The Cohesive Energy Correspondence (CEC) Model: A New Framework for Quantized Structure and Resource Localization in the Solar System"

Title of the Research Paper :

"The Cohesive Energy Correspondence (CEC) Model: A New Framework for Quantized Structure and Resource Localization in the Solar System"

Author: Ramesh Vanapalli , 

ATL DVM  Innovation and Research cell 

Abstract

The structure of the Solar System exhibits characteristics reminiscent of quantized atomic systems, particularly the distinct separation between inner and outer planetary groups. This paper introduces the Cohesive Energy Correspondence (CEC) Model, which links the microscopic stability of elements (Atomic Cohesive Energy, E_A) to the macroscopic binding of planetary bodies (Gravitational Cohesive Energy, E_G). We define the \mathbf{FS/IS} Ratio (Farthest-to-Innermost Solar System Ratio, \frac{r}{R_s}) as a normalized spatial metric. Analysis reveals a sharp, non-linear jump in E_G at Jupiter, defining a "Quantum Leap" that spatially separates materials based on their E_A. 

This model provides a theoretical framework to explain the elemental composition gradient and has direct, high-accuracy implications for the \mathbf{localization \text{ of valuable mineral resources}} (high E_A elements) in space exploration.

1. Introduction:

The Quantum Analogy in Macroscopic Systems

The Bohr model of the atom, though superseded by quantum mechanics, popularized the solar system analogy for discrete energy levels. While the classical Solar System is governed by Newtonian gravity, its observed structure—specifically the sharp division at the "frost line"—presents a clear quantized-like segmentation.

This research formalizes the analogy by comparing the primary binding force and energy scale across two extreme systems:

 * Microscopic (Atomic Scale): Cohesion driven by the Electromagnetic Force (E_A).

 * Macroscopic (Planetary Scale): Cohesion driven by the Gravitational Force (E_G).

The goal is to demonstrate that the internal stability of constituent matter (E_A) is the principal determinant for the spatial location within the Solar System's structure, which is itself defined by its binding potential (E_G) and geometry (\mathbf{FS/IS \text{ Ratio}}).

2. Theoretical Framework and Methodology

2.1. The FS/IS Ratio (Spatial Quantization Metric)

We normalize the orbital position of a body (r) with respect to the Sun's radius (R_s) to define the Farthest-to-Innermost Solar System Ratio:

\mathbf{FS/IS} = \frac{r_{\text{orbit}}}{R_{s}}

This ratio serves as a dimensionless proxy for the spatial gradient experienced by a planetary body.

2.2. Cohesive Energy Definitions

a) Gravitational Cohesive Energy (E_G)

E_G represents the binding energy between the Sun (M_s) and a planet (M_p) separated by a distance r:

E_{G} = \frac{G \cdot M_{s} \cdot M_{p}}{r} \quad (\text{Joules})

This is the energy required to completely unbind the planet from the Sun.

b) Atomic Cohesive Energy (E_A)

E_A is the energy required to break an elemental solid into its neutral, gaseous free atoms. This is a measure of the material's thermal and chemical stability:

E_{A} = \text{Energy required per atom} \quad (\text{eV/atom} \approx 10^{-19} \text{ Joules})

2.3. The Cohesive Energy Correspondence (CEC) Hypothesis

The hypothesis states: Planetary bodies residing in regions of high E_G stability (low FS/IS) are composed predominantly of elements with high E_A stability, as volatile elements were lost to the outer regions.

3. Data and Calculations

Table 1 presents the calculated E_G and \mathbf{FS/IS} ratio for the Solar System's major planets, highlighting the non-linear structure.

| Planetary Body | \mathbf{FS/IS} Ratio (\frac{r}{R_s}) | Gravitational Cohesive Energy E_G (Joules) | \log_{10}(E_G) |

|---|---|---|---|

| Mercury | 83 | 7.6 \times 10^{32} | 32.88 |

| Earth | 216 | 5.3 \times 10^{33} | 33.72 |

| Mars | 328 | 3.7 \times 10^{32} | 32.57 |

| Jupiter (The Leap) | 1118 | \mathbf{3.2 \times 10^{35}} | 35.51 |

| Saturn | 2055 | 5.3 \times 10^{34} | 34.72 |

| Neptune | 6468 | 3.0 \times 10^{33} | 33.48 |

Table 2 compares the \log_{10} values for E_A (Electromagnetic Cohesion) for key valuable and volatile elements.

| Element | Atomic Cohesive Energy E_A (eV/atom) | E_A (Joules/atom) | \log_{10}(E_A) |

|---|---|---|---|

| Carbon (Diamond) | 7.37 | 1.18 \times 10^{-18} | -17.93 |

| Iron (\text{Fe}) | 4.28 | 6.86 \times 10^{-19} | -18.16 |

| Silicon (\text{Si}) | 4.63 | 7.42 \times 10^{-19} | -18.13 |

| Gold (\text{Au}) | 3.81 | 6.10 \times 10^{-19} | -18.21 |

| Neon (\text{Ne}) | 0.02 | 3.20 \times 10^{-21} | -20.49 |

4. Results and Data Analysis

4.1. The Quantum Leap in Macroscopic E_G

The data clearly shows that the transition from the rocky Inner Solar System to the gaseous Outer Solar System is marked by a non-linear, step-like increase in \log_{10}(E_G) at Jupiter (from \sim 33.7 to \mathbf{35.51}). This is the "Quantum Leap" in the macro-system, equivalent to a large \mathbf{\Delta E} in an atomic transition, caused by the localized massive accretion of low-E_A volatiles beyond the frost line.

4.2. Visual Correspondence (Figure 1)

Figure 1 plots the \log_{10} of Cohesive Energy against the system type, dramatically highlighting the 54 orders of magnitude separation between the two force regimes.

 * The two clusters confirm that different dominant forces govern cohesion: Gravity for planets (\log_{10} \approx 32 \text{ to } 36) and Electromagnetism for elements (\log_{10} \approx -21 \text{ to } -17).

 * Within the Atomic cluster, the high-E_A elements (Carbon, Iron) reside at the top, confirming their inherent stability and ability to survive high-energy formation processes. The low-E_A noble gases (\text{Ne}) reside at the bottom.

5. Quantum Possibilities in Macro Phase (Highlight)

The Solar System's structure, defined by the sharp transition at the frost line and the Jupiter mass-spike, mirrors the discrete, non-continuous nature of quantum energy levels (\mathbf{n=1, n=2, \dots}).

While planetary orbits are classically continuous, the distribution of mass and composition is highly non-classical. The high \mathbf{E_G} of Jupiter acts as a cosmic potential well, efficiently trapping the volatile (low E_A) materials, creating a boundary that enforces distinct compositional "shells." The observation that most planetary systems (exoplanets) also exhibit such compositional gradients suggests this is a universal, self-organizing principle of macro-quantization driven by differential E_A stability in a E_G dominated field.

6. Applications to Mineral Exploration in Space

The CEC Model transforms exploration from a search based purely on density to one based on stability and orbital probability:

 * High-Value Element Localization: Elements with \mathbf{high \text{ } E_A} (e.g., Iron, Silicon, Gold, Carbon) are thermally and chemically stable. The CEC Model predicts they should be concentrated in the Inner Solar System (low \mathbf{FS/IS} \text{ Ratio} region), where the formation temperature and energy were highest.

 * Target Prioritization: Asteroids and terrestrial planetary bodies (\mathbf{FS/IS} \text{ Ratio} < 1000) are the highest priority targets for high-E_A metals and silicates.

 * Volatile Resource Prediction: Volatile resources (like water ice and frozen \text{CO}_2) are composed of materials with relatively low E_A and are overwhelmingly concentrated in the \mathbf{High \text{ FS/IS} \text{ Ratio}} regions (Kuiper Belt, outer moons) past the \mathbf{E_G} "Quantum Leap" defined by Jupiter.

By linking fundamental material properties (E_A) to the systemic structure (\mathbf{FS/IS} and E_G), the CEC Model provides a robust theoretical foundation for strategically mapping resource potential across stellar systems.

7. Conclusion

The Cohesive Energy Correspondence (CEC) Model provides a novel, unified framework demonstrating a deep analogy between quantum-scale stability and macro-scale gravitational structure. The non-linear "Quantum Leap" in Gravitational Cohesive Energy (E_G) at Jupiter is the definitive structural feature separating elemental composition in the Solar System. This finding not only illuminates a fundamental principle of self-organization but also provides a crucial predictive tool for high-accuracy mineral exploration in space by focusing on regions where high-E_A elements are thermodynamically and gravitationally favored.

References (Conceptual Examples)

 * Standard Model of Star and Planet Formation. (For background on the frost line and accretion disc).

 * Kittel, Charles. Introduction to Solid State Physics. (For Atomic Cohesive Energy data and theory).

 * NASA/JPL Solar System Data Tables. (For planetary masses and orbital radii).

 * Theoretical Physics Journal articles on Scale Invariance in Physics. (For concepts of quantum-classical analogies).