The Dynamics of Gravitationally Bound Systems:

17-09-2024 

Soumendra Nath Thakur

In classical mechanics, gravitational mass (Mɢ) is considered equivalent to matter mass (Mᴍ). However, modern physics recognizes that the gravitational effects of dark matter and dark energy can influence gravitational dynamics, particularly in regions dominated by dark energy, such as at least on the intergalactic scale. Within a gravitationally bound system, typically confined to a zero-gravity sphere, matter mass (Mᴍ) encompasses both normal (baryonic) matter and dark matter. The gravitating mass (Mɢ) represents the total effective mass that governs the gravitational dynamics of such a system. It includes contributions from both normal matter and dark matter, but not the effective mass associated with dark energy, which is primarily dominant in regions beyond the zero-gravity sphere. This comprehensive understanding is crucial for comprehending both the internal dynamics of gravitationally bound systems and the large-scale structure of the universe.

#GravitationalDynamics, #DarkMatter, #DarkEnergy, #GravitatingMass, #ZeroGravitySphere,

Definitions : Extended Classical Mechanics: Apparent Mass, Dark Energy Effective Mass, Effective Acceleration, Effective Mass, Gravitating Mass, Matter Mass

1. Apparent Mass (Mᵃᵖᵖ): A dynamic term that reflects the observed mass of an object under external forces. This mass can appear reduced due to negative effective mass. When a force F acts on an object, causing an increase in acceleration a, a significant negative component in the effective mass Mᵉᶠᶠ (i.e. −Mᵃᵖᵖ) results in an apparent reduction of the observed mass, which can be quantified as negative apparent mass (Mᵃᵖᵖ < 0). This phenomenon is prominent under conditions like high velocities or strong gravitational fields.     

2. Dark Energy Effective Mass (Mᴅᴇ): The effective mass associated with dark energy, which contributes to a repulsive force that influences gravitational dynamics negatively. This concept, introduced in Chernin et al.'s 2013 paper, is reinterpreted in this study as equivalent to negative apparent mass (−Mᵃᵖᵖ). According to the equation Mɢ = Mᴍ + Mᴅᴇ, where Mɢ represents the total gravitational mass, Mᴍ is the matter mass, and Mᴅᴇ is the dark energy effective mass, this formulation underscores the substantial impact of dark energy on the overall gravitational dynamics of the universe.     

      

3. Effective Acceleration (aᵉᶠᶠ): The rate at which an object's velocity changes, influenced by the interplay of positive matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ). Effective acceleration is determined by the overall effective mass (Mᵉᶠᶠ) of a system, which is the sum of matter mass and negative apparent mass. When the negative apparent mass is significant, it alters the effective mass and thereby affects the acceleration experienced by the object. The relationship is expressed as: F = (Mᴍ − Mᵃᵖᵖ) aᵉᶠᶠ where F is the force applied, Mᴍ is the matter mass, −Mᵃᵖᵖ is the negative apparent mass, and aᵉᶠᶠ is the effective acceleration. This modified effective acceleration accounts for the influence of negative apparent mass on the dynamics of motion.

4. Effective Mass (Mᵉᶠᶠ): A composite term that includes both matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ). Effective mass can be positive or negative depending on the relative magnitudes of the matter mass and the negative apparent mass.          

5. Gravitating Mass (Gravitational Mass) (Mɢ): The total effective mass that governs the gravitational dynamics of a system. It encompasses both the matter mass and any negative apparent mass, and it is equivalent to the mechanical effective mass (Mᵉᶠᶠ).         

6. Matter Mass (Mᴍ): The mass associated with normal (baryonic) matter and dark matter within a system. It contributes positively to the gravitating mass.

#ApparentMass, #DarkEnergyEffectiveMass, #EffectiveAcceleration, #EffectiveMass, #GravitatingMass, #MatterMass

Research Overview: Extended Classical Mechanics. Vol-1.

17 September 2024

The research, ‘Extended Classical Mechanics’, by Soumendra Nath Thakur offers a comprehensive exploration of the foundational principles of physics, particularly focusing on mass, gravity, and their interactions. The study delves into the Equivalence Principle, a cornerstone of classical mechanics, and extends its application to incorporate contemporary understandings of dark matter and dark energy.

Key Contributions

Redefining Gravitating Mass:

The research introduces a new perspective on gravitating mass, incorporating the concept of negative apparent mass. This challenges the traditional understanding of gravitational interactions, particularly in the context of dark energy.

Introducing Apparent Mass:

The study proposes the concept of apparent mass, a dynamic term that can influence the observed mass of an object under certain conditions. This innovation allows for a more nuanced understanding of mass and its role in gravitational dynamics.

Revisiting Newton's Law:

The research reinterprets Newton's Law of Universal Gravitation to account for the newly introduced concepts of apparent mass and effective mass. This modification provides a more comprehensive framework for understanding gravitational forces.

Integrating Dark Matter and Dark Energy:

The study seamlessly integrates contemporary theories of dark matter and dark energy into the classical mechanics framework. This integration offers a more holistic perspective on the universe's gravitational dynamics.

Methodology and Implications

The research employs a combination of theoretical reinterpretation, mathematical modelling, and numerical simulations to validate its findings. The implications of this work are far-reaching, potentially influencing our understanding of gravitational theory, dark energy, and the overall structure of the universe.

Overall Significance

"Extended Classical Mechanics" presents a significant contribution to the field of physics. By extending the classical framework to incorporate modern concepts, the research offers a more comprehensive and accurate understanding of the universe's fundamental laws. It has the potential to inspire further research and advancements in our understanding of gravity and its implications for cosmology.

Additional Insights

The study's focus on the Equivalence Principle highlights its central role in understanding the relationship between mass and gravity.

The introduction of negative apparent mass provides a new perspective on the nature of mass and its interactions.

The integration of dark matter and dark energy into the classical framework demonstrates the study's relevance to contemporary cosmological theories.

The research's potential implications for gravitational theory and our understanding of the universe's structure underscore its significance