Summary of the Dark Energy Equation and Its Integration with Classical Mechanics:

Soumendra Nath Thakur

28-08-2024

The derived equation Mɢ = Mᴍ + Mᵉᶠᶠ builds upon the foundational equation Mɢ = Mᴍ + Mᴅᴇ, established through empirical research by A. D. Chernin et al. in 'Dark Energy and the Coma Cluster of Galaxies,' and its consistent application within classical mechanics. In this formulation, Mᵉᶠᶠ represents the effective mass associated with dark energy. This approach adheres to classical mechanics principles and the author's rigorous mathematical framework, particularly in converting potential energy (including dark energy) into kinetic energy. This conversion affects both local gravitational dynamics and cosmic expansion.

The mathematical rigor underlying the equation Mɢ = Mᴍ + Mᵉᶠᶠ is evident from its derivation and application, as detailed in the research paper. It provides a robust theoretical framework by establishing the equivalence of negative effective mass with potential energy and its conversion into kinetic energy. This framework enhances our understanding of the interaction between classical potential energy, gravitational dynamics, motion, and cosmic structures, explaining galactic recession and the broader implications for cosmic expansion.

Conceptual Innovations in the Extension of Classical Mechanics:

Soumendra Nath Thakur

28-08-2024

The research paper titled "Extended Classical Mechanics: Effective Mass and Acceleration Boost in Motion and Gravitational Dynamics," authored by Soumendra Nath Thakur, is meticulously designed to naturally underscore the conceptual innovations inherent in this extension of classical mechanics. The work represents a significant advancement within classical science, introducing novel ideas that are crucial for readers to comprehend the ground breaking contributions to the field.

This extension not only deepens our understanding of classical mechanics but also provides a necessary framework for interpreting new physical phenomena. The structure of the paper is intentionally crafted to highlight these theoretical advancements, ensuring that the innovations are effectively communicated and appreciated within the broader scientific community.

The derived equation Mɢ = Mᴍ + Mᵉᶠᶠ builds upon the foundational equation Mɢ = Mᴍ + Mᴅᴇ, established through empirical research by A. D. Chernin et al. in 'Dark Energy and the Coma Cluster of Galaxies,' and its consistent application within classical mechanics. In this formulation, Mᵉᶠᶠ represents the effective mass associated with dark energy. This approach adheres to classical mechanics principles and the author's rigorous mathematical framework, particularly in converting potential energy (including dark energy) into kinetic energy. This conversion affects both local gravitational dynamics and cosmic expansion.

The mathematical rigor underlying the equation Mɢ = Mᴍ + Mᵉᶠᶠ is evident from its derivation and application, as detailed in the research paper. It provides a robust theoretical framework by establishing the equivalence of negative effective mass with potential energy and its conversion into kinetic energy. This framework enhances our understanding of the interaction between classical potential energy, gravitational dynamics, motion, and cosmic structures, explaining galactic recession and the broader implications for cosmic expansion.

#EffectiveMass, #ClassicalMechanics, #ConceptualInnovations, #GravitationalDynamics, #MathematicalRigour,

Calculation of Effective mass and Gravitating mass: Extension to Classical mechanics

Calculation file attached: Here

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

27-08-2024

This expression F = (Mᴍ + Mᵉᶠᶠ)aᵉᶠᶠ, reflects an extended classical mechanics approach where the total force F is associated with both the matter mass Mᴍ and the effective mass Mᵉᶠᶠ. Here, the effective mass Mᵉᶠᶠ is introduced as an additional term that modifies the system's dynamics in motion. The effective acceleration aᵉᶠᶠ represents the combined effect of traditional acceleration and the influence of effective mass.

F = (Mᴍ + Mᵉᶠᶠ)aᵉᶠᶠ, Mᵉᶠᶠ generated when F acting in motion (v)

• F is the total force applied to the object, measured in Newtons N.
• Mᴍ is the matter mass of the object, representing its traditional inertial mass, measured in kilograms (kg).
• Mᵉᶠᶠ is the effective mass, which arises due to the interaction of the object with the applied force during motion, measured in kilograms (kg).
• aᵉᶠᶠ is the effective acceleration experienced by the object, which accounts for both the matter mass and the effective mass in the system, measured in meters per second squared (m/s²).
Calculation in attached file.

#EffectiveMass #GravitatingMass #EffectiveMassCalculation #GravitatingMassCalculation

Dominance of Effective Mass vs. Matter Mass: Determining Positive or Negative Effective Acceleration

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

27-08-2024

Whether the effective acceleration (aᵉᶠᶠ) is negative or positive depends on which factor dominates the system—effective mass (Mᵉᶠᶠ) or matter mass (Mᴍ)—in both scenarios of motion or gravitational potential difference.

#EffectiveAcceleration #MassDominance #GravitationalPotential

Effective Mass and the Inverse-Square Law of Gravity: Implications for Gravitational Acceleration

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

27-08-2024

In scenarios involving the inverse-square law of gravity and the concept of effective mass, these factors collectively influence an object's motion.

According to the inverse-square law of gravity, as an object moves away from the Earth's surface, the gravitational force it experiences decreases with the square of the distance. In this context, the concept of 'effective mass' becomes crucial. Effective mass introduces an 'effective acceleration' (aᵉᶠᶠ) by effectively changing the object's resistance to gravitational force.

The reduction in gravitational influence due to effective mass occurs because this mass type is not static; it is generated as the object moves or elevates. As the object ascends, the 'effective mass' modifies the overall gravitational pull, enabling the object to accelerate more easily, even as it moves farther from Earth.

In the context of 'effective mass', the inverse-square law also applies. As an object moves away from the Earth's surface, the gravitational force decreases with distance, and 'effective mass' changes the object's resistance to this force. 'effective mass', which is generated through the object's elevation and motion, modifies the gravitational pull on the object, allowing it to accelerate differently depending on whether it is moving closer to or farther from Earth.

#EffectiveMass #effectiveacceleration #GravitationalAcceleration # InverseSquareLaw