The Pale Blue Dot? Chapter Ten: The Flat Circular Earth and the “Theory” of Gravity

Originally Written By Thomas Perez. July 23rd, 2019 at 11:29pm. Copyright 2019. Updated 2020.

An infinite Earth? The possibility of an infinite Earth is not far from the realm of possible reality.  After looking into what was called “Operation High jump,” the thought of an infinite plane came into my mind as  a plausible theory. Combining what we have read thus far in chapters one, two, and what is written in chapter seventeen, I started to think on this possibility a bit further.  The curvature, speed of light and finally the term “outer space” itself as the possible last final frontier, or if it even exists as it is shown to us by mainstream science, are all at best hypothetical theories, thought as a fact. It may be that, at the very least, outer space certainly does not exist the way they are portraying it to us. The Earth (its dome), I concluded, is infinite and may be expanding. However, the expansion theory has now come into doubt among physicists. Equations provided in chapter one which contained a formula that collapsed in proving a non-spherical Earth; and not to mention what we have already in chapter two, all support a flat non-spherical Earth. But how does a flat Earth model hold water when up against the theory of gravity?

The Mainstream Euclidean Approach to Gravity

Mainstream science tells us that the Earth; along with the stars, wandering stars (so called planets) and solar system is traveling at tremendous speeds with the acceleration of gravity holding everything together. With that in mind, I began to ask myself a simple question, “How would an infinite flat Earth with density (its bottom, so to speak) produce a gravitational acceleration according to Newton’s formula?” According to Walter Bislin; a graduated engineer in electronics, measurement and control technology (EMRT) with a master’s degree in systems engineering, who is currently a Senior Software Developer Engineer cites Newton’s formula as follows:

http://walter.bislins.ch/bloge/index.asp?page=Gravity+on+an+infinite+Flat+Earth+Plane

Wikipedia confirms this

According to Bislin, “If the earth were an infinite plane of a certain thickness b and homogeneous density ρ, you would get a homogeneous gravity field that acts perpendicular to the surface everywhere.”

“Such a Flat Earth would not collapse into a sphere, theoretically. But this plane would not be stable. The slightest irregularities in the density would disturb the equilibrium and crunch the earth, except if it is infinitely rigid. An infinite plane would also mean an infinite mass for the earth.” “The formula for calculating g for an infinite plane turns out to be really simple.”

The outline in Bislin’s preparation for an infinite flat Earth are as follows:

“Note: In the equation (5) for the gravitational acceleration g for an infinite plane there is no term for the altitude h like on the globe Earth! This implies that the gravitational acceleration is the same at every altitude.” “This is due to the homogeneous gravity field that such an infinite plane would create.” This is an assumption by Bislin; hence maintaining that all flat Earthers adhere to universal acceleration (UA). This is simply not the case.

The following equations by Bislin defend a flat infinite Earth, albeit begrudgingly:

And finally…

http://walter.bislins.ch/bloge/index.asp?page=Gravity+on+an+infinite+Flat+Earth+Plane

But despite all this Bislin denies an infinite flat Earth, citing, “If the flat Earth is infinitely large and has a thickness “b” and a homogeneous density “ρ,” all horizontal gravitational force components would cancel each other at every place on earth and only leave the sum of all vertical force components. There would be no center of mass like on the globe.” “But is the sum of the vertical force components of all volume elements of the infinitely large plane not infinite, assuming that Newton’s law of universal gravitation is applied like on the Globe Earth?”

Similarly, “If the earth were an infinite plane of a certain thickness b and homogeneous density ρ, you would get a homogeneous gravity field that acts perpendicular to the surface everywhere.” “Such a flat Earth would not collapse into a sphere, theoretically. But this plane would not be stable. The slightest irregularities in the density would disturb the equilibrium and crunch the Earth, except if it is infinitely rigid. An infinite plane would also mean an infinite mass for the earth.”

Bislin also cites, “How can we explain that gravity in reality is a gradient getting weaker as we gain altitude? Some propose that sun, moon and stars have a gravitational influence too.”

“But this does not work either. If the gravitational influence is restricted to a finite region, no matter how big, we have a point gravitational field towards a center of mass in the sky which adds with the homogeneous field from the earth:

  • Either the center of mass in the sky is far enough so that its gravity field is approximately homogeneous near the earth. But this does not lead to a gravity gradient that is decreasing with altitude.
  • Or it is near enough to distribute the homogeneity of earth’s field. But then net gravity would point to a single source in the sky so net gravity would not act perpendicular on earth anymore.”

“If the heaven were infinite like the earth, it would produce a homogeneous field like the flat infinite earth and adding both fields together does not produce a gravitational gradient as we observe: homogeneous + homogeneous => homogeneous.”

“So what do we observe? Is g constant at each altitude h from the surface of the earth or is it changing with 1/(R+h)2? Is it perpendicular to the water surface everywhere?”

“We know the gravitational acceleration g is changing with 1/(R+h)2 from measuring it with a scale and a weight at different altitudes or by using a gravimeter. And it also depends on latitude because the earth rotates and is not a perfect sphere. And it acts perpendicular to the Geoid surface which defines mean sea level.”… “So Gravity measurements falsify the hypothesis of an infinite Flat Earth plane. Observations of gravity on earth confirm a rotating ellipsoid.”

Bislin’s stance is based upon Newton’s gravitational acceleration law of gravitation, which is g = 9.806 m/s2 and hence applying that law unto a flat Earth hypothesis that has no center of gravity, but is the same magnitude everywhere, is preposterous.

“The 9.8 m/s^2 is the acceleration of an object due to gravity at sea level on earth. You get this value from the Law of Universal Gravitation. …If you put in the mass of the earth and the radius to sea level you will get 9.8 m/s^2 for a. This is what we call little g.” 9.8 m/s^2 is the limit of speed at which an object falls to the Earth as it gets closer and closer to the ground. However, this acceleration is based upon an assumption; an assumption based upon a theoretical constant. Further confirmation of this is cited in Socratic.org, “Since g is calculated using only constants, g is a constant. where Re is radius of the earth. As earth is not a perfect sphere, value of gravity g is not a constant at all the locations on the surface of the earth. …Therefore, for practical purposes we take acceleration due to gravity as a constant.

https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/gravity-newtonian/v/introduction-to-newton-s-law-of-gravitation

https://socratic.org/questions/why-is-acceleration-due-to-gravity-constant

Most people believe gravity is the same everywhere on Earth, but this is not the case.  Since mainstream science maintains that the Earth is not perfectly spherical or uniformly dense, gravity is weaker and varies at different locations, especially at the equator due to centrifugal forces produced by Earth’s alleged rotation. “This quantity is sometimes referred to informally as little g (in contrast, the gravitational constant G is referred to as big G). The precise strength of Earth’s gravity varies depending on location. The nominal “average” value at Earth’s surface, known as standard gravity is, by definition, 9.80665 m/s2.”

Wiki – Gravity of Earth.

A Non-Euclidean Approach to Gravity

John Davis; a software engineer, a computer scientist, who is well versed in epistemology and mathematics uses a different approach in reference to gravity and how it works on an infinite flat Earth plane. Many would be quick to cite, “No matter the density (of Earth) it will have infinite mass. Therefore it will have infinite gravity, which is absolutely impossible.” This line of reasoning is a misunderstanding of the given equations below. According to Davis, a non-Euclidean approach to a flat Earth in reference to gravity is based upon the following equations. The first set of equations come from a colleague and the second comes from Davis:

Davis: Longer version applied with the applications of Gauss’s law showing that an infinite plane would have a finite gravitational pull.

d = g / (2πG p)

Let us now apply Gauss’s law in a gravitational field – as in Bouguer gravity (gravity anomalies). These anomalies are referred to as Bouguer(s) gravity, named after Pierre Bouguer; mathematician, physicist and astronomer (1698 – 1758). “Gravity anomalies are often due to unusual concentrations of mass in a region. … Conversely, the presence of ocean trenches or even the depression of the landmass that was caused by the presence of glaciers millennia ago can cause negative gravity anomalies.”

https://earthobservatory.nasa.gov/features/GRACE/page3.php

The shorten version of this non-Euclidean approach is as follows; as taken from Eric Weinstein’s World of Physics with reference to infinite parallel planes, infinite plane, and sphere electric field.

Bouguer gravity:

“To an infinite slab of density p we obtain”

“Where A is the area of the “Pillbox,” G is the gravitational constant, and h is the thickness of the slab. Therefore, the gravitational acceleration is given by”

Infinite Parallel Planes:

“Given two parallel infinite planes separated by distance d with surface charge density  on one and  on the other, applying Gauss’s law shows that the electric fields cancel above and below the plates, while adding between them. The electric field is therefore given in cgs by”

“and in MKS by”

“Where  is the permittivity of free space.”

Infinite Plane

“Applying Gauss’s law using a cylindrical pillbox extending above and below a charged infinite plane in cgs, the electric field satisfies”

“Where  is the unit normal and  is the surface charge density. By symmetry, , so”

“and solving for E gives”

Sphere Electric Field:

“The electric field outside a sphere with total charge Q distributed with spherical symmetry can be found immediately from Gauss’s law. In MKS using spherical surface.”

“Where  is the permittivity of free space, so”

“Where  is a unit radial vector. This is the same result that would be obtained from a full-blown integration of Coulomb’s law, and is analogous to the result that the gravitational force from a sphere is equal to the force from a point mass equal to the total mass of the sphere and located at its center.”

From this all others follow suite: Coulomb Force, Coulomb PotentialElectric FieldHeaviside-Lorentz SystemInverse Square Law

http:/scienceworld.wolfram.com/physics/BouguerGravity.html

As you can see, Davis used the Gaussian Pillbox. “The Gaussian pillbox is the surface with an infinite charge of uniform charge density used to determine the electric field.”  Similarly, “This surface is most often used to determine the electric field due to an infinite sheet of charge with uniform charge density, or a slab of charge with some finite thickness. The pillbox has a cylindrical shape, and can be thought of as consisting of three components: the disk at one end of the cylinder with area πR², the disk at the other end with equal area, and the side of the cylinder. The sum of the electric flux through each component of the surface is proportional to the enclosed charge of the pillbox, as dictated by Gauss’s Law. Because the field close to the sheet can be approximated as constant, the pillbox is oriented in a way so that the field lines penetrate the disks at the ends of the field at a perpendicular angle and the side of the cylinder are parallel to the field lines.”

Wiki

Many would counter by citing that Gauss’s law cannot be used on non-Gaussian surfaces (like those seen on the right side in the picture below), such as a disk surface, a square surface, or a hemispheric surface; they would have boundaries as the following picture illustrates (red being its boundaries on the right). They do not fully enclose a 3D volume. Moreover, infinite planes requires infinite energy, which is said not to exist.

However, infinite planes can approximate Gaussian surfaces as demonstrated in the Weinstein approach. That being the case, would not an infinite plane require infinite energy? The answer to that question is “yes.” It is said that energy goes on forever (infinite), but the total energy it imparts is finite. However, a constantly expanding and accelerating universe, or plane for that matter, always requires infinite energy.

According to Davis:

“Now if you were to ask somebody how much gravitational pull an infinite amount of mass would exert, the common sense answer would be “infinite!” However, upon inspection we can see that certain configurations of mass would actually yield finite gravitational pulls. …

Usually used in electromagnetism, Gauss’s law actually applies to gravitational forces as well since they both share an inverse square relationship 1/distance2 to their strength. It can be stated as follows:

gn dA = -4πGm

“Lets say we have some mass m. We pretend to create a surface around the mass. We divide this surface up into infinitesimal parts, each with an area of dA. Remember that the integral is summing up an infinite amount of infinitesimal surfaces? We take the infinitesimal bits of the area (dA) and sum them over the entire closed surface. Each infinitesimal “bit” has an nn is a unit vector that is perpendicular, so facing away from the surface at a right angle away. You might want to visualize that n represents “up” since we are dealing with a plane. g is the acceleration due to gravity, pointing towards the mass. In our case, this should be “down.”

“We can use this to examine the gravitational influences of any body. If we were looking at point mass, we would use a sphere. If we were looking at an infinite plane, as we are, we will use a pillbox for our surface.”

“When we look at the pillbox, we can simplify things nicely. We see the curved surface of the pillbox will “cancel out” its own gravitational influence and contribute nothing. A simple way to think of this is that each point on the cylinder is counterbalanced with another point on the cylinder. This coincidentally also shows the infinite plane is a stable body as each point on the plane itself is also counter-balanced by the points around it horizontally, thus answering the common question “Why wouldn’t mass form into a sphere?” A more accurate way would be to realize this is that g is at a right angle to our “up” ( n ) at all points; all points have an opposite point that is facing the opposite direction as well, and so g•n = 0.”

“We are almost there – this leaves us with only the circle caps to deal with.”

“Looking at the caps we realize that g and n are parallel and opposite each other and so we realize gn = -g. This leaves the surface integral of just the pillbox ends. Since we have 2 of them and the integral is the sum of the parts of dA, we have -g∮dA = g2A leaving our equation as: -g 2A = -4πGm. From there its easy to see g’s value is finite – g= 2πGm / A. This is further realized by noting mass = (density * Area), giving us g A= 2πGpA, or g = 2πG p. This is clearly a finite value. If we wished we could continue from here to calculate the depth of the plane using the average density of Earth.”

“Given it also has depth we are looking at the case of m = (density * Area * depth). This gives us instead g = 2πG p d, where d is depth.”

g = 9.81 m/s/s
G = 6.754×10−11 m3 kg−1 s−2
p = 5.51 g/cm³ , the average density of earth

“Giving us d = g / (2πG p). This evaluates to around 4195.43 kilometers deep.”

The comparisons between the two; Bislin’s and Davis/Weinstein are the same, except for their conclusions in reference to the thickness of a flat plane/Earth. Both using different gravitational pull speeds. Bislin chose UA as a constant, utilizing a sphere in the long run. Davis and Weinstein, on the other hand, utilized Bouguer(s) gravity, a non UA, Gauss’s law, infinite planes and spherical electric fields which in turn provided no contradiction to the given physics at hand.

Bislin: 9.806 m/s2  – UA

Weinstein: 9.81 m/s/s Bouguer gravity

Bislin: g=2 π-G-p-b – flat Earth at

4241 kilometers deep.

Weinstein: d = g / (2πG p) – flat Earth at

4195.43 kilometers deep.

The calculations by Bislin, with comparative conjunction to my own findings, simply does not hold water. The equation of a ball Earth, and therefore a limited sphere hanging in space, with its curvature at M² x .7993624 = d, or as commonly written by globalists M² x 8 = d fails all observational empirical evidence by spherical globe standards, as demonstrated in chapter one; hence proving a flat Earth. However, as synchronized and forth telling these equations and formulas are, it should be remembered that math can virtually be used to validate or tear down any theory, depending on the spin it is given from its physicist. “Math has no tie to reality, but it is a useful tool to inspect reality if reality acts causally.”