# Newtonian vs. ‘LeSagian’ Gravitation in Our Solar System

Written by Raymond HV Gallucci, PhD, PE

Having introduced the concept of “pushing” gravity in my previous paper, first attributed to Fatio and LeSage, it is instructive to compare the effects of this type of gravitational force with the traditional “pulling” force of Newton, at least as manifested by his gravitational equations.

Our solar system provides a template for this comparison. This paper examines how the results for ‘pushing’ gravity between the sun and a planet compare to those for ‘pulling’ gravity, as per Newton.

**Newtonian vs. ‘LeSagian’ Gravitation in Our Solar System**

Raymond HV Gallucci, PhD, PE. 8956 Amelung St., Frederick, Maryland, 21704

e-mails: gallucci@localnet.com, r_gallucci@verizon.net

Classical Newtonian gravitation is considered to be an attractive force, although the mechanism by which this is manifested remains unknown. Speculation includes graviton particles, space-time warping, etc. LeSagian gravitation is considered to be a pushing force, the net result of which __appears__ to be attractive. It coincides with, but does not necessarily depend on, various aether theories where the universe is filled with moving ‘particles’ capable of exerting forces on whatever they contact. ‘Pushing’ gravity occurs when two objects ‘shadow’ each other by blocking the flow of these particles so as to create an area where the density of the particles is less than that ‘outside’ the shadow. The higher density outside the shadow impinges on a greater surface area than the lower density within the shadow, resulting in a net pushing force which appears to be an attraction between the two bodies toward one another (gravity). This paper examines how the results for ‘pushing’ gravity between the sun and a planet compare to those for ‘pulling’ gravity, as per Newton.

**Introduction**

Since first proposed by Fatio in in 1690 before the Royal Society in London, and submitted poetically in 1731 to the Paris Academy of Science, the concept of gravity as a pushing force has existed (and been roundly discredited by mainstream physicists). Popularized and allegedly enhanced by LeSage in 1748 (and equally dismissed as Fatio’s), this theory involves ‘shadowing’ of omnidirectional gravity particles that impinge on all matter so as to make gravity appear as an attractive phenomenon (Figure 1). [1]

__FIGURE 1__**. LeSage’s Original Illustration**

Despite its repeated rejection, this theory has survived and even been revived by dissident physicists as mainstream physicists continue to struggle with an explanation for gravity and search for the elusive ‘gravity waves’ or ‘gravitons’ implied by their theories. Of especial note is the recent book by de Hilster of the Gravity Group of the John Chappell Natural Philosophy Society (formerly the Natural Philosophy Alliance). [2]

This paper examines the theory of pushing gravity on the scale of our solar system, comparing results for the ‘LeSagian’ theory against those resulting from Newton’s Law.

**Gravity on a Solar System Scale**

Classical Newtonian gravitation is considered to be an attractive force, although the mechanism by which this is manifested remains unknown. Speculation includes graviton particles, space-time warping, etc. LeSagian gravitation is considered to be a pushing force, the net result of which __appears__ to be attractive. It coincides with, but not necessarily depends on, various aether theories where the universe is filled with moving ‘particles’ capable of exerting forces on whatever they contact. Gravity occurs when two objects (spheres, for convenience, which will be modeled in two dimensions as circles) ‘shadow’ each other by blocking the flow of these particles so as to create a trapezoidal area (truncated conic volume in three dimensions) where the density of the particles is less than that ‘outside’ the shadow. The higher density outside the shadow impinges on a greater surface area than the lower density within the shadow, resulting in a net pushing force which appears to be an attraction between the two bodies toward one another (gravity). Figure 2 illustrates this with the sun and a planet.

The sun, idealized as a circle (sphere) is impinged upon over a circle (sphere) with radius equal to its distance from the planet by these particles from all directions (orange [dotted] circle), resulting in normal forces radially inward over its entire surface, except for the green (dashed-dotted) pie-shaped area where it is shadowed by the planet. Similarly, the planet, also idealized as a circle (sphere) is impinged upon over an equally-sized circle (sphere) of the same radius from all directions, resulting in normal forces radially inward over its entire surface (green [dashed-dotted] circle) except for the orange (dashed) pie-shaped area where it is shadowed by the sun. Clearly, the fraction of the circle surrounding the planet that is shadowed by the sun exceeds that of the sun shadowed by the planet. As a result, the planet will be pushed closer to the sun than the sun will be to the planet, but due to the planet’s orbital motion, the sun and planet do not collide. Rather, the planet and sun rotate about their mutual barycenter, essentially the center of the sun.

The Newtonian gravitational attraction between the sun and planet is readily calculated as F = GMm/d^{2}, where ‘G’ = gravitational constant (6.67E-20 km^{3}/kg-s), ‘M’ = mass of sun (1.99E+30 kg), ‘m’ = mass of planet (kg) and ‘d’ = distance between sun and planet (km). For our solar system, the Newtonian gravitational force between the sun and each planet (retaining Pluto) is shown in Table 1 (column ‘Newton’) along with other planetary properties, including the orbital period, orbital speed and gravitational acceleration at the surface.

__FIGURE 2__**. ****Schematic Showing LeSagian ‘Shadowing’ between the Sun and a Planet**

Return to Figure 2 and define ‘R’ as the radius of the sun (6.98E+5 km) and ‘r’ as the radius of the planet (km). Given that d >> R (at a minimum, nearly two orders of magnitude for Mercury) > r (at a minimum, an additional order of magnitude for Jupiter). In three dimensions, the approximate volumes of the ‘shadows’ cast by the sun on the planet and the planet on the sun are, respectively, V_{s-p} = p(R^{2} + r^{2}+ Rr)d/3 and V_{p-s} = pr^{2}d/3. The volumes of the spheres around the sun and planet with radius equal to the sun-planet distance are each V_{c} = 4pd^{3}/3, yielding the following fractions of ‘shadowed’ volume, respectively,

f_{s-p} = V_{s-p}/V_{c} = (R^{2} + r^{2 }+ Rr)/4d^{2} and f_{p-s} = V_{p-s}/V_{c} = r^{2}/4d^{2}

Additionally, LeSagian gravitation assumes that some fraction of the particles interact within the volume of the spheres as they pass through, generating the pushing force. This can be characterized using the typical exponential function for attenuation, where the fraction of particles that ‘survive’ the passage through a distance ‘x’ is 1/exp(mx) (longer distance means more attenuation and greater push). The attenuation coefficient ‘μ’ is unknown, but a reasonable assumption is that it is proportional to the density ‘ρ’ of the sphere (denser sphere means more attenuation and greater push). Limiting the analysis to relative comparisons, for each sphere assume m r/r_{e} where ‘ρ_{e}’ is earth’s density (5.51E+12 kg/km^{3}). Again working with relative comparisons, the distance through each sphere scaled to that through the earth will be r/r_{e}, where ‘r_{e}’ is earth’s radius (6370 km), such that this ratio will be 1 for earth. Now, the LeSagian gravitational force acting on each planet will be proportional as follows,

L {f_{s-p}(1 – 1/exp[r_{s}R/r_{e}r_{e}])}{f_{p-s}(1 – 1/exp[r_{p}r_{p}/r_{e}r_{e}])}

where subscripts ‘s’ = sun and ‘p’ = planet. The pairs of terms inside each set of ‘{ }’ represent the fractional area shadowed by the opposing sphere times the fraction of particles that interact with the affected sphere. The results from these calculations for each planet are shown in Table 2 as the last column ‘LeSage.’

A quite interesting behavior results if the Newtonian gravity ‘F’ (last column in Table 1) and LeSagian gravity ‘L’ (last column in Table 2) are scaled relative to their respective values for earth (** bold italics**) and plotted against their distances from the sun (Figure 3). While there is a noticeable difference in the scaled values (up to several orders of magnitude, especially from Jupiter onward), the pattern is remarkably similar for the nine planets. Newtonian gravity depends directly on the product of the two masses and inversely on the square of the distance. LeSagian gravity depends on the product of some function of the two densities (exponential attenuation governed by the coefficient ‘μ,’ proportional to the density, has been assumed) and the ‘shadowed’ volume, which are direct functions of distance.

**Gravitational Acceleration at Each Planetary Surface**

Another phenomenon worth examining from the Newtonian vs. LeSagian gravitational viewpoint is the gravitational acceleration at the surface of each planet. For each planet, assume a 1-kg mass is sitting on the surface (a loosely defined term for the gas giants). As should be evident from Figure 2, if the sun is now replaced by a planet, the planet by the 1-kg mass sitting on the surface, and the distance ‘d’ by the planet’s radius ‘r,’ effectively half the circle of radius ‘r’ will constitute the area shadowed by the planet relative to the 1-kg mass. This will be true for any of the planets, so the fractional area that is shadowed (0.5) is the same for all and need not be considered further for relative comparisons. This leaves as variables the planet’s radius and density ‘ρ’ (which is still assumed to affect the attenuation coefficient ‘μ’).

Ignoring any attenuation by the 1-kg mass, the LeSagian gravitational acceleration is proportional as follows, dv/dt 1 – 1/exp(rr/r_{e}r_{e}). Calculating this for each planet and then scaling to earth’s LeSagian value yields Figure 4, which compares the scaled Newtonian and LeSagian gravitational accelerations. Except for Jupiter, where the scaled Newtonian gravitational acceleration (2.5) is about 2/3 higher than its LeSagian counterpart (1.5), the gravitational accelerations when scaled show very good agreement (follow the 45-degree slope).

__FIGURE 3__**. Newtonian vs. LeSagian Gravitational Force vs. Distance for the Nine Planets**

** **

__FIGURE 4__**. Newtonian vs. LeSagian Gravitational Acceleration for the Nine Planets**

**Conclusion**

The relatively good agreement between Newtonian and LeSagian gravitation exhibited in Figures 3 (similar trend although varying orders of magnitude) and 4 for our solar system are positive results for the ‘pushing’ gravity theory. While Newton’s Law does not attempt to explain how gravity works, it obviously provides an excellent model for the effects of gravity. Any theory purporting to ‘explain’ the mechanism of gravitation must at least align calculationally with the results from Newton, especially within our solar system upon which much of his original theory was based and where it has been repeatedly verified.

**References**

** **

*https://en.wikipedia.org/wiki/LeSage%627s_theory_of**_gravitation*- de Hilster, R.,
__Gravity is not Free – Pushing Gravity Beyond the Apple__, John Chappell Natural Philosophy Society, Caledonia, MI (2016).

**Appendix**

One might consider comparing the “shadowing” effects between the “solid” (denser) four inner planets and the four “gas giants” (less dense) to be somewhat of an “apples” to “oranges” comparison. After all, might the “impact” effect of the gravity particles differ significantly when impinging on a “solid” surface, such as Earth’s, vs. a “gaseous” one, such as Jupiter’s? To try to compensate somewhat for this possibility, consider treating the four gas giants as “solid” planets with a density equal to the average of those for the four inner planets (ρ_{av} = 5.030E+12 kg/km^{3}) and equivalent radii (r_{eq}) based on their respective masses (m), i.e., m = 4pr_{av}r_{eq}^{3}/3 = 4prr^{3}/3 ® r_{eq} = r(r/r_{av})^{1/3}, where ρ and r are the planet’s actual density and radius. This results in the following changes to Tables 1 and 2, shown in Table 3. Note that, in the interaction/attenuation calculation, the average density (ρ_{av}) and equivalent radius (r_{eq}) are now used instead of the originals.

As can be seen, the magnitude of the LeSagian forces all decrease (the maximum reduction is about a factor of 10 for Saturn, whose equivalent radius also decreases the most, just under a factor of two), suggesting that the “impact” aspect (based on the cross-sectional area) rather than the “interaction/attenuation” aspect (based on the density and radius/diameter) dominates. Figure 5 shows that the trends are essentially the same, but the differences are now about an order of magnitude less for the gas giants. Figure 6 indicates reduced agreement for the gas giants, with the exception of Jupiter, leaving unanswered the question of whether this “average density-equivalent radius” approach is an improvement. Nonetheless, the exercise is worthy of consideration.

## Robert Beatty

| #

I have my doubts that gravity can accurately be described as a pulling or pushing force. It seems to me that gravity is an example of an elastic link – a bit like a spring, but different in that a spring can store energy. An elastic link supplying gravity between two orbiting bodies consumes energy both in and out as the bodies orbit in an elliptical path. The neutral point occurs where EGS is matched between the two bodies, i.e. a circular orbit. The gravitational energy consumed reports as additional mass in the orbiting bodies.

The reason I suspect this is occurring is because the Earth has gained considerable size and mass over geological time – with due deference to the many geologists who would contest this allegation.

In mathematical terms it seems that the stronger the applicable gravitational field, the more mass is transferred. There appears to be no doubt material orbiting near a black hole gets sucked in because it is unable to maintain its orbit. This could result from a rapid increase in mass due to the very high gravitational force.