Orbital Distribution of the Planets

Frank Hoogerbeets — 15 January 2026, revised 16 January 2026

In a paradigm where EM-geometric harmonics dominate over gravity, we expect the coexistence of both forces to be reflected proportionately in the orbits of the planets around the Sun, with small deviations from the geometric slots logically explained by dominant neighboring gravitational forces. In "Geometry and Dynamics of the Solar System" I discussed these geometric slots based on the key harmonic 15 in detail. I show the table here, while referring to the article as to how the mathematical numbers for r as the geometric harmonic slots are derived. I exclude dwarf planets like Ceres and Pluto in this analysis due to their small mass and their presence within the asteroid and Kuiper belt. I added a column with positive and negative offsets in percentage from the exact geometric slot. Note that Neptune is near the exact geometric midpoint between Uranus and Pluto (Kuiperbelt), as explained in the article referred to above.

planet	math r	real r	offset (%)	mass (kg x 1024)
-	15	-	-	-
Mercury	60	57.9	-3.50	0.33
Venus	105	108.2	+3.05	4.87
Earth	150	149,6	-0.27	5.97
Mars	240	228.0	-5.00	0.64
Jupiter	780	778.5	-0.19	1,898.00
Saturn	1500	1432.0	-4.53	568.00
Uranus	2940	2867.0	-2.48	86.80
Neptune	4380	4515.0	+3.08	102.00

(table 1)

Analysis

The first conclusion that we can draw is that the overall spread stays within a 5% envelope. This level of agreement is strikingly tight for a system spanning billions of kilometers.

Looking more closely at these deviations, what stands out immediately is that the two most massive bodies in their respective orbital regimes (Jupiter as the dominant gas giant, Earth as the most massive inner rocky planet) lock in with the tightest adherence to their respective geometric slots. The deviations are only -0.19 and -0.27% respectively. Apparently, their dominant mass guarantees a very stable orbit extremely close to their geometric slot.

Relative to larger mass we see a clear trend: neighboring planets with a smaller mass are drawn toward their more massive neighbor.

• Mercury being close to the Sun, has an inward offset of 3.50%, as the Sun's mass dominates over Venus' mass.
• Venus (0.820 Earth masses) has a positive offset (outward) toward Earth, as Earth's mass dominates over Mercury's mass.
• Mars has a negative offset (inward) toward Earth. As Mars is much less massive (0.107 Earth masses) and relatively close in the inner solar system, we see the largest offset: -5%. No larger mass exists in the asteroid belt that could dominate or compete with Earth, while Jupiter is much farther away.
• Saturn (0.300 Jupiter masses) has a large inward offset of 4.5% toward Jupiter. Uranus' mass is too small to compete here.
• Uranus (0.153 Saturn masses) has an inward offset of -2.48% toward Saturn. While Neptune also tugs on Uranus, Saturn is 5.57 times more massive than Neptune, so the inward shift is logical and consistent.
• Neptune with 1.18 Uranus masses and far from the Sun shows a "free" outward offset by as much as 3%.

In all cases, the offset does not exceed 5%, which is enforced by the EM-geometric harmonics of the Solar System and apparently close enough to the critical resonance to maintain stability. On the atomic level we observe a similar behavior with electrons; both planets and electrons have a dipole magnetic field. So while the Titius-Bode law has often been dismissed as a "rough" but otherwise insignificant estimate, upon closer look we see how the dynamics of interacting forces maintain a remarkable stability over billions of years. This is a realistic and expected pattern for any resonant or field-enforced system, whether acoustic harmonics, electromagnetic standing waves, or plasma instabilities. Small perturbations naturally introduce minor offsets, but within a maximum tolerance (~5%) which guarantees overall stability of the system. It is similar to atoms in their natural state whereby electrons assume a stable, 'natural' orbit around the nucleus.

I would like to sidestep for a moment here and emphasize the parallels between planets and electrons, because this comparison is highly significant in light of a unified field rooted in the EM force.

• Dipole nature — Both create a field that looks very much like a bar magnet, with distinct north and south poles (no isolated monopoles!).
• Link to angular momentum/rotation:
  • Electron: Intrinsic spin angular momentum → produces magnetic moment (opposite direction due to negative charge).
  • Planet: Bulk rotation of the planet helps organize convective currents in a conducting fluid (molten iron in Earth's core, metallic hydrogen in Jupiter) → generates a dynamo that sustains a large dipole field aligned roughly with the rotation axis.
• Interaction with external fields — Both can precess (wobble) or align in response to an applied magnetic field:
  • Electron spin precesses in an external B-field (basis of MRI, electron spin resonance).
  • Planetary magnetospheres interact dramatically with the solar wind's magnetic field.

Back to the analysis, the fact that all deviations stay within 5% (much less for anchors) demonstrates the robustness of the geometric harmonic enforcement — perturbations are real but contained within the geometric blueprint, never breaking the pattern. This self-regulating, scalable symmetry strengthens geometric primacy over purely gravitational/chaotic formation models (e.g., no need for ad-hoc migrations or dark components).

Mass as a Scaling Factor for Field Coupling

Mass plays a pivotal role in this mechanism, not as an independent gravitational agent, but as condensed energy (E=mc²) that enhances a body's local interaction with the solar EM field. Higher-mass planets exhibit stronger field coupling strength, which can be conceptualized as follows:

• Coupling Strength ∝ Mass (Condensed Energy): A more massive body, with its greater energy density, induces a more pronounced local polarity response within the global field. This strengthens its anchoring to the nearest harmonic slot, minimizing deviations. For instance:
  • Jupiter with its ~318 Earth masses couples so powerfully that its deviation is a mere ~0.19% toward the Sun, effectively "locking" it as the system's primary outer anchor.
  • Earth as the dominant mass in the inner zone similarly anchors with ~0.27% deviation toward the Sun, its mass providing sufficient coupling to resist shifts.
• Lower-Mass Neighbors Experience Directional "Tugs": Less massive bodies have weaker intrinsic coupling, making them more susceptible to field-mediated influences from nearby high-mass anchors. These influences manifest as subtle displacements toward the stronger partner, creating the observed pairwise patterns:
  • In the Venus-Earth duo, Venus (0.82 Earth masses) is slightly displaced outward (+3%), as if "attracted" to Earth's stronger coupling, while Mars (0.107 Earth masses) shifts inward (-5%), likewise toward Earth.
  • Similarly, Saturn shifts inward (-4.53%) toward Jupiter, Uranus toward Saturn (-2.48%), while Neptune — slightly more massive than Uranus — and far from the Sun, gains enough coupling "freedom" to sit outward (+3.08%) from its harmonic midpoint.

This scaling is scalable and predictive: the deviation direction and magnitude correlate inversely with relative mass, with anchors showing near-zero shifts and subordinates exhibiting bounded offsets within 5%.

Gravity's Role as a Secondary Perturber

In contrast to Newtonian or general relativistic paradigms, where gravity is the fundamental orchestrator of orbits, the geometric framework treats gravity as a derived, weaker effect, emerging as a byproduct of mass-induced polarity interactions within the EM field. Specifically:

• Gravity as Resultant Byproduct: As I demonstrated in the framework, the gravitational parameter GM (and thus G itself) arises geometrically from the 15-harmonic structure (e.g., GM=4π2×15³, with G ≈ 1/15 scaled to 10^-9 as a secondary inverse factor). Gravity manifests as a low-energy approximation of these EM-polarity enforcements, akin to how van der Waals forces emerge from quantum EM fluctuations in molecules.
• Secondary Influence on Deviations: Gravitational perturbations (mutual tugs, resonances like Jupiter-Saturn's 5:2) act as "fine-tuners" within the EM framework, introducing the observed directional biases without destabilizing the geometric resonance. For example, Jupiter's gravitational dominance amplifies its EM-coupling advantage, "nudging" Saturn inward via both field-mediated and direct gravitational effects. However, these are secondary: without the primary EM-geometric structure, gravity alone (as in disk migration models) fails to predict the precise harmonic slots or the ~5% tolerance envelope.

Unified Mechanism

The consistent patterns of pairwise orbital deviations observed across the Solar System are not merely coincidental alignments or artifacts of chaotic formation processes. Instead, they emerge as natural consequences of a unified mechanism rooted in the Solar System's underlying EM-geometric and polarity field structure. This mechanism prioritizes the Sun's EM field as the primary enforcer of the 15-based harmonic slots, with planetary mass acting as a key modulator of coupling strength to this field. Gravity, traditionally viewed as the dominant force, is clearly a secondary perturber, a byproduct of mass that subtly influences dynamics without overriding the stronger EM-geometric enforced design.

At the heart of my proposed unified mechanism is the concept of the Solar System as a resonant, EM-dominated network. The Sun generates and sustains a pervasive electromagnetic/polarity field, structured around tetrahedral symmetries and polarity cycles. This field creates natural or tuned geometric positions (harmonic slots), where planetary bodies are firmly embedded due to amplified resonant interactions. Planetary positions are thus "enforced" not through inverse-square gravitational attraction but via dynamic coupling to this field. Bodies resonate with the field at their assigned slots, much like electrons in atomic orbitals or standing waves in a plasma filament. The 5% deviation tolerance reflects the system's inherent dynamics and flexibility: the EM field is strong enough to maintain overall coherence while allowing minor perturbations from interplanetary interactions.

This unified mechanism provides a parsimonious explanation for the Solar System's structure: a single EM-geometric field, modulated by mass, generates the entire suite of observed patterns, from tight anchor fits to systematic pairwise echoes. It aligns with quantum field theory (QFT) principles, where fields are primary and particles (or condensed masses) are excitations therein, while evaporating clashes with general relativity by reframing gravity as emergent.

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