The Evolution of Earth's Rotation: Insights from Gravitational Angular Velocity

The Earth's rotation has evolved significantly over the vast expanse of geological time. During the Proterozoic Eon, approximately one billion years ago, Earth's rotation was considerably faster than it is today. Estimates suggest that a day on Earth back then lasted between 18 to 22 hours, as opposed to the current 24-hour day. This marked a significant acceleration in Earth's rotational speed, indicating it completed a full rotation in less time than it does now.

Factors Influencing Earth's Rotation

The faster rotation observed during the Proterozoic Eon could be attributed to a combination of Earth's formation and the gradual slowing of its rotation over geological time due to tidal forces exerted by the Moon and the Sun. The Moon, in particular, has played a crucial role in this process. As the Moon gradually moved away from Earth due to tidal forces, its gravitational influence has caused Earth's rotation to slow down over millions of years. This phenomenon highlights the complex interplay between celestial bodies and the impact they have on Earth's dynamics.

The Role of Gravitational Angular Velocity (GAV)

Understanding the Earth's rotational history is complex, especially without information on the planet's mass and density during different epochs. However, an innovative approach to this problem involves finding an equation with the minimum number of variables to describe the planet's rotational motion. This method is in line with Occam's Razor, which suggests that the simplest solution is often the most likely.

Gravitational Angular Velocity (GAV) is a fundamental intrinsic property of a planet where the influence of gravity is noticeable. Unlike artificial rotation, such as spinning a ball, GAV describes the natural rotation due to gravitational forces. The relationship between GAV and the mass and density of a planet can be described by the following equation:

GAV[intrinsic property] f(mass, density)

Equatorial Rotation Velocity as a Function of Mass and Density

To further validate this relationship, equations have been developed to describe the equatorial rotation velocity of both Jovian and Terrestrial planets as a function of mass and density. While more empirical data, particularly from exoplanets, is needed to fully validate these models, the current derivations offer a promising framework for understanding planetary rotation.

Jovian Planets

For massive Jovian planets, the rotation velocity can be calculated using a specific equation derived from gravitational dynamics. While the exact parameters and constants are still under study, this approach provides a starting point for future research. For instance, the rotation velocity of Uranus can be calculated using both equations, leading to consistent results.

Terrestrial Planets

Terrestrial planets, with their denser and often smaller masses, exhibit different rotation characteristics. The rotation velocity for these planets can be described using a slightly different set of equations, reflecting the unique properties of rock and metal-rich bodies in the inner solar system.

Deriving Additional Properties from Gravitational Angular Velocity

Once the relationship between GAV, mass, and density is established, additional properties such as rotational energy density (E/V) and angular momentum (J) can be derived. These properties play crucial roles in understanding the dynamics of planetary systems.

The rotational energy density can be expressed as a function of mass, which can then be input into the Stress-Energy Tensor. Similarly, angular momentum can be calculated as a function of both mass and density, and be used in the Kerr Metric to describe frame-dragging effects. Both rotational energy density and angular momentum are critical in our understanding of gravitational influence within the context of General Relativity.

Planetary Rotation and General Relativity

The study of planetary rotation intersects with one of the most fundamental theories in physics: General Relativity. Concepts such as Gravitoelectromagnetism (GEM) and the Lense–Thirring Metric, which describe the interaction between gravity and rotating frames of reference, are integral components of this intersection. These metrics offer a deeper insight into the complex dynamics of rotating celestial bodies.

Notes:

Use equation 1 or 2 for Uranus and you will arrive with the same value of rotation velocity. The constants are not dimensionless but have units of length, time, and mass. Everything must be made as simple as possible. But not simpler. Any intelligent fool can make things bigger, more complex and more violent. It takes a touch of genius—and a lot of courage—to move in the opposite direction.

As we continue to explore the dynamics of planetary motion, our understanding of planetary rotation is crucial. The insights provided by GAV and the derivations of related properties offer a promising direction for future research in astrophysics. By simplifying and validating these concepts, we move closer to a deeper understanding of the complex dynamics of our universe.