-mail: abas@orig.ipg.msk.su\\
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Screening of the Newtonian potential of a test moving body
in an homogeneous system of gravitating bodies is investigated on
the base of the collisionless kinetic equation and the Poisson equation.
The modified potential is expressed in terms the test particle velocity
and the gravitational susceptibility of the system. As all bodies in
such a system execute a thermal motion an effective gravitational potential
in the system can be determined by the way of averaging the test body
potential over the body velocities with the Maxwellian distribution
function. It is found that the resulted effective potential not only decays
faster the Newtonian potential but oscillates as well with
the period of order of the Jeans length. A dark matter allowance in the
system gives rise to a significant decrease of the oscillation period.
We discuss here some consequences of the above solutions of the simplest
model problem with no touch with relativistic aspects as before.
1. The form of the renormalized potential causes us to interpret rotation
curves $v(R)$ for our and other galaxies in a fresh manner. Characteristic
oscillations of $v(R)$ for
$NGC\,891,\,4151,\,4236,\,4258,\,5055,\,\,M\,31,\,81$ and many others can
be manifestations of the dynamic screening effects and relevant
oscillations of the renormalized potential ${\Phi}(R)$.
2. The corrections to virial masses of galaxies, their clusters or
super clusters may be significant and run to 10--30 \% drawing together the
normalized density of the University in {\it Hot + Cold Dark Matter Models}
and the demands of the most inflational models:
$\Omega_{infl}=\mu \,[\Omega_s +\Omega_{cd} + \Omega_{hd}]\, \to\,1$
and to the similar effects for models with the Einsteinian $\Lambda$--term.
3. The dynamic screening effect is manifested itself in such systems as
the Solar planetary system as well. It is of some orders more weak due to a
suppressive influence of the central potential $\Phi_\odot$ and small
relative planet masses $m_i/M_\odot<10^{-3}\, (\simeq 2\cdot 10^{-6}$ for
the Earth). Besides, it is complicated by strong differences in masses and
relative distances of the planets. Nevetherless this effect raises the
problem of the ephemeris time drift relative atomic clock time in a new
manner.
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