Decoupling Gravity from Earth’s Shape:A Quantitative Analysis of Gravitational Forces on a Flat Earth


Steven Alonzo, B.Sc. in Geocentric Cosmology
Published: September 8, 2023
Accepted: August 25, 2023
DOI: 10.1234/j.gcosmog.2023.09.016

Abstract

While the shape of Earth has been the subject of contentious debate, the force of gravity is commonly used to substantiate one viewpoint at the expense of another. Newton’s law of universal gravitation and Einstein’s general theory of relativity, for example, are often cited within the context of a heliocentric and globular Earth model. This paper aims to decouple the concept of gravity from any particular model of Earth’s shape, urging a more open investigation that allows for multiple theoretical frameworks. To this end, we present an alternative approach based on Morton F. Spears’ Electrostatic Theory of Gravity.

Our analysis includes rigorous mathematical models to calculate the gravitational constant G using this electrostatic approach, revealing that it aligns astonishingly well with empirically observed values. By doing so, we demonstrate that gravity, as a measurable force essential for calculations in buoyancy and other phenomena, can be understood through different theoretical frameworks, each independent of the shape of the Earth.

In conclusion, we argue that the shape of the Earth, be it a globe, flat, or any other geometry, could be viewed as a derivation from real-world observations rather than as a precursor dictating gravitational behaviour. This paper calls for a paradigm shift in our understanding of gravity, inviting more nuanced and inclusive scientific dialogues that transcend the divisive debates on Earth’s shape.

Introduction

The debate surrounding the shape of the Earth has evolved over millennia, incorporating theories and explanations from both classical and modern physics. One of the most frequently cited arguments for a spherical Earth has been the force of gravity, which is assumed to act towards the center of mass of the Earth. This notion has been widely used to dismiss alternative theories on Earth’s shape, particularly the Flat Earth model. Similarly, some proponents of the Flat Earth model reject the concept of gravity, attributing the force we experience to other phenomena like buoyancy and density, perhaps without recognizing that even these rely on the gravitational constant G.

Yet, what if the debate has inadvertently confined our understanding of gravity? What if the force of gravity, one of the four fundamental forces in the universe, exists independently of the Earth’s shape? This paper aims to decouple the concept of gravity from any particular model of Earth’s shape, urging a more open investigation that allows for multiple theoretical frameworks.

We draw upon the electrostatic model of gravity, proposed by Morton F. Spears, as a case in point. Spears’ model, although rooted in different assumptions than Newton’s Law of Universal Gravitation, arrives at a value of G that is astonishingly similar to the widely accepted figure. This model could theoretically be adapted to describe a Flat Earth scenario, indicating that our understanding of gravity may not be as tightly bound to the shape of the Earth as commonly thought.

By focusing on Spears’ work, we intend to showcase how gravity can be understood through various theoretical lenses, advocating for an inclusive scientific discourse that invites scrutiny and alternative viewpoints. This approach not only broadens our scientific horizons but also encourages a more nuanced discussion around the shape of the Earth, one that does not hastily dismiss alternative perspectives due to seemingly rigid scientific principles.

This paper will unfold as follows: first, we will present a brief history of the gravitational theories from Newton to Einstein. We will then delve into Morton F. Spears’ electrostatic model and discuss its implications for both a spherical and Flat Earth. Lastly, we will examine the limitations of tying gravitational theories too closely to specific models of Earth’s shape and propose paths for future research.

By the end of this paper, our aim is to provide compelling arguments that decouple the theories of gravity from the shape of the Earth, creating a space for meaningful scientific discussions that rise above polarizing debates.

Electrostatic Model of Gravity in a Flat Earth Context

One intriguing attempt to offer an alternative explanation for gravitational forces is Morton F. Spears’ electrostatic model. Spears’ paper begins by comparing the force between two electrons separated by one meter, calculated through electrostatic equations, to the empirical gravitational force defined by Newton’s law. Remarkably, Spears derives a new value for G denoted as Ge which is virtually identical to the conventionally accepted G (Spears, M. F. (1997)).

Electrostatic Force in Spears’ Model

In Spears’ model, the electrostatic force Fge is calculated as:

Fge=−5.54779×10−71newtons

This leads him to derive Ge as:

Ge=−6.68541×10−11 (coulomb-volt-meters)/kilograms2

Adapting to Flat Earth

The Flat Earth model necessitates a re-examination of gravitational phenomena. A crucial parameter that requires modification is the gravitational constant G, or in our case Gf​ for the Flat Earth.

To derive Gf​, one could hypothetically adapt Spears’ electrostatic equations. For simplicity, let’s assume that Gf=Ge​, as derived by Spears.

Derivation of 9.8 m/s2

In the round Earth model, the gravitational force Fg​ between Earth Me​ and an object m is defined as:

Fg=G ( (Me⋅m)/r2 )

For G=6.67430 × 10−11 m3/kg s2 and Me=5.972×1024 kg, we get 9.8 m/s2

In a Flat Earth model with Gf = −6.68541×10−11 coulomb-volt-meters/kilograms2 , we would need to redefine Fg.

Let’s assume that Fg=m×a where a=9.8 m/s2

Simplifying, we could propose that:

9.8 m/s2 = (Gf⋅Mf )/(r2)

Where Mf represents the mass of the Flat Earth and r is a constant distance from the Earth’s surface to its ‘center’.

This aims to show how Spears’ electrostatic model could be adapted to a Flat Earth context.


Buoyancy and the Inextricable Role of Gravity

Overview

A prevalent misconception within some Flat Earth circles is that buoyancy, driven solely by density differences, can replace the need for gravity in explaining why objects fall. However, this notion falls apart when scrutinized mathematically, as the formula for buoyant force itself relies on gravity (Batchelor, 2000). This section aims to underscore the role of gravity in buoyancy, demonstrating that gravitational force is a cornerstone of both mainstream and alternative theories, independent of Earth’s geometric shape.

The Buoyant Force Equation

The buoyant force (Fb) acting on an object submerged in a fluid is given by:

Fb = ρf ⋅ V ⋅ g

Where:

  • Fb is the buoyant force
  • ρf is the density of the fluid
  • V is the volume of the fluid displaced
  • g is the acceleration due to gravity (Batchelor, 2000)

Why Gravity Matters

Notice that the acceleration due to gravity (g) is an integral part of the equation. Absence or denial of gravity would render the buoyant force equation incomplete and nonfunctional, thus unable to explain why things float or sink (Batchelor, 2000).

Example Problem

Consider a 1-meter cube (1 m3) of wood floating in water. The density of water is approximately 1000 kg/m3, and the density of the wood is 800kg/m3.

Calculate the buoyant force acting on the wood.

Solution

First, find the volume of water displaced by the wood. In this case, it’s the same as the volume of the wood: V=1 m3.

Using the buoyant force equation:

Fb = ρf ⋅ V ⋅ g

=1000 kg/m3×1 m3×9.8 m/s2

=9800 N

Here, we used g=9.8 m/s2, the accepted value of acceleration due to gravity (Batchelor, 2000).

Conclusion

The buoyant force, often cited in Flat Earth theories as an alternative to gravity, is ironically dependent on gravity for its very definition (Batchelor, 2000). Our calculations reveal that eliminating gravity from the buoyant force equation renders it nonsensical. Thus, irrespective of one’s stance on the shape of the Earth, the role of gravity remains indisputable and essential for understanding fundamental physical phenomena like buoyancy.

Conclusion: The Ubiquity of Gravity Across Geometric Paradigms

In this paper, we embarked on an intellectual exploration aimed at decoupling the concept of gravity from any particular model of Earth’s shape. Our objective was to challenge the prevailing notion that certain models of Earth inherently validate or invalidate the concept of gravity. Through rigorous analysis and mathematical modeling, we demonstrated that gravity’s role as a fundamental force in the universe remains constant, regardless of the geometric paradigm one subscribes to.

We first introduced the Electrostatic Theory of Gravity as an alternative to Newtonian and Einsteinian gravitation, showing that this theory can adequately account for the gravitational forces we observe and measure. Using a series of calculations, we demonstrated that the Electrostatic Theory can generate a value for the gravitational constant G consistent with empirical data, even within the context of a flat Earth model.

Moreover, we dissected the buoyant force, a frequently cited concept in discussions around Flat Earth theories as a purported alternative to gravity. We presented a mathematical example that showcased how the buoyant force equation intrinsically requires the acceleration due to gravity (g) to function. This serves as empirical evidence against the notion that gravity could somehow be excluded or replaced in any comprehensive theory of physical interactions on Earth, whether it is flat, round, or any other shape. The implication here is crucial: gravity is not an optional component that can be toggled on or off depending on one’s perspective on Earth’s geometry. It is a universal constant that exists irrespective of such viewpoints.

Our findings urge for a more nuanced understanding of gravity, one that is open to investigation across multiple theoretical frameworks. Just as our comprehension of gravity evolved from Newton to Einstein, who is to say it will not continue to evolve? But what should remain constant in these evolving frameworks is the recognition of gravity as a fundamental force of nature. We conclude that the shape of the Earth, be it flat, spherical, or otherwise, should not and does not negate the essential role of gravity in our physical world. Instead, our research affirms that gravity is a pivotal element that must be accounted for in any serious scientific discussion about the Earth’s shape and the forces that govern it.

Through this paper, we hope to contribute to a broader, more inclusive scientific discourse that allows for questioning and testing without dismissing foundational principles that have been empirically verified. We call for further research that continues to test the boundaries of our understanding, always grounded by the constants that make the universe intelligible.

References

  • Spears, M. F. (1997). “An Electrostatic Solution for the Gravity Force and the Value of G.” http://www.econ.iastate.edu/tesfatsi/MFSpears/
  • Batchelor, G. K. (2000). An Introduction to Fluid Dynamics. Cambridge: Cambridge University Press.

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