The Influence of Distance from Earth's Center on Gravitational Force

Gravity is a fundamental force that governs the motion of celestial bodies and the daily experiences of living beings on Earth. In this article, we will explore how the gravitational force on the body varies as it moves farther from the center of the Earth. This knowledge is crucial for understanding the dynamics of celestial mechanics, geophysics, and everyday phenomena. We'll delve into the mathematical and theoretical underpinnings of gravity, focusing on Newton's Laws and more recent models like DOPA Gravitational Theory.

Newton's Gravitational Law

According to Sir Isaac Newton's gravitational law, the force of gravity F between two masses Me (Earth's mass) and M1 (the mass of an object) is given by the formula:

F G Me M1 / r^2

Where F is the gravitational force, G is the gravitational constant, Me is the mass of the Earth, M1 is the mass of the object, and r is the distance between the centers of the two masses. In the context of an object at various distances from the Earth's center, r is the distance from the object to the center of the Earth.

Gravitational Force on a Body Inside the Earth

For an object below the Earth's surface, the effective gravitational force depends on the mass of the Earth that lies within a sphere of radius r. As one moves deeper into the Earth, the mass above the object decreases, leading to a decrease in the gravitational force. However, the force does not decrease continuously but rather in a non-linear fashion. According to DOPA Gravitational Theory, the net gravitational force increases from zero at the Earth's core to 9.81 m/s2 at the Earth's surface.

Thought Experiment: Moon's Orbit and Orbital Speed

Let's analyze a thought experiment to understand the relationship between orbital speed and distance. Our Moon orbits the Earth at 2295 miles per hour (MPH) from a distance of 239,000 miles. To calculate the Moon's orbital speed if it were at Earth's 3,959-mile radius, we use the formula:

rMoon 239,000 / 3,959 ≈ 60.369

Taking the square root of 60.369 gives us approximately 7.70. Therefore, if the Moon were to orbit at Earth's radius, it would do so at 7.7 × 2,295 MPH ≈ 17,672 MPH.

Now, consider an object at 2,000 miles from the Earth's center. The ratio of the Earth's radius to this distance is 3,959 / 2,000 1.98. To find the orbital speed at this distance, we divide the orbital speed at Earth's surface (17,672 MPH) by the square root of 1.98, which is approximately 1.407. This gives us:

17,672 / 1.407 ≈ 12,560 MPH

Thus, the orbital speed at 2,000 miles from the Earth's center would be 12,560 MPH.

Gravitational Force and Density Layers

The gravitational force on a body inside the Earth increases according to its distance from the core. The force tends to increase more rapidly near the center due to the high density of the core and lower layers. Conversely, towards the surface, the increase in gravitational force is less pronounced due to the lower density of the outer layers.

Practical Application and Further Reading

For those interested in a more in-depth exploration of gravity and its creation, Russet Publishing offers a book titled GRAVITY - How Gravity is Created. This book, available for purchase at ￡5.47, explains the concepts in a non-mathematical manner, making it accessible to a wide audience.

If you have any questions or need further clarification on these concepts, feel free to reach out. Understanding the intricacies of gravity provides a deeper appreciation for the mechanics of our universe.