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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
Where is the gravitation finished?
The critical mass of gravitation.
Introduction.
The law of gravitation is universal, but it is not all-embracing.
Clouds do not fall on the earth because cloud droplets are not act by
gravitational force.
The critical mass depends on tension of gravitational field. The
smaller tension of gravitational field the larger critical mass and on
the contrary.
mcr  L 
R2
M
The rings of planets are formed by particles with critical mass coming
from their satellites.
The critical masses of particles for every planet and satellite are
calculate, if their masses and distances from the Sun are known.
The clouds of planets can consist of water, ice, snow, sulfuric acid,
sand, frizzed ammonia and methane.
The more number of satellites and the less their sizes and masses the
more number of rings around the planet and the larger sizes of
particles in them.
The solar system is surrounded by the clouds of comets with critical
mass relatively the Sun.
Critical masses of gravitation and corresponding sizes of particles
disposed near planet and its satellite.
Introduction.
The world, in which we live, strong obeys laws of nature.
Nothing disturbs uniform movement of planet in a circle around the
Sun. The astronomers predict the solar eclipses with large precision.
We know the time of great opposition of the Mars, when this planet
comes nearly to the Earth. One of most distant planet of solar system
the Neptune was discovered by mathematical calculations. The
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
trajectories of flight of interplanetary stations to the Moon, the
Venus, the Mars, the Jupiter were calculated using laws of ballistics
very precisely. The laws of heavenly mechanics are beyond any doubt.
But there are events and objects, which do not obey laws of the
Newton’s mechanics. They are small particles and bodies filling
interplanetary and interstellar spaces. The part of them moves under
the action of gravity of satellites, planets, and stars. Another part
with certain critical mass ignores gravitational action of large
heavenly bodies. For instance, the clouds consisting of small water
particles are spilled by rain, when the latters will have masses more
certain critical one. In this case, the water particles are acted by
attraction of the Earth. The rings of planets are formed from
particles with critical masses, which are thrown out by their
satellites. The comets staggering our imagination come flying at
distant outskirts of solar system where they are bodies with critical
masses relatively to the Sun. The particles and bodies with critical
masses play an important part in the Universe.
The law of gravitation is universal, but it is not all-embracing.
The law of gravitation acts between particles of dust and
between massive bodies - planets. The stars in the Galaxy and galaxy
also obey the law of gravitation. However, the study of cosmic space
by means of interplanetary stations discovered interesting regularity.
It was found that the further the particles from the Sun, the more the
particle sizes in the planet atmosphere and in rings of major planet.
In very dense atmosphere of the Venus the particle sizes and droplets
of acidic clouds are small, whereas in the rare Martian atmosphere the
dusty storms raise very large grain of sand to high altitude. The
Jupiter ring is inaccessible for Earth-based observations, because of
small particles forming this ring, while the Saturn is surrounded by
numerous splendid rings consisting of massive blocks of ice.
What is at the bottom of such particle size distribution in the
solar system? It is necessary to ignore the radiation pressure force,
because the ratio of latter to the gravitation force is independent of
distance from the Sun. Probably, the observed particle size
distribution in the solar system depends on the tension of the
gravitational fields formed by the Sun, planets and satellites. It
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
should be assumed that the particle having mass that is smaller than
critical one is not attracted by the planets and satellites. In the
nature, we often observe such particles. These are cloud droplets,
particles in rings of major planet, at last, comets.
Clouds do not fall on the earth because cloud droplets are not act by
gravitational force.
Everyone observes the fanciful behavior of clouds. They can
join together, and then destroy. They can fly with large velocity, but
at windless days, they can be in the air on one place. Only from dark
clouds, the droplets of rain fall on the earth. The small droplets
fall very slowly; large ones fall with great velocity. There is
sufficient difference between cloud and rain droplets.
Nonprecipitation water clouds consist of droplets with radii from 4 to
25-30 microns. The mean size of precipitation droplets is from about
200 to 500 microns with a very broad distribution. The cloud droplets
grow very slowly, if their sizes are smaller than 10 microns. But if
the sizes of cloud droplets increase up to 30-40 microns, these
droplets begin to fall with coalescence growth producing
precipitation. Thus, the radius of droplet, which is equal to 30-40
microns, is critical. The droplets with smaller sizes are not acted by
gravitational force. Undoubtedly, this conclusion is seditious. The
opponents can produce the following argument: the clouds do not fall,
because they are supported by rising air flows. But is known that the
clouds are pierced by rising and descending air flows and they must
destroy and fall. The clouds do not fall, because the cloud droplets
are weightless. The opponent can tell that the speculative conclusions
cannot be basis for fundamental law. It is necessary to have the
direct argument in order to demonstrate weightless of cloud droplets.
In order to convince weightless of cloud droplet we try to weigh it on
a balance. But before to weigh this microscopic small ball, we
calculate its mass. The mass of cloud droplet is approximately equal
to 0.0000002
{2x10-7}g. It is very small mass. The mass of rain droplet is
ten-hundred time greater: from 10-6 to 10-5 g. Let us assume that by
means of microscope we put down cloud droplet on very precision
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
balance. We cannot weigh cloud droplet, because the balance does not
have a sensation of its weight. The sensibility of any balance does
not exceed 10-6 g. It means that the cloud droplet is not acted by
gravitational force, because the principle of balance is based on
action of gravitation. Thus, the mass of cloud droplet with radius
from 30-40 microns equal to 2x10-7g is critical for the Earth.
Does the gravitational force act on the molecules of air and
steam of water, which are much smaller than cloud droplets?
The gravitational force acts on the gas and steam of water as
physical bodies, in which molecules are joined together. Only on the
top of rare atmosphere the molecules of air and steam of water are not
joined one with together, therefore they are not acted by gravity, and
these molecules can come into cosmic space. In this way, our planet
loses atmosphere.
The critical mass depends on tension of gravitational field. The
smaller tension of gravitational field the larger critical mass and on
the contrary.
Thus, we have determined the critical mass of particles
disposed near the Earth. Is the critical mass the same for another
planets and their satellites? Obviously no, because the tension of
gravitational field in the solar system changes from one point to
another one. The gravitational field in the solar system is determined
by the Sun, planets and their satellites. Let us consider a particle
located near a planet or its satellite. When the distance from the Sun
increases, a particle critical mass must increases to the same degree
as gravity decreases; i.e. a critical mass rises to the second power
of the distance from the Sun.
In the presence of a planet or a satellite, near which a
particle is disposed, the magnitude of a critical mass decreases. As
far as the distance of a particle from a planet is insignificant as
compared with the distance from the Sun, the effect of a planet mass
on the tension of gravitational field should be taken into account.
Thus, a critical mass of a particle located near a planet or its
satellite obey the expression:
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
mcr  L 
R2
M
In this expression mcr is a critical mass of a particle, M is
mass of a planet or a satellite, R is the distance between the
particle {a planet or a satellite} and the Sun, L is a constant.
The rings of planets are formed by particles with critical mass
coming from their satellites.
Now, let us consider the behavior of a particle if its mass is
larger, smaller or equal to critical one. If the mass of a particle is
larger than critical one, a particle will fall on surface of a planet
at the velocity calculated from the Stock’s equation. {This equation
accounts the resistance of air}. If the mass of a particle is smaller
than critical one, a particle can come on the top of atmosphere, and
then - into cosmic space. If the mass of a particle is equal to
critical one, with the same probability a particle can fall on the
surface of a planet or come into cosmic space. The atmosphere of the
Earth and another planets are filled by huge quantity of aerosols,
which are thrown out by volcanoes at eruption. Rising on the top of
atmosphere the particles with critical masses can circulate there a
long time. The part of them accumulates on the surface; another part
comes into cosmic space. A source of aerosols is also the large
meteorites. At collision of a meteorite with surface of a planet or a
satellite huge kinetic energy is formed. The part of this energy turns
into thermal one; another part is passed to small particles formed at
collision. These particles obtain large velocity, and they can come
into cosmic space, if their mass is smaller or equal to critical one.
The behavior of particles in the interplanetary space is of two kinds.
Or coming to the Sun they will burn, or {and that is much probable}
they will fetch up at the gravitational field of nearest large planet,
for which the critical mass is smaller. Approaching gradually to a
planet, these particles begin to revolve on it. In this way the rings
of planets are formed. Although the eruptions of volcanoes and the
collisions with huge meteorites are very rare, the large quantity of
dust and different fragments are accumulated on the orbit of major
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
planets during tens and hundreds million years. In due course, the
orbit of particles comes down and latters fall on the surface of a
planet. Thus, the rings of planets are dynamic formation, which lose
and acquire the particles simultaneously. We observe enchanting fixed
picture of planet surrounded by rings.
The critical masses of particles for every planet and satellite are
calculate, if their masses and distances from the Sun are known.
In order to calculate the critical masses of particles located
near planets and satellites, it is necessary to determine a constant L
in the expression. Substituting the known value of critical mass for
the Earth mcr =2x10-7g, the value of mass of the Earth M= 5.976x1027g
and the distance of it from the Sun R=1.496x1013cm in the expression,
we specify constant L =5.35x10-6g2/cm2. Then, from expression we
calculate the absolute critical masses of particles disposed near the
planets and satellites. The results of calculation are summarized in
the Table. The sizes of particles with critical masses are calculated
too. In the Table the sizes are given for particles, which consist
both of the matter of the planet and satellite {dry land} and water
{for the Venus, Earth, Mars} or ice {for the Jupiter and other planets
and satellites}. The Table includes the satellites with a radius that
is greater than 50 km. It is unreasonable to include small satellites,
because it is very difficult to expect the volcano activity on them
and considerable ejections of particles due to erosive meteorite
impacts. In the Table for planets the critical masses and sizes are
given for particles, which are in rings of planets?
The clouds of planets can consist of water, ice, snow, sulfuric acid,
sand, frizzed ammonia and methane.
Practically only the planets have the exclusive right on
atmosphere. From the satellites, only the Titan has the dense
atmosphere. From the planets, only the Mercury has not atmosphere. The
satellites and small planets lose their atmosphere very fast because
of small gravitational force. Besides, the gases go out from bowels of
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
small heavenly bodies also fast because of small masses and sizes.
From bowels of large planets, the gases go out a long time and they
are held out by large gravitational forces a long time. If on planet
volcanoes act and the losses of gases are small, the density of
atmosphere can be considerable. Such event occurs on the Venus where
the atmospheric pressure is very high. The vigorous volcano action is
observed on the Io - satellite of the Jupiter. In due course, the Io
will surround itself more or less dense atmosphere. In the same time,
we observe the losses of atmosphere by the Mars. At one time on this
planet the huge volcanoes acted, it was raining; the rivers flowed in
valleys. The volcanoes burn out, and the atmosphere gases came into
cosmos. At present, the density of Martian atmosphere is in hundred
times less than the Earth one. On the Earth due to the moderate
volcano action and comparatively small losses of gases into cosmos the
favorable atmosphere for life was formed. If the humanity would not
break the equilibrium of atmosphere by unreasonable actions, the Earth
will serve for shelter of living things.
On the Mercury the volcano, action is absent; therefore, this
planet has not atmosphere. The Mercury is bombarded by meteorites
always because of absence of atmosphere. Therefore, near the Mercury
the particles with radius of 30 microns must be in the state of
weightless. The concentration of such particles depends on frequency
of collisions of meteorites with the surface of the Mercury. The sizes
of droplets and aerosols in atmospheres of planets depend on the
altitude of their situation. On the top of atmosphere, the submicron
particles predominate, which must come into cosmos. At the surface of
a planet, the quantity of large particles increases, and they fall on
surface gradually. That proves correct by observation of the Venus
atmosphere. According to the Earth-based observations above 60 km from
surface of this planet the submicron particles predominate, below the
particles with radius of 1-2 microns appear. That proves correct by
observation from interplanetary stations. In the dense Venus
atmosphere, the clouds consisting of sulfuric acid float across the
sky. The American interplanetary station Pioneer recorded the droplets
with radius of from 4 to 18 microns in the clouds of the Venus. The
observed sizes are consistent with the predicted sizes, which is
reflected in the Table for the Venus.
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
The Martian atmosphere contains insignificant amount of water.
Therefore, in the calm atmosphere of the Mars the clouds are silicates
with a mean particle radius of several microns {according to
observations of American interplanetary station Mariner-9}. But the
calm is not characteristic for the Martian atmosphere. On the Mars,
great dust storms arise periodically. During dust storms enormous
amount of silicate, particles are raised to a high altitude. The dust
storms continue a long time and astronomers have time to estimate the
sizes of silicate particles flying in the Martian atmosphere. During
the dust storm of 1971 particles with a radius groom 1 to 40 microns
have been observed. The upper limit of suspended particle radius was
about 100 microns. Such large particles can maintain in very rare
Martian atmosphere due to a great critical mass and corresponding
sizes of particles {the predicted radius is about 60 microns for
silicate particles}. This value is close to observed one.
The Jupiter is covered by ten-tenth clouds. The clouds of
Jupiter mostly consist of ammonia ice and ammonia water. There are
only submicron particles with a mean radius of about 0.01 microns in
the Jupiter stratosphere. A mean particle radius from 1 to 1.5 microns
in the aerosol layer has been determined using the polametric
observation in the Jupiter’s polar region. The expected mean particle
radius in the ammonia ice and ammonia water clouds is greater than 10
microns. According to measurements made by means of interplanetary
station Voyager-1, the radius of ammonia ice particles in the Jupiter’s
clouds is from 3 to 30 microns. The predicted sizes of particles in
the Jupiter’s atmosphere are close to the expected ones for ammonia ice
particles. The enormous mass of the Jupiter forms large tension of
gravitational field, which allows being in weightless only to very
small particles.
There are very few experimental data concerned with microphysics
of the Saturn’s clouds. It is known to be difficult to find the
particle size from the Earth-based observations. In upper layer of
Saturn’s atmosphere, there are the particles with radius from 1 to 3
microns. The microphysics of lower layer is unknown. It can be seen
from the Table, that microphysics of the Earth’s and Saturn’s clouds
must be similar.
There are very few observations of the cloud layers of the
Uranus and Neptune. The structure and sizes of aerosols in the haze of
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
the Uranus, atmosphere are unknown. Our estimations shows that the
particle sizes in the atmospheres of the Uranus and Neptune must be
greater than 100 microns.
The more number of satellites and the less their sizes and masses the
more number of rings around the planet and the larger sizes of
particles in them.
According of theory of author all planets have the rings, if
there are the satellites. Only two planets- The Mercury and the Venus
- have not the rings because of absence of satellites. The Earth also
has the ring, which is formed by the Moon. At the altitude from 200 to
300 km from the surface of the Earth the dust belt exists consisting
of small particles. The Moon are bombarded by meteorites continually
because of absence of atmosphere. At impacts the formed large
particles fall on the surface of the Moon, the small ones come into
cosmos, and then they are attracted by the Earth, for which the
critical mass is smaller than that one for the Moon. By this way, the
dust belt is formed around the Earth.
The Mars possesses two satellites: the Phobos and the Demos.
However, it is difficult to assume great ejects of particles from
small areas of these satellites and the formation of dust belt around
the Mars. Therefore, the Mars has no ring as the Mercury and the
Venus.
The gigantic Jupiter is surrounded by the massive satellites:
Io, Europa, Ganimede and Calisto. According to author’s calculations
the volcanoes of the Io can erupt the particles with a maximum radius
of 0.5 mm The volcanic action on other satellites is not found, but at
impacts with meteorites the particles of the same sizes can come into
cosmos. However, the size of most amounts of particles is equal to
several microns. Therefore, the Jupiter’s ring is inaccessible for the
Earth-based observations. Only the rough estimations of sizes of
particles in Jupiter’s ring were made by astronomers from several
microns to several part of millimeter. The author’s calculations agree
with astronomical observations.
The more number of satellites and the smaller their sizes and
masses the more number rings around the planet and the larger sizes of
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
particles in them. The Saturn is graphic evidence. It has huge suite
of satellites and magnificent rings. According to author’s
calculations, the big particles with a radius from 0.5 to 1.5 mm come
into cosmos from the surfaces of the Saturn’s satellites. Collecting on
the orbits around the Saturn, these particles collide with each other
and form huge blocks of ice and snow, because of the surfaces of
numerous satellites are covered by ice. The particles with a radius
from 1 to 10 mm and blocks with size to 20m were observed from
interplanetary station Voyager-2.
The ring particle sizes of the Uranus are uncertain. It is
supposed that the rings can be made of organic matter or frozen
methane ice. The ring particle sizes are photometrically acceptable
{from millimeters to meters}. When the Voyager-2 made its flyby of the
Uranus, it has revealed that the Uranus, rings system is covered with a
dense dust envelope. According to author’s calculations, the relatively
small satellites of the Uranus can generate particles with a radius
from 2 to 13 mm. The predicted particle sizes are consistent with the
lower limit of the observed particle sizes. There is very little
information on the Neptune’s ring. It is supposed that the ring can be
fragmented and discontinuous, with most of the ring material
congregated at proffered longitudes. According to author’s calculations
based on the expression the satellites the Triton and the Nereid are
able to generate particles with a radius from 2.5 to 60 mm. Perhaps,
the main fraction of dust forming the ring is derived from surface of
the big satellite- Triton. In contrast to the Saturn’s and Uranus,
rings, the ring of the Neptune must be very rarefied.
There is not information on the ring of the Pluto. According to
author’s theory the Pluto and its satellite the Charon must be
surrounded by a common dust envelope including particles with a radius
from 4 to 8 mm and less than that, because the critical masses of
particles disposed near the Pluto and the Charon are similar.
The solar system is surrounded by the clouds of comets with critical
mass relatively the Sun.
The particles with critical mass fill not only interplanetary
space, but also interstellar one. Our Galaxy has the central nucleus.
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
The stars revolve on it together with their planets. Hence, we can
calculate the critical mass of particles or bodies disposed near the
Sun using obtained expression. At calculations we assume that a
constant L in our expression is the same, i.e. L=5.35x10-6 g2/cm2. The
nature demonstrates us various forms of movements, but it is chary of
laws, which control these movements. The laws of the nature maintain
minimum number of the physical constants. Therefore we substitute in
expression L=5.35x10-6 g2/cm2 in order to calculate the critical mass of
bodies disposed near the Sun. The distance between the Sun and center
of the Galaxy is equal to R=3x1022 cm. That is very large distance. The
mass of the Sun is known. It is equal to M=1.989.x1033 g. That is also
enormous value. The critical mass of particles or bodies calculated
from our expression is equal to 3x106 g {3 tons}. Such blocks
consisting of ice and friable snow dispose by the Sun a great way of
it {several milliard kilometers}. The state of these bodies is
unstable. They can come up to the Sun, but they can leave the solar
system and go into interstellar space. The astronomers call these
bodies comets. The comets appeared as by-product at formation of
planets from gaseous protonebula several milliard years ago. Perhaps,
each star in our Galaxy is surrounded by gigantic cloud consisting of
enormous number of comets. The further the star from center of the
Galaxy and the less its mass the larger mass of comet by this star.
The comets move from star to star. Therefore, sometimes huge comets
come flying into the solar system from outskirts of the Galaxy, for
instance, the Galley’s comet. The unity of the world is provided not
only with the common laws, but with the change of common matter by
means of particles and bodies with critical masses, which do not obey
the law of gravity. The clouds, rings of planets, comets have a common
base. The world without the particles and bodies with critical masses
would lose variety and life.
Critical masses of gravitation and corresponding sizes of particles
disposed near planet and its satellite.
Table № 1.
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Author: doctor of technical sciences, professor Anatoliy I. Lutkov
Name of
Critical
Predicted radius of
Observed
planet and
mass of
particle with critical mass
radius of
satellite
particle, g
, mm
particle
From dry
From water
with
land
or ice
critical
mass, mm
Mercury
6х10-7
0,03
Venus
1,3х10-7
0,018
Earth
2х10-7
Moon
1,6х10-5
0,15
Mars
4,2х10-6
0,063
0,1
0,001-0,1
Jupiter
1,7х10-8
0,014
0,016
0,01-0,03
Amalthea
1,3
4,4
6,8
Io
3,6х10-4
0,28
0,45
Europe
6,6х10-4
0,36
0,56
Ganimede
2,2х10-4
0,3
0,38
Calisto
3х10-4
0,36
0,43
Himalia
7,8
Saturn
1,9х10-7
-
2,9
8,0
9,1
12,8
13,5
15,5
Tethys
0,17
3,2
3,6
Dione
9,4х10-2
2,5
2,6
Rhea
6х10-2
2,2
2,5
Hyperion
9,2
13,0
13,5
Japetus
4,8х10-2
1,7
2,3
14,0
16,0
Uranus
5х10-6
Miranda
8,2
Ariel
Umbriel
0,1
0,11
12,0
13,0
1,26
6,2
6,9
0,44
4,2
4,8
12
-
several
15,0
meters
Minas
several
17,0
ters to
15,0
-
20 meters
0,037
21,0
Phoebe
microns to
13,0
Janus
Enceladus
-
from several
-
from 1-10 millimeters to
0,04
0,03-0,04
from
10,0
-
hundreds microns
-
0,008-0,018
millime
0,025
-
Author: doctor of technical sciences, professor Anatoliy I. Lutkov
Titania
9х10-2
1,9
3,7
Oberon
7,2х10-2
1,9
2,6
Neptune
1х10-5
0,11
0,14
-
Triton
5х10-2
-
2,5
-
Nereid
9х10-2
-
60,0
-
Pluto
0,14
3,4
-
-
Charon
1,56
7,8
-
-
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