Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
08-09-2024
Abstract:
This study provides a detailed examination of the mechanical and cosmic mass descriptions within closed systems, focusing on the mass dynamics in galactic clusters and the universe under extended classical mechanics. The total gravitating mass (Mɢ) within a galactic cluster is presented as the sum of matter mass (Mᴍ), which includes both dark and baryonic matter, and dark energy effective mass (Mᴅᴇ), a negative mass component representing dark energy’s "antigravity" effects. The study also defines matter mass density (ρᴍ) and dark energy density (ρᴅᴇ) and relates these to the total mass of the universe (Mₜₒₜₐₗ). In the context of extended classical mechanics, the effective mass (Mᵉᶠᶠ) combines apparent mass (Mᵃᵖᵖ) with matter mass to describe the gravitational dynamics within a system. This formulation, Mɢ = Mᵉᶠᶠ, allows for the integration of apparent mass and dark energy effects, demonstrating how these components influence the gravitational behaviour in closed systems.
Keywords: Galactic Clusters, Dark Energy, Effective Mass, Matter Mass Density, Gravitational Dynamics
1. Total Mass within Galactic Cluster:
Mɢ = Mᴍ + Mᴅᴇ
• Matter Mass (Mᴍ): Represents the total mass of both dark matter and baryonic matter within a specified radius of the galactic cluster.
• Dark Energy Effective Mass (Mᴅᴇ): Defined as a negative mass component arising from the gravitational effects of dark energy. It accounts for dark energy's contribution as a uniform background, resulting in an "antigravity" effect.
• Gravitating Mass (Mɢ): The total effective mass determining the gravitational dynamics of the cluster, combining matter mass and dark energy effective mass.
2. Matter Mass Density within Galactic Cluster:
The density of matter mass (ρᴍ) within the Coma Cluster is given by:
ρᴍ = Mₜₒₜₐₗ/V
where Mₜₒₜₐₗ is the total mass of matter, and V is the volume of the cluster.
3. Effective Mass Density of Dark Energy within Galactic Cluster:
The density of dark energy (ρᴅᴇ) in the universe is:
ρᴅᴇ = Eᴅᴇ/V
where Eᴅᴇ represents the total energy of dark energy, and V is the volume. In cosmological models, ρᴅᴇ is often uniform and related to the cosmological constant (Λ).
4. Total Mass of the Universe:
The total mass of the universe combines matter mass and dark energy effective mass:
Mₜₒₜₐₗ = Mᴍ + Mᴅᴇ
5. Total Mass within a System in Extended Classical Mechanics:
The effective mass of dark energy (Mᴅᴇ) is always negative and is greater in magnitude than the combined matter mass (Mᴍ):
Mᴅᴇ > Mᴍ
• Mechanical Effective Matter Mass (Mᵉᶠᶠ):
This can be positive or negative, depending on the relative magnitudes of matter mass and apparent mass. The effective mass is the difference between matter mass and apparent mass (Mᵃᵖᵖ):
Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)
where Mᵃᵖᵖ is always negative.
Mechanical Effective Mass Characteristics:
• Positive when Mᴍ>∣Mᵃᵖᵖ∣
Mass Equation in Extended Classical Mechanics:
Mɢ = Mᵉᶠᶠ
• Matter Mass (Mᴍ): Represents the total mass of both dark matter and baryonic matter within a system.
• Apparent Mass (Mᵃᵖᵖ): Defined as a negative mass component arising from gravitational effects and the motion of mass within the system. It reflects the contribution of the mass in motion as a negative value affecting the effective mass.
• Gravitating Mass (Mɢ): The total effective mass determining the gravitational dynamics of the system. It is equivalent to the mechanical effective mass (Mᵉᶠᶠ).
• Effective Mass (Mᵉᶠᶠ): Defined as a mass component that combines the effects of apparent mass and matter mass. It accounts for the system’s gravitational dynamics, incorporating the "antigravity" effect that occurs when apparent mass exceeds the magnitude of matter mass.
This formulation describes the total gravitating mass (Mɢ) as equivalent to the mechanical effective mass (Mᵉᶠᶠ). The effective mass (Mᵉᶠᶠ) reflects the combined effects of apparent mass and matter mass within the system. The apparent mass is a negative component that influences the effective mass, creating an "antigravity" effect when it exceeds the matter mass.
List of Terms:
• Eᴅᴇ: Total Energy of Dark Energy — The total energy associated with dark energy within a given volume.
• Mᵃᵖᵖ: Apparent Mass — The mass component associated with negative values that affects the effective mass calculation.
• Mᴅᴇ: Dark Energy Effective Mass — The negative mass component resulting from dark energy’s gravitational effects.
• Mᴍ: Matter Mass — The total mass of matter, including dark matter and baryonic matter, within a specified volume.
• Mᵉᶠᶠ: Mechanical Effective Matter Mass — The effective mass that can be positive or negative, derived from the difference between matter mass and apparent mass.
• Mɢ: Gravitating Mass — The total effective mass determining gravitational dynamics within the system.
• ρᴅᴇ: Dark Energy Density — Density of dark energy in the universe.
• ρᴍ: Matter Mass Density — Density of matter mass within a given volume of the cluster.
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