FINAL SOLUTION TO GRAVITATIONAL ATTRACTION
Bert Schreiber
4519 Holly St.
Bellaire, TX 77401-5802
[email protected]
Abstract: For over 200 years the only equation that existed to calculate the effect of gravity by two masses
on one another was that of Sir Isaac Newton. His equation is well known to be dimensionally incorrect
and has numerous flaws. However, it being the only one available was hence used in all scientific works.
The author derived another equation that replaces Newton’s. It contains no ambiguities or paradoxes and
is dimensionally correct, because it has no specific dimensions.
SPECIAL NOTE: This paper is a very condensed version of the 21 page original. It is also based
(background) on some of the results of over 200 pages of other supporting discoveries by the
author. Therefore, some of those results mentioned will need to be accepted at face value. For
brevity, only the first few digits of the physical constants will be used. It is understood that they
extend to their known digits and that the calculations used sufficient digits in them.
1. Brief Introduction
Newton’s equation for the gravitational attraction between two masses gives the static force
between them. It requires the usage of the Newtonian Constant of Gravitation; symbol G, that is
a constant of proportionality. This is due to the fact the masses in it are their energy mass or said
mass if they could be converted to energy from:
(1)
E = mc2
Newton’s equation is:
G(m1m2)
F =
(2)
r2
Furthermore, dimensions were added to G that is just a number (creating a nonexistent entity), in
order to make the equation work, i.e., a force fit.
To find the gravitational force effect (accelerate a mass) on said masses requires the insertion of
the calculated force into the force equation:
F = ma
(3)
At this point the author must bring in a new discovery or concept on what exactly is Planck’s
Constant, symbol h. h is recognized as the quantum unit of action/energy and only occurs in full
(whole numbers) multiples of itself. The dimensions of h are: mass-length2/second, or,
gm-cm2-t-1 and most important, length squared is area.
Therefore, h is some mass moving through some area in or per one second. Brevity prohibits the
long derivation, but the simple end result is for the electron and proton:
mass proton x diameter proton x speed of light = h
(5)
mass electron x diameter electron x speed light = h
(4)
What these two equations say, is the electron or the proton can only move in quantum jumps of
their diameter so that h as a quantum whole number value can exist, i.e., fractional quantum
values of mass, length, charge, and time could not possibly exist.
It is the proton that is of interest as far as this paper is concerned, hence, that value
(diameter) of the proton is also its Compton wavelength and the de Broglie
wavelength of the proton if it could move at the speed of light, c. This number,
1.321 x 10-13, is also the slowest speed a proton can go to or reach. Simply mass x
some Sweep Area in/per/during one second must be h.
Sweep area = h/mx
(6)
2. Deriving the equation
It is only necessary to equate the force effect equation against the static force equation that gives:
G(m1m2)
(7)
ma =
r2
Dividing both sides by m and transposing, but now assigning m as M:
M = a/G x r2
(8)
but, a is the minimum possible acceleration due to h and is a constant (minimum length or the
quantum of length = proton’s values so listed) and G is likewise a constant resulting in another
constant, symbol k that makes (8) the final equation as:
(9)
M = r2 x k
This immediately results in the destruction of many current beliefs (a.k.a. proven scientific facts)
only a few of that are:
1. There exists a singular gravitational force as M is a single entity.
2. The parameters of said mass have nothing to do with the effect of gravity.
In case this is not clear, it matters not what that mass’s density is, whether it is layered, as the
Earth is, nor it shape, or anything else. So much for those “exercises” shown in physics
textbooks on, the now nonexistent, layering effects. Hindsight is better than foresight, but this
should have been obvious when every textbook says: All mass acts as if its mass were at its point
center, i.e., it makes no difference where or how said mass is arranged around said mass’s point
center, only its total mass.
At the sake of overkill, take any specific mass; say a 1 kg sphere made of lead. Now compare it
to any other mass that is 1 gram at some fixed length away. Now distort said sphere into a disk,
at any angle, a hollow large sphere, or a rod or whatever and there is absolutely no change in the
force between said 1 kg mass and that 1 gram mass when their centers of mass are at a fixed
length apart.
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3. It does not require a second mass for a gravitational field to exist.
4. It does require a second mass for the effects, measurements to be made or for the action of
any effects to be observed.
There are only two parameters that define the effect of one mass on another. Those are the mass
chosen to be compared to all others and the length said second mass’s point center is from the
exact point center of the first mass inaccurately called “radius” that should be length, L, not l. l is
the numerical value for the symbol of length, i.e. l(L). No longer taught, long forgotten.
Using the current SI values in cgs system; k is 1.980355 x 10-6.
Readers must now accept the unacceptable. There are no units (dimensions) specifically
attached to any of the symbols in (9). What is calculated is that that is the resultant of said
calculations and then the dimension(s) so desired are arbitrarily (by stipulation) assigned, giving
the answer the concept desired. Such are: speed, acceleration, mass, and length. This is because
force is a human concept, just a word, and has no specific dimensions.
To give some illustrations as to how (9) works and why one assigns the dimensions to the results
as shown in the cgs system:
A. Insert the avg. radius of the Earth for r:
M = 40.554 x 1016 x 1.980355 x 10-6 = 80.31 x 1010 grams that is
8.031 x 105 kilotons.
What is this answer, a mass? M = M. It is the size (not weight) mass that when dropped near the
surface of the Earth at that radius will cause the Earth to accelerate 1.3214 x 10-13 cm-sec-2.
For brevity, calculations not shown, inserting this mass in (2) will show the acceleration of the
Earth, using (3), to be the diameter of the proton per second per second and is proof that (9) does
work as it gives the identical answer as the usage of Newton’s equation.
B. As a further illustration, a spaceship who’s mass is over this value, say 10 x 105 kilotons
when leaving the Earth, causes the Earth to follow the ship for a short period.
This immediately destroys two more cherished beliefs.
1. The strong equivalence principle. [All mass falls at the same rate so that a 1 gram mass, and if
stopped in orbit, the Moon, the Earth, and even Jupiter would fall likewise into the Sun.]
2. Newton’s Third Law cannot be violated.
It proves:
1. The equivalence principle a.k.a. the feather-apple paradox, because any mass smaller than
that calculated value will fall at the same rate to the surface of the Earth vs. the old belief at
the same apparent rate and the Earth will not and cannot move, no recoil.
2. Any mass equal too and larger will cause the Earth to accelerate or recoil.
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What this means is; any mass smaller than that calculated down to the smallest mass, say a
neutron, will fall at the same rate to the surface from that r. A falling neutron experiment was
done at the Savanna River Complex and the neutron fell like a stone at the same apparent rate as
any other small mass.
3. There is a limit to the effect of gravity from this primary (chosen) mass.
This will be an entirely new concept for the readers and another cherished belief destroyed. It is
true that the source of any force (its field) does go from it to the far edge of the Universe and
every mass attracts another mass. What is not true, is it will not have any effect beyond a certain
range on another mass. Planck’s Constant was overlooked, the limit to the Unit of Action. (For
brevity, (9) can be changed for the force effect of charge or magnetism, but will not be for here.)
3. Selected applications
There are at least 15 more results from (9) so therefore only a few of the most important will be
given.
By inserting 1 gram for the mass, the range for said 1 gram mass (solve for r), to another of the
identical mass is then about 7 meters. Beyond that, the two masses will just sit there and ignore
one another. The effect is below h and therefore cannot exist.
The gravitational range of our Milky Way Galaxy to another of the same mass is about 10.5
million light years. The start of to discrediting untold numbers of beliefs in cosmology.
Since the force is zero at the exact point center of any source, then to be able to act or be
effective, it can only start some length away from said center. This value (also found by A.
Duesterhus [1] and hence confirmed) is about 1.9 x 10-21 cm.
The larger the masses, individual or collectively, the slower the acceleration or deceleration per
elapsed time (speed gain or loss) that means that there is no way that galaxies, nor groups, can be
accelerated by one another to achieve anywhere near their current theoretical speeds. Our galaxy
is moving relative to a point of absolute rest in space about 600 km/sec toward the Constellation
of Leo. [2]
Ends Black Holes, Schwarzchild Radius, gravitational collapse, Gravity Waves, worm holes, ad
nauseam, and nothing more needs to be said on this matter.
Shows that the current “strong nuclear force” is actually the force of gravity.
Permits the parameters of the Universe to be calculated, that, if the author is correct (everything
is speculation on these matters) that makes our Universe have a radius of 6.75 x 1040 cm, a mass
of 9.11 x 1075 grams, a density of 7.37 x 10-48 grams/cm2, and a volume of 1.12 x 10123 cm3. [3]
With the proper software program easily solves the multi-body “problem” and can be done, for
maybe 50 masses, on the current desktop computer workstations almost in real time.
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4. How the gravitational force effect actually works
What will happen when the Moon’s radius is inserted for r? It will give the acceleration of a
mass dropped near the surface of the Moon, about 1/6th. the Earth’s gravitational acceleration.
What is the result of this?
It is the identical value for a mass placed in a hole through the Earth from its surface to or
through its center at that radius from said center. This result then provides the final clue to the
effect of gravity throughout the Universe.
What all the calculations, results, new equations, etc., really amounted to is; that there is an
imaginary “solid” Universe and if some specific Mass is dropped down an imaginary hole
through said Universe going to its center, at some specific starting radius from that center,
the end results are identical.
The real Universe may be considered a “gas” composed of what is floating around in it, gas,
stars, galaxies, etc.; so it is equivalent to just a large volume of mixed “gasses”, hence needs not
be “solid”.
The last and final tie in is this: Any two Masses, anywhere in the Universe, act as one is
considered at the center of the Universe, and when one is larger (when alike, either one), it
is at the center, and then the other can be moved away/toward from it. Each central Mass
then “thinks” that it is at rest if no acceleration of it can be detected, and it is at the center
of the Universe, and all the other smaller Mass(es) are moving relative to it.
That has a very familiar, erroneous, ring to it. Up to (9) understood.
One can then get into various inane semantic arguments. What constitutes measurement (actual
practical or theoretical), and to which observer on what, and to what is being used to make the
measurement(s) (actual practical or theoretical), or to yet another observer(s) out in space at
“rest” or moving, i.e., Relativity.
What is most important is, every mass, even an electron, acts as if the entire mass of the
Universe was located at its exact point center. And furthermore, the size of the masses is
immaterial, as it is the mass ratios between them and naturally, their length apart, within the
limits that is.
CONCLUSIONS:
There is a new equation that can replace Newton’s and works far better. It permitted many old
beliefs, theories, postulates, and hypotheses to be shown to be false, nonexistent, or absurdities
There will be yet more applications of (9) in the future. It will require all current textbooks to
have to be re-written as far as gravity is concerned.
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It essentially destroys, in toto, Albert Einstein’s Theory of Relativity (GRT and SRT) and
definitely destroys those absurd extrapolations beyond reality given to it, over Einstein’s
objections, by the current scientific establishment.
References:
[1] A. Duesterhus, A NEW BASIS FOR PHYSICS, Toth -Maatian Review,
Vol. 13, Number 1, page 5939
[2] Wm, Van Deusen, THE SILVERTOOTH EXPERIMENT, R&M #20,
Sept./Oct. 1996, pages 20-22
[3] QUANTUM - QUANTA THEORY * * * THE THEORY OF THE
UNIVERSE, Charles Bert Schreiber, 4th. Revison, April 1999, self published
[3] At time this paper was written is now:
QUANTUM-QUANTA UNIVERSAL PHYSICS * * * THE THEORY OF THE UNIVERSE in
SEGMATICS, Charles Bert Schreiber, First Edition, two volumes, July 2006, self published.
Revised January 2007
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