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UNIVERSAL GRAVITATION
Ricardo L. Carezani 801 Pine Ave. # 211 Long Beach, CA 90813 U S A Abstract. Newton's Universal Gravitation
has no underlying machinery. Its action-at-a-distance is non-temporal
and has no projection in time. Einstein's
Universal Gravitation is simply the space-curvature of the Minkowsky
Universe. Its action-at-a-distance
is temporal, without projection in time. Even though the graviton is
not new, the theory elaborated here is original, regarding the overall
machinery of the process. Its
action-at-a-distance is temporal, and it has a projection in time. Gravitons absorbed by matter, transferring
their momentum, create gravitational pressure.
The action-at-a-distance is transmitted at light velocity or
greater. Starting from the
Mercury perihelion advance, the theory explains the perihelion advance
of Venus, Earth and Mars and Binary Stars like DI Herculis and Binary
Pulsar PSR J1518+4904. Graviton absorption by matter
transforms matter itself. The
production of gravitons by a catastrophic event is also possible. Matter evolves with time. The described mechanism transforms the second
law of Thermodynamics, creating a new process for stellar evolution.
For Autodynamics the entropy is constant because “singularities” of
small entropy are constantly created. Due to the larger gravitational
energy, the Friedmann equation is not valid and a new conception of
our actual Universe must be a logical conclusion.
1.-
INTRODUCTION. Though the author is in the
situation described by Richard P. Feynman in the book " The Feynman
Lectures on Physics"(1),
regarding his statements about the discovery of a new theory of universal
gravitation, he doesn't agree with Feynman's opinion about the "machinery"
of the process. Feynman's lecture will be repeated because it is concise
and explains his ideas very clearly. Further, the reasons will be
given for this author's disagreement.
"7-7 What is gravity? "But is this such a simple
law? What about the machinery of it? All we have done is to describe
how the earth moves around the sun, but
we have not said what makes
it go. Newton made no hypotheses about this; he was satisfied
to find what it did without getting into the machinery
of it. No one has since given
any machinery. It is characteristic of the physical laws that
they have this abstract character. The law of conservation of energy
is a theorem concerning quantities that have to be calculated and
added together, with no mention of the machinery, and likewise the
great laws of mechanics are quantitative mathematical laws for which
no machinery is available. Why can we use mathematics to describe
nature without a mechanism behind it? No one knows. We have to keep
going because we find out more that way." "Many mechanisms for gravitation
have been suggested. It is interesting to consider one of these, which
many people have thought of from time to time. At first, one is quite
excited and happy when he "discovers" it, but soon finds
that it is not correct. It was first discovered about 1750. Suppose
there were many particles moving in space at a very high speed in
all directions and being only slightly absorbed in going through matter.
When they are absorbed, they give an impulse to the earth. However, since there
are as many going one way as another, the impulses all balance. But
when the sun is nearby, the particles coming toward the earth through
the sun are partially absorbed, so fewer of them are coming from the
sun than are coming from the other side. Therefore, the earth feels
a net impulse toward the sun and it does not take one long to see
that it is inversely as the square of the distance because of the
variation of the solid angle that the sun subtends as we vary the
distance. What is wrong with that machinery? It involves some new
consequences, which are not
true. This particular idea has the following trouble: the earth,
in moving around the sun, would impinge on more particles, which are
coming from its forward side than from its hind side (when you run
in the rain, the rain in your face is stronger than that on the back
of your head!). Therefore there would be more impulse given the earth
from the front, and the earth would feel a resistance
to motion and would be slowing up in its orbit. One can calculate
how long it would take for the earth to stop as a result of this resistance,
and it would not take long enough for the earth to still be in its
orbit, so this mechanism does not work. No machinery has ever been
invented that "explains" gravity without also predicting
some other phenomenon that does not exist."
2.-
COMMENTS ON FEYNMAN'S STATEMENT. Feynman's arguments are irrelevant
for a few reasons: First of all, they are anti-scientific, because
in science it always will be possible to explain tomorrow what we
cannot explain today. From AD relativistic viewpoint his "rain"
effect is insignificant. In the theory espoused in this paper, the
mass increment of sun and planet is the cause of the motion and it
would take an increment bigger than that needed for the motion itself,
to counteract the "rain effect". (It is necessary to remember
here that the Sun loss, approximately, 4x106 tons of matter
each second, as radiant energy, which could be necessary to replace). 3.- ENERGY OF GRAVITATION
The graviton absorption, given
their momentum to the absorbing atom's constituent particles represents
a radiation pressure. We cannot give more detailed machinery with current knowledge. Each celestial body will absorb
gravitons in proportion to its mass, and the force between any two
bodies will change as the inverse of the square of the distance between
them, because of the variation in the solid angle that a body subtends
as we vary the distance. Newton made no hypothesis about
the mechanism of gravitational force, or about its velocity regarding
action-at-a-distance, but this force changes constantly the relative
position of all celestial bodies. The hypothesis espoused here produces
a force that not only changes the celestial bodies' relative positions
but the composition of their matter via the quanta of energy absorbed
by all elemental particles. We have, then, a new dynamic to transform
matter itself. The gravitational field belongs now to Mechanics: AD’s
Mechanics. It is well known that Mercury's
perihelion advances 574 second in a century and it is possible to
explain, by perturbation from other celestial bodies, only 531 seconds,
living and additional 43 seconds per century even though other explanation
is possible(3). This value is explained by the general
theory of relativity and this value, as observational value, will
be used in our calculation to get the solar mass increment in that
period of time (t). Later we will discuss the matter in detail. If M is the actual solar mass,
and X the factor that will give the increment per second in units
as fraction of M, (See Appendix 14) we can write: Mt = M (1 + 1/X)t (1)
The equation that relates the
angle f to M as a function of X is:
df = [(G2 Mt) / r3]1/2 dx (2)
df = [(G2 M)/r3]1/2
(1+ 1/X)t/2 dX (3)
Where r is Mercury's orbital
radius and G is the universal constant of gravity. The integral of
equation (3) (See Endnote E1) is:
The interesting values calculated
are in Table I. It is necessary here to make
another statement: The Feynman(2) explanation for how radiant
energy from the sun is changing, is also irrelevant with respect to
the ideas espoused in this paper, because to double the sun mass 3.075
109 years are needed and the mass increment will probably
change not the radiation power but the radiation time. Regarding his
comment: "If we calculate what happens to the orbit of the earth
when the gravity is changing, we find that the earth was then closer
in". With the ideas in this paper the earth will not have
been "closer in" because the mass increment will only increase
the earth's orbital velocity (advance its perihelion) which will increase
the centrifugal force to counteract the increasing force of gravity. For calculation we will take
43''1 per century for the advance of Mercury
perihelion, because the variation of values introduced by different
researchers will only cause a very small difference in the result
calculated with equation (4). It is well know that a solar probe, circling the sun much closer
than Mercury, would be most helpful in the study of the gravitational
effect. Of course, the quantity of
mass received per each gram of mass present, per second, Ms, Me, Mm,
is a constant value, and this value will be of universal application
to all celestial bodies. Another constant value, the
constant of universal gravitation is the ratio between the mass, in
grams, received by each square centimeter of a spherical body, per
second, and the acceleration of gravity: Sc/gs for Sun, Ec/ge for
Earth, Mc/gm for Moon. This constant is equal to 1.22895716612 10-11
having the following dimensional units: (gr sec/cm3). With the Avogadro number and
an average Sun density of 1.46 gr/cm3 and given an atomic
weight of 9.8(4), an atom in the Sun receives (As, Table
I) a mass equal to 1.7111 10-40 gr per sec. For comparison,
if this energy is carried by only one pico-graviton
its mass is (n) 5.3235 1012 times smaller than the electron
mass, and its energy, in electron Volt, is 9.5989 10-8
(ne). Using the gravitational constant,
if we divide the value of the mass received by each square centimeter
of the Earth's surface, per second, by this constant, the result is
the Earth's acceleration of gravity. The same is true for all celestial
bodies. We made the calculation of
ne (Table I) supposing that all the energy needed to give the gravitational
force is carried by only one graviton, but the general conception
should be to suppose that the energy is carried by many gravitational
quanta. 4.- SR AND AD COMPARISON. General relativity equation
of the planets perihelion advance is:
6 p G M f = ------------- (5) c2 r (1- e2) Where e = eccentricity, c = light speed and G, M, and r the usual meaning
in this paper. This equation yield, in a century: 42.99" for Mercury 8.62" for Venus 3.83" for Earth 1.35" for Mars (6)
GR cannot explain the values
for Venus, Earth and Mars. AD relativity found the same equation and,
have course, with the same limitation. In AD gravitation the equation
for the perihelion advance for each planet is equation (4), that is,
proportional to the square root of the division of the solar mass
by the orbital radius power 3[1]. fp = ( M/r3)1/2
(7) If the Mercury value is take
as 43" the values for the other planets are: Venus = 16.8" Earth = 10.4" Mars = 5.5"
(8) These values are equal to the
Hall's empirical values and close to the expected calculated by Newcomb. The big difference between
SR and AD is when the distance to the Sun is smaller. If the distance
is 1/3 of the Mercury radius the values are: GR = 129" AD = 223" (9)
If the radius is 1/5 of Mercury
the values are: GR = 214" AD = 481" (10)
It is visible that the proportional
difference increase with decreasing radius. Putting a probe close to the
Sun will be easy to test, in a short time, if its perihelion advance
is a natural phenomenon beyond the planetary perturbation and if the
values are given by GR or AD gravitational equation.
5.- PRECESSION
OF THE BINARY STAR DI HERCULIS AND BINARY PULSAR PSR J1518+4904. It has long been known that
Newton's and Einstein's theories fail to describe the precession of
binary stars(5). GR's application to the DI Herculis precession
grossly fails, giving 3.6 times the periastron of the star, whose
values are 0.65 deg/cent (2340 sec/cent) (6), or 1 deg/cent
(3600 sec/cent) (5). GR's lower predicted value is 8403
sec/cent with the mass of the smaller star, or 8960 sec/cent with
the two star masses averaged. Taking the sum of the two stars mass,
as should really be done, the values increase to 17977 sec/cent. Autodynamics' (7)
Universal Gravitation explains 79% (1839.6 sec/cent) of DI Herculis'
observed precession (2340 sec/cent.), calculating proportionally with
(M/r^3)^1/2, leaving 500.4 sec/cent. (21 %) to explain by the classical
tidal force and rotational deformation. Reference (5) also
mentions, for a tidal and rotational deformation of the star, a value
of 1.93 +_0.26 deg/cent. It is obvious that this value is wrong because,
by itself it is larger than the observed value. The right solution
equates the sum of the two values with the observed value. This solution
is given by the Autodynamics Universal Gravitation equation, as explained
above. Autodynamics also explains, using preliminary data, (9)
the binary pulsar PSR J1518+4904. The observed value is 0.011
deg/yr or 3960 sec/cent. The GR calculated value is 5640 sec/cent
with mass averaged. AD calculated value is 2262 sec/cent, 57 % of
3960 sec/cent., leaving 1698 sec/cent., or 43 % to other reasons. 6.- CONCLUSIONS. The Newtonian concept does
not give a machinery of motion. GR only gives a curvature in the Minskowsky's
Universe. What is espoused here suggests machinery for the force that
keeps celestial bodies united and is the cause of their motion. The
machinery in this case is not too important because the motion of
each body in the Universe is the result of another previous motion.
The actual machinery is only important because it provokes an increment
of velocity on the orbiting bodies, and because it gives a mechanism
for matter transformation as a function of time. The gravitational
energy absorption and matter disintegration drove AD to maintain the
universal entropy constant because singularities of small entropy
are constantly created. 7.- FRIEDMANN
EQUATION. The gravitational energy per cm3 of space,
equal to 4.219 10-24 gram/cm3, is comparable
to the average of matter concentration in our Galaxy, 10-23
gram/cm3. Contrarily, the Friedmann equation, calculated
through Universal expansion give an energy 2 million times smaller,
5 10-30 gram/cm3. AD has a totally new conception
of our actual Universe.
ACKNOWLEDGMENT. The
author thanks James M. Gavin and Amnon Meyers for assistance in preparing
the English language version of this paper. Endnote
E1. Fig. 1 show, graphically, the simple step needed to get equation E4(1), being X the factor that dividing M give the mass increment as fraction of M, by unit of time.
Fig.1
First second = M + M/X (1)
Second second = M + M/X + M/X + M/X^2 = M + 2M/X + M/X^2 (2)
Thirth second = M + M/X + M/X + M/X
+ M/X^2 + M/X^2 + M/X^2 + M/X^3 = M + 3M/X + 3M/X^2 + M/X^3 = M ( 1 + 3/X + 3/X^2 + 1/X^3 ) (3)
In t seconds is:
To get equation (E4-4)[2] from equation (E4-3) the following step are needed.
Making
The Integral of equation E4-3 is:
As all the values are known in the left term of this equation, the second term ‘s value is easy to get starting with an approximate value, and using iteration, the exact value is found. Calculated values are shown in Table 1 at the end of E4.
REFERENCES (1).- Feynman Richard P., Lighton Robert B. and Sands Matthew. The Feynman Lectures on Physics, page 7-9, Addison-Wesley Publishing Company. Reading, Massachusetts, 1963. (*).- This is not true for very precise calculations. (2).- Ibis, page 7-11.
(3).- R. Nedved. Physics Essays 7, 374(1994).
(4).- This value is encountered as consequence of take in account the ratio between Solar and Earth density, to make equal the two way of calculation.
(5).- E. F. Guinan, J. J. Marshall and F. P Maloney, Dept. of Astronomy and Astrophysics, Villanova University, Villanova, PA 19085, USA, taken from "Commission 27 and 42 of the AU Information Bulletin on Variables Stars," Number 4101, Kenkely Observatory, Budapest, October 12, 1994, from the WWW.
(6).- E. F. Guinan and F. P. Maloney, Astron. J., 90 1519(1985)
(7).- D. R. Walz, H. P. Noyes and R. L. Carezani, Phys. Review A, 29 2110(1984). The conclusion espoused in the paper by Noyes is irrelevant, because the electron receives external energy from the Klystron electromagnetic field, confirming the Bertozzi experiment (8) and the Special Relativity equation for kinetic energy. It is impossible then to compare one equation against the other, because Autodynamics applies to decay cases. (8).- W. Bertozzi. Amer. Journal of Physics, 32, 551(1964)
(10).- [48.03] Binary Pulsar PSR J1518+4904: Orbital Precession and Mass Estimates. D. J. Nice (NRAO), R. Wsayer, J. H. Taylor (Princeton), from the WWW. ø 43'' (Sec/cent.) Advance of Mercury's perihelion. X 3.07503085281e7 Final value for a century. Ic 6.46172378781474e25 (gr/cent) Solar mass increment per century. Is 2.0475707e16 (gr/sec) Solar mass increment per second. Mas 1.03048351974e-17 (gr/sec) Mass received for 1 gr. per sec. As 1.71115929339e-40 (gr/sec.atom) Mass received by each atom. n 5.323519402998e12 Times smaller than the electron mass. ne 9.59891307454e-8 (eV) The gravitons are carrying this energy. Td 3.07503085281e9 (years) Time needed to double the Sun mass. gs 2.74487579939e4 (cm/sec2) Sun gravitational acceleration. ge 9.80297286843e2 (cm/sec2) Earth gravitational acceleration. Sc 3.37333478376e-7 (gr/cm2 sec) Mass received by each Sun cm2. Ie 1.94349269521443e20 (gr/cent) Mass received by Earth per century. Ec 1.20474337559e-8 (gr/cm2 sec) Mass received by each Earth cm2. Rse 2.80004426844e1 Ratio of Sun/Earth, mass received by each cm2. Rg 2.80004426844e1 Ratio of Sun/Earth gravitational acceleration. Me 1.03048351974e-17 (gr/sec) Mass received by 1 gr per second. Earth. Ns 1.22895716612e-11 (gr sec/cm3) N, Gravitational constant.(From Sun). Ne 1.22895716612e-11 (gr sec/cm3) N, Gravitational constant. (Earth). Mm 1.03048351974e-17 (gr/sec) Mass received by 1 gr per second. (Moon). Mc 1.99347367243e-9 (gr/cm2 sec) Mass received by each Moon cm2. gm
1.62208555952e2 (cm/sec2)
Moon gravitational acceleration. Nm 1.22895716612e-11 (gr sec/cm3) N, Gravitational constant.(Moon). Mae 6.46607248058e-40 (gr/sec atom) Mass received by each atom (Earth). Mam 3.91456989037e-40 (gr/sec atom) Mass received by each atom (Moon). Table I.
1 This 43” per century is not the value calculated by SR. It is the value astronomical observed as it is explained in Section 3. It is possible to start the calculation using any known value, i.e., the acceleration of gravity on Earth or any other value. [1] It
is not necessary, in each case, to calculate X to later calculate
f. The procedure is redundant
and the proportion give the correct value as a simple proportion. [2] In the first version
of this paper, written by Carezani 40 years ago, the integration
was approximate because the rigorous solution give a second degree
equation and the numerical calculation was difficult then to do.
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