Ruud Loeffen/Cosmic Influx Theory/Chapter 2

Chapter 2: The Role of VRMS in Planetary Structuring

Introduction

One of the fundamental insights of the Cosmic Influx Theory (CIT) is that the structure of planetary systems is not random but follows a predictable pattern based on the **Root Mean Square Velocity (VRMS)** of the original protoplanetary disk.

This chapter explores:

• The definition and significance of **VRMS** in planetary dynamics.
• How VRMS determines the **Preferred Distance (D_pref)**.
• The role of the **Universal Scaling Constant (κ_CIT)**.
• The link between VRMS and observed exoplanetary systems.

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2.1 Understanding VRMS and Its Significance

The Root Mean Square Velocity (VRMS) is a statistical measure of the average velocity of particles or objects within a system. In planetary formation:

• The **original protoplanetary disk** had a characteristic VRMS.
• This velocity reflects the **kinetic energy distribution** of gas, dust, and forming planets.
• Planets tend to **align themselves at distances determined by VRMS**.

Mathematically, VRMS is defined as:

$v_{\text{RMS}}=\sqrt{\frac{\sum v_i^2}{N}}$

where:

• $v_i$ are individual velocities in the system.
• $N$ is the total number of objects.

In CIT, VRMS determines the **optimal distance** at which large planets form.

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2.2 The Preferred Distance (D_pref) and its Calculation

CIT introduces the concept of the **Preferred Distance (D_pref)**, which is the distance at which the most massive planets tend to form.

The equation for **D_pref** is:

$D_{\text{pref}}={\kappa }_{\text{CIT}}\times M_{\text{star}}$

where:

• ${\kappa }_{\text{CIT}}$ is the **Universal Scaling Constant for Planetary Structuring**.
• $M_{\text{star}}$ is the mass of the central star.

This relation explains why:

• Jupiter and Saturn formed at their observed distances.
• Exoplanets tend to cluster at specific locations.
• The structure of planetary rings and gaps in protoplanetary disks follows a predictable pattern.

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2.3 Empirical Confirmation from Exoplanetary Systems

The predictions of CIT align closely with observed exoplanetary systems:

• The distribution of exoplanets shows clustering at specific distances.
• Protoplanetary disks exhibit gaps that correlate with **D_pref**.
• The TRAPPIST system may host a yet-undiscovered giant planet near **D_pref = 7.825 × 10^{10} m**.

Further observational data from the **James Webb Space Telescope (JWST)** could provide additional confirmation.

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2.4 Implications for Planetary Formation Models

The connection between **VRMS and planetary structuring** suggests that: 1. **Planetary migration models** may need to incorporate VRMS-based structuring. 2. **The gravitational constant (G)** may have a deeper relation to VRMS. 3. **Galactic structure formation** may follow similar VRMS-based principles.

Future research could extend CIT beyond planetary systems to **galactic evolution**.

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Summary

This chapter introduced:

• The concept of **VRMS** and its role in planetary dynamics.
• The equation for the **Preferred Distance (D_pref)**.
• How **CIT aligns with exoplanet observations**.
• Implications for **planetary formation models**.

In the next chapter, we will explore **how the Cosmic Influx affects the gravitational constant (G)**.

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Notes

• This is a **draft version** of Chapter 2 of the Cosmic Influx Theory.
• Once finalized, it will be linked to the