THE
INVERSE SEMI-CUBE OF DISTANCE:
THE VOLUMETRIC GEOMETRY OF
GRAVITY AND THE RELATIVISTIC
CONVERGENCE OF 1.75
Otacilio
Alves Meirelles
Independent Researcher
E-mail: otacilio.meirelles@gmail.com
https://doi.org/10.5281/zenodo.18458652
January 31, 2026
Abstract
ABSTRACT
This study proposes a fundamental
revision in the propagation metric of radiant and
gravitational fields. While area
is sufficient to measure light tangentially striking
opaque objects without
penetrating them, estimating gravity—which acts entirely
upon every atom of the involved
bodies—leads us to deduce that static volume
might offer the solution.
However, deeper investigation reveals that static volume is
also insufficient. The
exclusivity of the Inverse Square Law (1/r2)—based on two-
dimensional surfaces—is
questioned in favor of a three-dimensional model termed
the “Inverse Semi-Cube of
Distance.” It is demonstrated that by considering energy
propagation as a continuous flux
filling spherical shells, density dilution follows a
geometric factor of 1/7 when
doubling the radius, rather than 1/4 (area) or 1/8
(total volume). The involvement
of spacetime and motion attenuates the effective
volumetric density, reducing its
total charge by 12.5% relative to the 87.5% larger
space in the second half of the
radius, reflecting the fact that gravity between two
bodies encompasses them entirely
(volumetrically), and not merely superficially. The
study concludes by presenting a
robust mathematical correlation: the ratio between
the proposed volumetric dilution
(7) and the classical surface dilution (4) yields
the factor 1.75—precisely
matching the gravitational deflection value predicted by
General Relativity and confirmed
by the Eddington expedition in 1919.
Keywords: Inverse
Semi-Cube. Gravity. Volumetric Geometry. Inverse Square
Law. General Relativity. Light
Deflection.
1. INTRODUCTION: THE LIMITATION OF THE SURFACE
Historically, Newtonian physics
established that the intensity of light and gravity de-
creases with the square of the
distance. This premise is based strictly on the geometry of
the area of a sphere (A = 4πr2).
However, this classical approach treats physical propa-
gation as a mere phenomenon of
surface interception, ignoring the intrinsically volumetric
nature of space.
The present thesis postulates
that light and gravity are not merely “shells” touch-
ing two-dimensional surfaces, but
fluid contents in evolution that occupy and fill three-
dimensional spacetime. To gauge
the true energetic density of these entities—although
light flowing volumetrically may
touch objects superficially—regarding gravity, it is im-
perative to abandon area geometry
in favor of volume geometry (V ∝ r3) and
consider
the continuous flux determined by
the speed of light (c). In this study, it is demonstrated
that the factor 1/7 accurately
expresses the spherical volume in continuous flux. When
confronting the data with the
number derived by Einstein and Eddington, we find 1.75
for the curvature of light from
the Hyades near the Sun.
2. THE SOURCE BODY AND THE PROPAGATION OF ENTITIES
When emanating from the source
body—in this case, specifically gravity—these enti-
ties flow from the center of the
bodies as if starting from a singular point.
1. After 1 second: The entity
will fill the space forming a sphere with a radius of
300,000 kilometers around the
source body.
2. After 2 seconds: The first
layer moves to a second zone (between 300,000 and
600,000 km), allowing a new layer
of 300,000 km to occupy the initial space.
3. After 3 seconds: A third layer
appears, occupying the first radius of 300,000
kilometers.
4. The second layer, previously
in the first space, expands to occupy the second zone,
giving way to the third.
5. The first emitted layer,
having passed through the second zone, now occupies the
third, situated in the range of
600,000 to 900,000 kilometers from the source body,
and so on.
6. From the central point, when
doubling the distance, the first half of the total radius
will present a gravity 7 times
more intense, concentrated in a space 7 times smaller.
7. In the second half of the
radius, gravity will be 7 times less intense, dispersed in a
space 7 times larger.
8. This gravity will envelop the
bodies entirely—in a mutual sense—exerting force
according to the mass and
distances of the bodies orbiting each other, or even in
multi-body systems with
gravitational interrelations.
3. SPACE KINETICS: MOTION AS A VOLUME GENERATOR
To understand the real density of
a field, one cannot treat space as a pre-existing static
container. The space occupied by
light or gravity is generated intrinsically, in real-time,
by the dynamic propagation of the
source. The radius vector (r) is not a line drawn in
a vacuum; it is the physical
manifestation of constant motion (c) acting integrally over a
time interval (t).
Consequently, the solar irradiation
necessary to reach Earth exceeds predictions based
on the Inverse Square Law (1/r2).
From this perspective, it is demonstrated that the
solar energy flux, traditionally
calculated by the surface dilution of the inverse square,
underestimates the real
dissipation. To compensate for the proposed volumetric dilution,
the magnitude of emission at the
source must be rescaled by a factor of 1.75 (or +75%),
correcting the discrepancy
between spherical shell geometry and surface geometry. This
principle is fundamentally
extensible to gravitational interaction.
Although under the perspective of
Newton/Soldner light would curve 0.87 arcseconds
when passing by the Sun, and
under Einstein/Eddington it would curve 1.75 arcseconds,
what is affirmed here is based not
on estimates, but on the real response that the in-
verse square of the distance
delivers when confronted with the Inverse Semi-Cube of
Distance, which asserts that
entities flow not in static volume, but in constant flux.
The Fundamental Equation of the
Kinetic Radius is defined as:
r = c · t
(1)
Consequently, Volume (V ) ceases
to be merely a static spatial function to become a
direct function of time and
motion:
V (t) = 4
3π(c · t)3
(2)
3.1
Continuous Flux and Dynamic
Dilution
This kinetic formulation reveals
that volume grows with the cube of the flow time. If
we consider the motion of light
or gravity flowing from an instant t1 to an instant t2 = 2t1:
• The entity travels with
constant linear velocity c.
• However, the Volume Creation
Rate is accelerated. The motion needs to “sweep”
and fill an increasingly larger
amount of cubic space for every additional second it
travels.
When passing from the first to
the second time interval (t → 2t), the linear motion
merely doubles the radial
distance, but the need for volumetric filling multiplies. The
“Factor 7” (the basis of the
Inverse Semi-Cube) arises from the tension between Constant
Linear Velocity (c) and Cubic
Volumetric Expansion (t3).
Motion is the agent that,
by advancing, dilutes the density
of the entity, as the energetic content of the source
cannot multiply in the same
explosive proportion that the volume generated by the motion
demands.
4. GEOMETRIC FOUNDATION: THE EXPANSION FACTOR 7
Deepening the kinetic analysis
from a geometric perspective, we consider isotropic
propagation. For every unit of
time, the source emits a quantity of energy that must
occupy a volumetric spherical
shell.
When analyzing the evolution of
volume between a unit radius r and its double 2r,
we observe the quantitative
phenomenon:
1. The total accumulated volume
of a sphere of radius 2r is eight times larger than the
sphere of radius r (23 = 8).
2. However, the energy emitted in
the second interval does not occupy the total volume
from the origin, but flows to
fill only the newly created layer (the physical space
between r and 2r).
The physical volume of this
second layer (∆V ) is defined by the difference:
∆V = V2r − Vr = 8Vr − 1Vr = 7Vr
(3)
Geometric Corollary:
It is concluded that the energy
contained in the first unit volume, upon expanding to
occupy the second layer, must
fill a physical space seven times larger. Therefore, the Vol-
umetric Energy Density undergoes
dilution by a factor of 7. This is the mathematical
principle of the “Inverse
Semi-Cube of Distance.”
5. THE NATURE OF GRAVITY: PERMEABILITY AND INTEGRAL
INTERACTION
The distinction between metrics
becomes crucial when analyzing the nature of the
interaction.
While the Inverse Square Law
(area) works adequately for opaque light
sensors (which intercept
radiation superficially), it fails conceptually when describing
gravity.
Gravity is a phenomenon of
absolute permeability. It does not recognize surfaces, shad-
ows, or shielding. The
gravitational field traverses mantles, cores, and crusts, interacting
with the totality of the internal
mass of bodies.
• Volumetric Immersion: Upon
reaching Earth, the Sun’s gravitational field (the
expanded volumetric shell) does
not merely touch the planet’s surface. The total
volume of Earth is immersed and
engulfed by the volumetric density of the solar
field.
• Mutual Resonance: Reciprocally,
Earth’s field, although weaker, fully permeates
the Sun’s volume.
Since gravity is a force that
acts upon mass (density × volume) and permeates the
interior of bodies, the metric to
calculate its intensity must be, obligatorily, volumetric
(Semi-Cube) and not superficial
(Square).
6. THE CONVERGENCE OF 1.75: THE LINK TO RELATIVITY
The most robust validation of
this model lies in the emergence of a fundamental
numerical constant that connects
the Semi-Cube geometry to modern physics. When we
confront the two dilution metrics
upon doubling the distance:
1. Classical Model
(Newton/Surface): Predicts dilution by a factor of 4 (22).
2. Proposed Model (Volume/Semi-Cube):
Predicts dilution by a factor of 7 (23−
1).
The ratio between the volumetric
reality (the space to be filled) and the classical
superficial expectation reveals
the necessary correction factor:
Convergence Factor = Volumetric
Dilution (7)
Surface Dilution (4)
= 1.75
(4)
6.1
The Meaning of 1.75
Historically, 1.75 arcseconds was
the exact value predicted by Albert Einstein for the
deflection of light when passing
through the Sun’s gravitational field, confirmed by the
celebrated expedition of Arthur
Eddington in 1919. Newtonian physics, based on the
inverse square, predicted only
half of this value (0.87, Soldner’s calculation), failing to
explain reality.
6.2
Thesis Conclusion
The Inverse Semi-Cube model
suggests that the “extra curvature” of spacetime de-
scribed by General Relativity is,
geometrically, the manifestation of the difference between
a universe observed in areas
(factor 4), static, and a real universe of volumes (factor 7)
of entities in motion. The factor
1.75 is not an anomaly, but the mathematical signature
of volumetric density flowing and
imposing itself over plane geometry. Gravity acts with
a magnitude “1.75 times
different” from the classical expectation because it operates in
the fullness of the
three-dimensional volume. Thus, this model offers the geometric and
mechanical substrate for
Einsteinian spacetime curvature.
References
[1] EINSTEIN, A. The Foundation
of the General Theory of Relativity. Annalen der
Physik, 49, 1916.
[2] NEWTON, I. Philosophiæ
Naturalis Principia Mathematica. London, 1687.
[3] DYSON, F. W.; EDDINGTON, A.
S.; DAVIDSON, C. A Determination of the De-
flection of Light by the Sun’s
Gravitational Field, from Observations made at the
Total Eclipse of May 29, 1919.
Philosophical Transactions of the Royal Society of
London, 1920.
[4] SOLDNER, J. G. On the
Deflection of a Light Ray from its Rectilinear Motion.
Berliner Astronomisches Jahrbuch,
1801.
https://doi.org/10.5281/zenodo.18458652
