Here I hypothesize that the Solar System is either a large scale ${}^{10}$C (10-Carbon isotope), ${}^{10}$Be (10-Beryllium isotope) atom or a localized superposition of such atoms in a relatively special state (regarding scaled pressure/temperature) and provide evidence for the equivalence of large (U${}_1$) scale systems with standard (U${}_0$) scale systems through the analysis of the Solar System in the context of Complete Relativity [1] (CR).

I hypothesize that formation of planetary systems in general starts with the inflation of gravitons from standard scale atoms (or lower scale equivalents), likely in the events of annihilation at relative event horizons of larger scale.

I propose that, in this process, the electro-magnetic component of the general force has been exchanged with the neutral gravitational component resulting in the dominance of gravity over electromagnetism at this scale.

However, I also propose that such exchange may be natural on standard scale - particles could be cycling between polarized and neutral states. In case of U${}_1$ systems, the system likely starts inflation from U${}_0$ electro-magnetic with gravitation becoming dominant afterwards. At the end of the lifecycle gravitons collapse (deflate) to U${}_0$ again, now exchanging gravity for electromagnetic force. It is the opposite for U${}_0$ systems inflating from U${}_{-1}$ scale - inflation starts gravitational but ends up in electro-magnetic equilibrium.

In any case, obviously, the hypothesized equivalence between the Solar System (or any planetary system, in general) and an atom should be taken relative. Note also that various interpretations will be presented and explored here, some of which may be mutually incompatible, while some may be simultaneously true.

Implications of discrete vertical energy levels [and CR in general] on nature are large and particularly affect the understanding of life. Existence of these levels is required for conservation of relativity but one consequence is relativization of components of living beings (eg. living tissue, blood, etc.) between scales - they operate on different timescales and generally have different composition. In example, standard blood (blood of U${}_0$ scale), scaled to U${}_1$ scale will not be the same substance simply containing zillion extra standard blood cells, rather, to an U${}_0$ scale observer it will appear much different. Indeed, what I will consider the blood of a planet is commonly interpreted as magma. Thus, the planets can be living beings and here I will analyse Earth not only as a particle but as an evolving, albeit extremely introverted, living being.

Table 1 shows commonly used constants in the paper.

The values of planetary constants are taken from NASA Planetary Fact Sheet [2].

Definitions of terms and expressions that may be used in the paper. Note that these may be different than standard or common definitions in everyday use.

Some terms in use in this paper have been defined in CR and reader should be familiar with these (and CR in general) if the aim is to understand this paper properly.

In planetary systems, outer planets (gas planets in case of Solar System) are [groups of] electrons, while inner planets (terrestrial, in the Solar System) are [groups of] positrons whose gravitational maxima have been extracted from the system nucleus to balance the electrons.

A planet can be in 1e or 2e configuration (state), while the star is a superposition of nuclei partons (quarks). Inner and outer primary dwarf planets in a planetary system are bound anti-neutrinos and neutrinos, respectively.

Primary components of the Solar System are shown in Figure 4.

The current Solar System seems to have 10 nucleons, it may be the equivalent of a ${}^{10}$C atom, ${}^{10}$Be atom or a ${}^{10}$B atom, but the most likely may be a superposition (relative transition between two of these configurations), this will be explored in the following chapters.

Figure 5a) shows the configuration of a ${}^{12}$C atom (stable on standard scale, possibly unstable on U${}_1$), on the left is the configuration of positrons, on the right is the configuration of electrons.

In this interpretation, energy levels are mirrored between positive and negative charges (relative to the [relative] event horizon in between).

Figure 5b) shows a possible configuration of a ${}^{10}$C atom at time of inflation (configuration unstable on standard scale, relatively stable on U${}_1$ scale).

The spin momentum here (represented by up and down arrows) is a magnetic momentum. Mass and charge can have different spin momenta and can be on different orbitals or energy levels. In the Solar System, bound particles have been localized (forming planets and dwarf planets, with coupled real mass) and this affects the interpretation. It may then appear that in some cases Pauli exclusion principle (two fermions coupled in the same orbital cannot have equal spin orientation) is violated, however, localization of large scale gravitons is localization of energy levels as well and Pauli exclusion principle should be respected within the planet (two gravitons within the planet may appear to share the same orbital about the Sun but they are on different orbitals within the planet - once delocalized, they would be on different orbitals about the Sun). Singlet, doublet and triplet states, all may be possible in localized energy levels.

Electric charge here is subdued (gravity dominates) and magnetic fields can be induced fields rather than associated with intrinsic magnetic momentum. Also, time is slower on this scale and real mass coupled to gravitons transitions continuously between energy levels, so planets can appear to be in transition between states (which is unobservable in standard scale atoms). Some initial states may have been unstable at time of inflation (${}^{10}$C is unstable on standard scale) and this may appear fossilized due to slow evolution (continuous transition) of real mass (Venus and Uranus may be candidates for such states). Nevertheless, initial symmetry/inversion between inner and outer particles should be relatively conserved.

Even though the dominant force on this scale is gravity, being formed through the inflation/deflation of gravitons (conserving many small-scale characteristics), the Solar System can be modelled as an atom with 10 nucleons. Here I assume this is a large scale 10-Carbon isotope equivalent. Due to specific conditions some of its components are at the lowest energy level - multiple nucleons are condensed into a single nucleus, orbitals are two dimensional (collapsed from spherical cloud structure), highly aligned (same plane), and momentum carriers are [scaled] point like structures - they are strongly localized.

Scale invariance of physical laws (as postulated in CR) requires that non-dimensional ratios - those of radii, masses and velocities (energies in general) in two systems of the same species (carbon in this case) in the same state but of different scale (vertical energy level) are equal.

Radius of the outermost electron in a standard ${}^{10}$C atom can then be obtained from Neptune spin and orbital radius:

This gives [localized] electron radius R${}_{U_0}$ = 3.834298096 ∗ 10${}^{-16}$ m. Note that radii of particles inside the atom can be different than outside of the atom (radii depend on localization energy). Generally, radii are affected by kinetic energy and oscillate with mass.

Sun core radius from ${}^{10}$C nucleus radius and outermost electron radius:

The above gives Sun core radius of 173894.6069 km, or 1/4 of the apparent Sun radius, in agreement with experimentally obtained values of Sun core size. More precisely, this is the Sun outer core [discontinuity] radius and also [approximately] U${}_1$ classical electron radius.

Proton radius approximation:

The factor P/N = 6/4 = 3/2 is the ratio of protons to neutrons in Carbon-10 (${}^{10}$C) atom, factor 10 is the number of nucleons (P+N).

The above gives 0.722296 ∗ 10${}^{-15}$ m = 0.722296 fm for the proton radius, close to experimentally obtained value of 0.8414(19) fm (2018 CODATA [8]).

The same result can be obtained using spin radii:

A precise value can be obtained by taking into account the influence of quarks instead of P/N (this will be elaborated later): which gives 0.8426785306 fm, a value in agreement with the CODATA value.

Radius of the proton cannot be absolutely constant, due to hypothesized entanglement between vertical scales, apart from required oscillation, it should probably be shrinking as the universe expands.

Comparing masses:

This gives:

The above shows mass ratios agree not only to the order of magnitude but are actually very close in value. The excess energy is: and it must be the locally accumulated relativistic energy of the Solar System (discrepancy arises due to non-invariant reference frames in the mass measurement - the mass of the standard ${}^{10}$C atom is measured from an external frame, while the mass of the Solar System is derived from within the system and improperly treated as rest mass).

Although the Solar System is at rest relative to us, relativistic energy (deviation from rest velocity) of the system relative to underlying space is always locally real and must be stored somewhere within the system. The likely capacitor is local space of the system and the energy is stored in the form of gravitational potential.

From this one can calculate the scaled speed of light (information) for the U${}_1$ scale (c${}_1$):

If v is interpreted as the cumulative velocity against the CMB (Constant Microwave Background) radiation, a sum of secondary velocity v${}_s$ (velocity of the Solar System against CMB) and primary velocity v${}_p$ (equal to velocity of the local galactic group against CMB), for v${}_s$ = 368 km/s and v${}_p$ = 628 km/s, one obtains:

Obtained c${}_1$ is equal to one of possible values calculated in CR [9], but will also be confirmed here later in a different calculation.

As noted before, Solar System is likely the product of inflation (likely through annihilation) of smaller scale particles or/and deflation [through annihilation] of particles of larger scale.

Suppose that at the moment of annihilation the carbon atom was briefly ionized and its mass and charge were condensed into the core when it started inflating. With the electrons inflating along, eventually, due to attraction, the core charge would separate from mass again.

The energy provided for transition between adjacent energy levels is generally higher than required, thus, the flattened carbon atom probably initially expanded to multiple times its current radius, then compressed to current size, reaching the stable state of the energy level.

The atom nucleus in the process expanded up to the main asteroid belt, then compressed, leaving behind orbiting gravitons which collapsed (localized) to form terrestrial planets. The collapses were recorded in the Sun, forming discontinuities. With the inflation of scale, electro-magnetic potential was exchanged for (or annihilated into) gravitational potential.

In the transition from charged two-dimensional ring to three-dimensional sphere, equatorial spin momentum has been fragmenting and [due to spin decoupling] spreading to (forming) polar regions.

Latitude variable rotation may have been initially established as the product of conservation of momentum in such redistribution of mass, even if it now may be sustained differently.

Besides the long lived energy level changes, short lived (temporary) inflation/deflation of gravitons will occur with the absorption/emission of [properly scaled] gravitational waves, which may be electrically polarized (electro-magnetic).

Such disturbances will generally occur at regular intervals, with periods generally increasing proportionally to the scale of the system and the scale of disturbance. On the scale of stellar systems, common minimum periods are on the order of millions of years (although smaller periodic disturbances of the system should exist too, these may be of different nature).

Large scale events are always preceded and superseded by smaller scale events so accelerated evolution may proceed for years on smaller scales before the actual disruption on larger scale occurs.

One may now attempt to calculate how much such disturbances last on the large (cataclysmic) scale.

With no change in energy level, orbital areal velocity of bodies, per Kepler’s 2nd law, must remain constant and there should be no change in constitutional mass either.

Assuming img mass is greater than real mass, with the temporary collapse of the major graviton of the Sun, escape velocity is extremely reduced and orbiting neutral real mass will be increasing orbital radii (although solid mass will generally preserve volume due to smaller scale electro-magnetic and neutral gravitational forces).

In order for this to be a temporary disturbance (no loss of structural entanglement), collapse must not exceed a specific time period - orbital period of the constituting mass of the system. This then implies that semi-major axes (and thus orbital periods) of orbiting bodies are not affected by the disturbances, only orbital eccentricities are increased.

Applying the same to the Sun’s constitutional mass, approximating gravitational maximum as a point maximum (linear ejection of mass from centre) and assuming Sun’s constitutional mass barycentre at the [inner] core radius at the time of collapse of the Sun’s graviton, maximal allowed ejection distance r at the time the gravitational well is fully restored is:

R${}_{\odot }$ = Sun radius = 695700 km

r${}_c$ = inner core radius = 1/5 R${}_{\odot }$ = 139140 km

Maximal time between the collapse and full restoration of the well is then: where f${}_c$ (1644 nHz [44]) is the rotation frequency of the Solar core.

In the context of CR, evolution of systems generally does not proceed at uniformly constant rates, it is generally a process with cyclic strong (cataclysmic) changes and a slow (weak) continuous evolution through the cycle.

Changes in energy of the Solar System cannot be exempt from general oscillation and remain uniform over its lifetime.

For the Solar System, I hypothesize the following 3 periods (some evidence for which will be provided in this paper, some in follow-up papers) for the first three orders of general oscillation:

These are cycles of existence of the Solar System and its bodies.

Only the 1st and the 2nd order cycles may result in horizontal energy level changes of large scale gravitons, but all these disturbances are probably sourced in gravitational stresses and have strong effect on the evolution of the system (and all life within), which is temporarily accelerated at the end of each cycle.

The 1st order period could be interpreted as lifespan (or lifecycle) of the Solar System as a whole. At the time of [1st order] death, gravitons of the Sun [and likely all planets] collapse in scale (and probably into superposition or, two distinct superpositions) exchanging localized momenta for galactic orbital angular momenta. Eventually, this system will couple with real mass and inflate again, possibly even into the same species (${}^{10}$C/${}^{10}$Be in this case). It may even couple with the same real mass again (recycling it) - if it doesn’t change the galactic energy level (orbital radius), in which case the collapse may be interpreted as temporary loss of consciousness (this recurring coupling should be manifested as reignition of the star after the explosion/expansion of plasma during collapse). The finite orbital speed of gravitons then puts constraints on the periods of time between the collapse and reignition. If these gravitons would orbit at the standard speed of light, reignition of a star at the distance of 25800 light years from galactic centre would occur after about 162106 years. However, assuming these gravitons orbit at the speed c${}_1$ (U${}_1$.c) reignition occurs after about 16.6 million years (note that possibility for coupling is quantized by this period, if 1st re-coupling fails another try can occur after another 16.6 million years, although probability for re-coupling probably decreases exponentially with time). Assuming img mass of a planetary system is significantly greater than real mass, decoupling will cause significant drift (from the original orbit) and spreading of leftover real mass. This then decreases the probability of re-coupling (reignition) but possibly not much as the original orbit of naked gravitons is probably eccentric. In fact, it is possible that decoupling occurs once the tidal energy is dissipated and the orbit is circularized (not necessarily due to circularization, rather synchronized with it). Gravitons may have innate tendency toward specific eccentric orbits (possibly even specific inclination). Circularization, then, would be increasing tension in coupling and since this tension is maximal in a circular orbit, that is also the state of greatest probability for [natural] decoupling (death, or temporary loss of consciousness in case of reignition) which may also be interpreted as breakdown of entanglement with particular real mass. Orbital momenta of naked gravitons should, however, be understood as relative - as decoupled gravitons of planetary systems could be inflating (rather than deflating) in scale so the orbital radius of the original system becomes the radius of the graviton (which now can be interpreted as a wave, or a non-localized graviton, in some reference frames). Regardless of interpretation, period between collapse and reignition should be on the same order of magnitude (smaller by 6 million years at most in case of speed c${}_1$) and probably the same in value as well (which would imply that the system is inflating/deflating and rotating/orbiting at the same time).

The system of naked gravitons may also inflate or deflate through annihilation or fusion with another system, and then start evolving as new lifeform of another generation or new species, acquiring real mass in vicinity.

In any case, death and new conception are relatively synchronized, and, for these species death is likely not the same as death on our scale. Here, discarded real mass may be fully reused by another soul - with no significant decay and decomposition of the mass involved (regarding the individual components of the system, this seems more likely for planets but not as likely for stars as planets are not expected to expand fast with the graviton collapse).

The 2nd order period could be interpreted as the lifespan (lifecycle) of Sun’s core and Jupiter, and possibly all outer planets. Based on current evidence, these collapses should be temporary regardless of nature (death or loss of consciousness). Naturally, even if the large bodies of real mass of gas giants are not disturbed much, the collapses should cause orbital disturbances, and are likely to induce bombardment of terrestrial planets with asteroids.

These should thus be correlated with large extinctions on these planets.

The 3rd order period could be interpreted as lifespan (lifecycle) of Earth and possibly all inner (terrestrial) planets (at least in the order of magnitude). Based on evidence, this collapse too is temporary.

Collapse of Earth’s graviton should be synchronized with accelerated evolution of life on its surface. Evidence exists for accelerated human evolution 1.4 - 1.6 Ma [48]. Thus, another such event (effective time compression) should be happening right about now if the 3rd order period is 1.512 My.

All of these periods are time averaged, deviations will exist, but larger periods should be relatively quantized by smaller periods.

Ongoing extinction on Earth may be correlated with the end of a 3rd order period, however, everything suggests this is also the end of a 2nd order period. And, considering the age of Earth and the Solar System, we may be at the end of a 1st order period too. Thus, major cataclysmic changes should be relatively imminent. While I am convinced that the ongoing 6th major extinction on Earth is synchronized with the end of the current 2nd order cycle, the end of the 1st order cycle may be more synchronized with the end of an additional 2nd order cycle, some 26 million years away.

Currently accepted age of Earth and the Solar System, based on uniform evolution and absolute decay rates of elements, is probably wrong. Per CR postulates, decay rates of elements cannot be constant over all time, they must change, either directly with changes in pressure and density of space (eg. at times of graviton collapses), or effectively - eg. with cosmic ray bombardment.

The rates may be relatively constant during weak evolution, however, at the end of a cycle that is synchronized with graviton collapse (eg. the 2nd order cycle) the rates should be significantly, even if temporarily, disturbed (eg. accelerating decay). Full collapse is probably not even required. Most likely, the rates are disturbed with the end of a cycle of any order, only the magnitude of disturbance is proportional to the cycle magnitude (period). The magnitude of disturbances will be calculated later.

It is probably safe to assume that the type of induced decay (beta decay or inverse beta decay) depends whether graviton energy level is being increased or decreased. If the graviton is oscillating between energy levels, then, in some cases, assumption of constant decay rates (although incorrect) will not produce anomalous results. However, if energy levels are exclusively increasing (as it is probably the case with planets in development) or decreasing with each jump (probably the case near death) the assumption of absolutely constant decay rates will produce incorrect results.

Orbits of bodies in gravitationally bound systems are generally expected to obey the following equation (orbital law):

G = gravitational constant

where v and r are orbital (Keplerian) velocity and radius, respectively, while M is the mass contained within the radius r.

In planetary systems, most of the mass M is contained within the star, while in galaxies, greatest mass concentration is in the central supermassive black holes, although, as hypothesized here, in older galaxies most mass will be in stars rather than in the central black hole.

However, in both systems, there are orbits at which the equation is apparently not satisfied - v is either higher or lower than expected for observed mass M.

In galaxies, it is assumed that the discrepancy is caused by exotic gravitational mass - dark matter.

In planetary systems, spin of bodies does not obey the equation, but this is considered natural and largely ignored.

In CR, the source of gravity in bodies such as living stars and planets are both large scale gravitons and the coupled real mass (ordinary matter). Only dead bodies should be composed solely of ordinary matter.

Thus, a potential equivalent dark matter problem may exist in stars, planets, dwarf planets and larger moons (asteroids and comets, at least those smaller and irregular, are relatively homogeneous composites of smaller scale wells [held together in most part by electro-magnetic force] so their spin momentum should not be Keplerian, even if their orbits about a larger body should).

The solution for terrestrial bodies lies in the dominance of ordinary matter, which has been, very early on, transforming orbital momenta to radial and more random momenta (eg. with heat produced in collisions).

Due to interaction of the atmosphere with a solid body beneath (or the magnetosphere), neither the gases of the atmosphere may obey the orbital law.

If the gas is in the form of plasma (as in the case of Sun), it is more likely to be entangled with the charge component of graviton’s [general] force, which then, apart from temperature, could be the source of its non-Keplerian motion - whether this motion is a residual momentum (leftover from early accretion) or actively maintained.

However, stability of a gravitational maximum is proportional to its mass and inversely proportional to gravitational stress.

That gravitational stress affects the number of sunspots has already been shown [72], and here I propose that a sunspot pair is the result of a collapse of a quantum of a neutral gravitational maximum (which may generally be a superposition of multiple large scale gravitons) into a pair of [electrically] oppositely charged and relatively unstable smaller maxima.

The neutral component of a naked graviton is gravitational energy that is manifested as dark matter, while visible or ordinary matter is real mass attracted to the gravitational well of such maximum. The velocity curves of the Sun and the Milky Way galaxy likely have the same solution - in the form of gravitational maxima and relativity of their nature due to exchange between polarized and non-polarized potentials of general force.

Rotation frequencies of the Sun (from the core up) and rotational velocities of several spiral galaxies are shown in Figure 8.

On the left, Figure 9 shows the rotational velocities of the Sun based on rotation frequencies from two independent studies, one for the core (r < 0.2R${}_{\odot }$) and other from the core up (black dots are interpolated values, red dots show velocities at 30${}^{\circ }$ latitude).

On the right, Figure 9 shows the complete velocity curve (with interpolated connection between two curves) and dispersion of velocities (shaded area) due to differential rotation in the convective zone.

What is obvious from the figures is that Sun rotates like a composition of two solid or rigid bodies (diverging only toward the polar regions of the convective zone), consistent with condensation of U${}_1$ particles into two ground states (+1s/-1s).

Evidently, velocity curve of the Sun is similar to a typical velocity curve of a spiral galaxy - in both cases there is an initial sharp increase in velocity in the core, followed by a decline, with each next increase in velocity being less steep than the previous one. Note that latitude dependent differential rotation may also be common at specific places in galaxies too.

If the spin momentum of the Sun is effectively immune to [large scale] collisions (even if the core would be solid, everything approaching the Sun is vaporized before reaching the surface), the only disturbance of Keplerian orbits must come from incomplete conversion of electro-magnetic potential and increase of temperature.

Assuming that orbital velocity is decreasing (from Keplerian velocity) proportionally to electro-magnetic potential, as hypothesized, orbital velocity of plasma should keep increasing with radius until it becomes equal to Keplerian velocity, beyond which point there should be no accumulation of charge and the radial component of the solar wind should dominate.

Using approximation of the velocity/radius dependence based on the velocity curve of the Sun (up to 130000 km from surface [75]), and equalizing with orbital law: one obtains the orbit of such discontinuity:

First results from the Parker solar probe indicate a significant rotational velocity of the solar wind about 40 R${}_{\odot }$, peaking at the closest approach. The results indeed indicate a high probability of a maximal velocity about 33 R${}_{\odot }$ in case a rigid rotation of the solar wind is maintained up to that point.

Note that, even without rigid rotation, the discontinuity should occur near the point where velocity becomes Keplerian, otherwise, higher velocity would indicate dark matter presence - another maximum.

If the same is applied to the core of the Sun, the velocity at 0.2 R${}_{\odot }$ should be equal to Keplerian velocity. Here, however, this velocity is the sum of Keplerian velocity of the surface maximum and a core maximum. For a surface maximum at R${}_{\odot }$: s, s${}_{\odot }$∈ {-1, 1}

where M is the mass of the core maximum, s is the spin polarization of gravity of the core maximum and s${}_{\odot }$ is the spin polarization of gravity of the surface maximum.

Equalizing this velocity with measured velocity at the core discontinuity: and setting spin polarization positive for counter-clockwise rotation [of the surface maximum], gives s = -1 and gravitational mass of the core roughly 3/2 the Jupiter mass: which gives mean core density of: implying the primary gravitational mass of the Sun is above the core. Difference in mass between the core and outer layers is roughly equal to the mass difference between inner and outer planets.