# Chapter 7: Units, Dimensions, and Fundamental Constants in Cosmic Influx Theory (CIT)
## 7.1 Unit Conversions in CIT

Cosmic Influx Theory (CIT) frequently employs standard physical units but also introduces specific derived quantities. The following unit conversions are critical for ensuring consistency in calculations:
* Velocity (v): meters per second (m/s)
* Time (t): seconds (s)
* Distance (D): meters (m)
* Mass (M): kilograms (kg)
* Gravitational Constant (G): m³/(kg·s²)
* Energy (E): joules (J) = kg·m²/s²
* Force (F): newtons (N) = kg·m/s²
* Acceleration (a): meters per second squared (m/s²)
* Density (ρ): kg/m³
* Pressure (P): pascals (Pa) = N/m²
CIT also explores the relationship between vacuum properties, electromagnetic constants, and gravitational interactions. These involve:
* Vacuum Permittivity (ε₀): F/m (farads per meter)
* Vacuum Permeability (μ₀): H/m (henrys per meter)
* Speed of Light (c): 299,792,458 m/s, derived from:
These constants serve as foundational elements in CIT’s derivations.

## 7.2 The Five Dimensions in CIT: Space, Time, and Expansion

Unlike classical physics, which operates in a 3D spatial and 1D temporal framework, CIT introduces a fifth dimension related to expansion. The five fundamental dimensions in CIT are:
* x, y, z – Spatial dimensions.
* t (Time) – The fourth dimension.
* e (Expansion) – A fifth dimension describing the gradual increase in mass-energy and planetary structuring over time.
This fifth dimension accounts for:
* Continuous increase in mass-energy, affecting celestial evolution.
* Expansion of planetary and stellar bodies, observed in phenomena such as plate tectonics and exoplanet distributions.
* Alignment with the Lorentz Transformation of Mass-Energy (LTME), which suggests energy influx is converted into mass.
This expansion dimension provides a deeper understanding of cosmic structuring and planetary positioning within CIT.

## 7.3 Derivation of Constants in CIT

CIT provides unique insights into the fundamental constants governing gravitational interactions, particularly:

### 7.3.1 The Gravitational Constant (G) and its Relation to VRMS

CIT derives the Newtonian Gravitational Constant (G) using the Root Mean Square Velocity (VRMS) of planetary systems:
$G={\frac {(\gamma -1)}{4\pi }}$
An alternative expression is:
$G={\frac {v_{\text{RMS}}^{2}}{8\pi c^{2}}}$
Another key relation is:
$G=\left({\frac {0.5c^{2}}{4\pi }}\right)\times \kappa$
where:
* $\gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$ is the Lorentz factor.
* $v_{\text{RMS}}$ is the root mean square velocity of planetary systems (~12,278 m/s in our Solar System).
* $c$ is the speed of light.
* $\pi$ is the mathematical constant.
* $\kappa$ is the Einsteinian coupling constant.
Although this expression is unitless, its exact equality with the traditional definition of G implies that it should carry the same units: ${\text{m}}^{3}/({\text{kg}}\cdot {\text{s}}^{2})$. A similar transformation applies to ${\frac {v_{\text{RMS}}^{2}}{2c^{2}}}$.
This derivation suggests G is fixed and universal, as VRMS represents an intrinsic property of planetary formation and structuring.

### 7.3.2 The Universal Scaling Constant for Planetary Structuring (κ_CIT)

A major discovery in CIT is the introduction of the Universal Scaling Constant (κ_CIT), which determines the preferred distance ($D_{\text{pref}}$) at which planetary mass concentrations occur:
$D_{\text{pref}}=\kappa _{\text{CIT}}\times M_{\text{star}}$
where $\kappa _{\text{CIT}}$ is found to be:
$\kappa _{\text{CIT}}={\frac {1}{8\pi c^{2}}}=4.4\times 10^{-19}{\text{ m/kg}}$
This constant is also expressed as:
$\kappa _{\text{CIT}}={\frac {D_{\text{pref}}}{M_{\text{star}}}}$
This formulation accurately predicts the location of giant exoplanets in other star systems, reinforcing CIT’s validity.

### 7.3.3 The Einsteinian Coupling Constant (κ) and Cosmic Expansion

From the Einstein Field Equations, the Einsteinian Coupling Constant (κ) in CIT is expressed as:
$\kappa ={\frac {8\pi G}{c^{2}}}$
which is the original form that Einstein used in The Principle of Relativity, A Collection of Original Papers On the Special and General Theory of Relativity.
In CIT, this expression represents an essential relation linking gravity and energy influx, influencing planetary expansion and structuring.

## 7.4 Conclusion

This chapter has provided a structured overview of:
* The unit conversions required in CIT.
* The five-dimensional framework, incorporating expansion.
* The derivation of fundamental constants, particularly G and κ_CIT.

## 7.5 Overview of Important Constants Related to Cosmic Influx Theory (CIT)

The following table summarizes the fundamental constants used in Cosmic Influx Theory (CIT), along with their derived relationships:
| Constant Name | Symbol | Units | Expression in CIT | Value |
| Hubble Parameter | H₀ | 1/s | 67,798.637 m/s per Mpc | 2.1972 × 10⁻¹⁸ |
| Gravitational Constant | G | m³/(kg·s²) | VRMS² / (8πc²) | 6.674 × 10⁻¹¹ |
| Einsteinian Coupling Constant | κ | m/kg | (8πG) / c² | 1.866 × 10⁻²⁶ |
| Einsteinian Coupling Constant (Alternative Expression) | κ | m/kg | 8H₀ / (πc) | 1.866 × 10⁻²⁶ |
| Einsteinian Coupling Constant (Alternative Expression) | κ | m/kg | VRMS² / c⁴ | 1.866 × 10⁻²⁶ |
| Kappa-CIT | κ_CIT | m/kg | G / VRMS² | 4.4271 × 10⁻¹⁹ |
| Kappa-CIT (Alternative Expression) | κ_CIT | m/kg | (κ × c²) / (8π VRMS²) | 4.4271 × 10⁻¹⁹ |
| Kappa-CIT (Alternative Expression) | κ_CIT | m/kg | 1 / (8π c²) | 4.4271 × 10⁻¹⁹ |
| Kappa-CIT (Alternative Expression) | κ_CIT | m/kg | D_pref / M_star | 4.4271 × 10⁻¹⁹ |
| Preferred Distance | D_pref | m | (ε₀ × M_star) / (2 × 10⁷) | Depends on the star |
| Preferred Distance (Alternative Expression) | D_pref | m | M_star / (8π c²) | Depends on the star |
| Preferred Distance (Alternative Expression) | D_pref | m | G × M_star / VRMS² | Depends on the star |
| Vacuum Permittivity | ε₀ | kg/m | (1 / (8π c²)) × (2 × 10⁷) | 8.541 × 10⁻¹² |
| Vacuum Permittivity (Alternative Expression) | ε₀ | kg/m | (G / VRMS²) × (2 × 10⁷) | 8.541 × 10⁻¹² |
| Vacuum Permeability | μ₀ | H/m | 4π × 10⁻⁷ | 1.256 × 10⁻⁶ |
This table provides a structured overview of how fundamental constants are interconnected within Cosmic Influx Theory.
These principles solidify CIT’s framework, linking gravitational dynamics to energy influx and planetary structuring. The next step involves integrating these derivations with observational data from exoplanet studies and planetary surface expansion measurements.
🚀 This chapter is a work in progress and will be refined further before publishing on Wikiversity.