Solar System. Angular Momentum. New Physics

The most widely accepted model of Solar System formation, known as the Nebular hypothesis, does not solve the Angular Momentum problem—why is the orbital momentum of Jupiter larger than rotational momentum of the Sun? The present manuscript introduces a Rotational Fission model of creation and evolution of Macrostructures of the World (Superclusters, Galaxies, Extrasolar Systems), based on Overspinning Cores of the World’s Macroobjects, and the Law of Conservation of Angular Momentum. The Hypersphere World-Universe model is the only cosmological model in existence that is consistent with this Fundamental Law.


Introduction
This paper is based on the World-Universe Model (WUM) [1] . To be consistent with the Law of Conservation of Angular Momentum, WUM is modified as follows: Angular momentum is completely analogous to linear momentum, first presented in Uniform Circular Motion and Gravitation. It has the same implications in terms of carrying rotation forward, and it is conserved when the net external torque is zero. Angular momentum, like linear momentum, is also a property of the atoms and subatomic particles. Figure 5. The Solar System coalesced from a cloud of gas and dust that was originally rotating. The orbital motions and spins of the planets are in the same direction as the original spin and conserve the angular momentum of the parent cloud. In case of human motion, one would not expect angular momentum to be conserved when a body interacts with the environment as its foot pushes off the ground. In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity-the total angular momentum of a closed system remains constant. In three dimensions, the angular momentum for a point particle is a pseudovector r × p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics The angular momentum (symbol L) of an object is its angular velocity (ω, the rate at which the angle is changing) times the moment of inertia (I, equal to the mass of the object multiplied by its distance from the pivot point squared). In mathematical terms, $ \mathbf{L} = I \omega \ = \omega m r^2 $. It

Short History of Solar System Formation
The most widely accepted model of Solar System formation, known as the Nebular hypothesis, was first proposed in 1734 by Emanuel Swedenborg The Nebular hypothesis is not without its critics. In his "The Wonders of Nature", Vance Ferrell outlined the following counter-arguments [5] : ・ It contradicts the obvious physical principle that gas in outer space never coagulates; it always spreads outward; ・ Each planet and moon in solar system has unique structures and properties. How could each one be different if all of them came from the same nebula; is also equal to the cross product of the position vector (r) and linear momentum (p), and is therefore a pseudovector: $ ・ A full 98 percent of all the angular momentum in the solar system is concentrated in the planets, yet a staggering 99.8 percent of all the mass in our Solar system is in our Sun; ・ Jupiter itself has 60 percent of the planetary angular motion. Evolutionary theory cannot account for this. This strange distribution was the primary cause of the downfall of the Nebular hypothesis; ・ There is no possible means by which the angular momentum from the Sun could be transferred to the planets.
Yet this is what would have to be done if any of the evolutionary theories of Solar System origin are to be accepted. Speaking of the mass-angular momentum problem, Bergamini says: "A theory of evolution that fails to account for this peculiar fact is ruled out before it starts" [David Bergamini, The Universe, p. 93].
Lunar origin fission hypothesis was proposed by George Darwin in 1879 to explain the origin of the Moon by rapidly spinning Earth, on which equatorial gravitative attraction was nearly overcome by centrifugal force [6] . ・ The planets were expelled from the Sun one by one from the equatorial bulge caused by rotation; ・ One of these planets shattered to form the asteroid belt; ・ The moons and rings of planets were formed from the similar expulsion of material from their parent planets.
Tom Van Flandern further extended this theory in 1993 [9] . Flandern proposed that planets were expelled from the Sun in pairs at different times. Six original planets exploded to form the rest of the modern planets. It solves several problems the standard model does not: ・ If planets fission from the Sun due to overspin while the proto-Sun is still accreting, this more easily explains how 98% of the solar system's angular momentum ended up in the planets; ・ It solves the mystery of the dominance of prograde rotation for these original planets since they would have shared in the Sun's prograde rotation at the outset; ・ It also explains coplanar and circular orbits; ・ It is the only model that explains the twinning of planets (and moons) and difference of planet pairs because after each planet pair is formed in this way, it will be some time before the Sun and extended cloud reach another overspin condition.
The outstanding issues of the Solar fission are: ・ It is usually objected that tidal friction between a proto-planet and a gaseous parent, such as the proto-Sun, ought to be negligible because the gaseous parent can reshape itself so that any tidal bulge has no lag or lead, and therefore transfers no angular momentum to the proto-planet; Angular momentum is completely analogous to linear momentum, first presented in Uniform Circular Motion and ・ There would exist no energy source to allow for planetary explosions.
・ Neither L. Jacot nor T. Van Flandern proposed an origin for the Sun itself. It seems that they followed the standard Nebular hypothesis of formation of the Sun.
In this work, we will concentrate on furthering the Solar Fission theory.
Let's consider rotational and orbital angular momentum of all gravitationally-rounded objects in the Solar system, from Mimas, a small moon of Saturn (3.75 × 10 19 kg), to the Sun itself (2 × 10 30 kg). Their angular momenta are presented in Table 1.
From the point of view of Fission model, the prime object is transferring some of its rotational momentum to orbital momentum of the satellite. It follows that the rotational momentum of the prime object should exceed the orbital momentum of its satellite.
From Table 1 we see that orbital momenta of most satellites are indeed substantially smaller than the rotational momenta of their prime objects, with three exceptions (explored in Section 6): ・ The rotational momentum of the Sun is smaller than Jupiter's, Saturn's, Uranus's, and Neptune's orbital momentum; ・ The rotational momentum of the Earth is substantially smaller than Moon's orbital momentum; ・ The rotational momentum of Pluto is considerably smaller than Charon's orbital momentum.
In Section 5 we will address the origins of these angular momenta.

Rotational Angular Momentum of Overspinning Objects
Let's calculate rotational angular momentum for an overspinning spherical object L rot . It can be found according to the following equation: where I is momentum of inertia and ω is angular speed. Let's assume that a spherical object has a linear density distribution ρ : where ρ max and ρ max are values of density at the center and the edge of the object, R is its radius, and δ is the density ratio: In case of spherical objects with homogeneous density, δ = 1 , then momentum of inertia I is simply In Table 1, we assumed homogeneous density when calculating the rotational momentum L rot of gravitationallyrounded objects. When the density differential is large (which is the case of the Sun, discussed in Section 5), δ ≪ 1 , the momentum of inertia I reduces to: It is worth noting that the linear approximation of density distribution is good enough when calculating the rotational angular momentum L rot . In case of non-linear density distributions L rot will not change substantially.
For overspinning spherical objects, the angular velocity equals to: where v esc is an escape velocity of the object and G is a gravitational parameter. Then, the rotational angular momentum of overspinning objects equals to: In accordance with WUM, parameters G, M, R for Macroobjects Cores are time-varying: G ∝ τ −1 , M ∝ τ 3/2 and R ∝ τ 1/2 , where τ is a cosmological time. It follows that the rotational angular momentum of Cores is proportional to: Let's introduce Age parameter θ F that is a ratio of cosmological time of Core fission τ F to the age of the World in present Epoch A W : θ F = τ F /A W . Finally, for L rot at the time of Core fission we obtain the following equation: (3.1) where for parameters G, M, R we use their values in the present Epoch. In the next Section we discuss the nature of overspinning spherical Cores of Macroobjects.  ・ The maximum potential of interaction U max between any particle or macroobject and FCS made up of any fermions does not depend on the nature of fermions;  According to Wikipedia,

Macroobjects Cores Made up of Dark Matter Particles
Gravitation. It has the same implications in terms of carrying rotation forward, and it is conserved when the net √ A WIMP is a new elementary particle which interacts via gravity and any other force (or forces), potentially not part of the standard model itself, which is as weak as or weaker than the weak nuclear force, but also non-vanishing in its strength.
It follows that a Fifth Fundamental force needs to exist, providing interaction between DMPs with strength far exceeding gravity, and with range considerably greater than that of the weak nuclear force.
According to WUM, strength of gravity is characterized by gravitational parameter 8πhc is an extrapolated value of G at the Beginning of the World and dimensionless time-varying quantity Q is a measure of the age of the World: where t 0 is a basic unit of time that equals to: t 0 = a/c = 5.9059674 × 10 −23 s Q in the present Epoch equals to [1] : The range of the gravity equals to the size of the World R: In WUM, weak interaction is characterized by the parameter G W : which is about 30 orders of magnitude greater than G. The range of the weak interaction R W in the present Epoch equals to: (4.1) R W = aQ 1/4 = 1.65314 × 10 −4 m that is much greater than the range of the weak nuclear force that is around ~10 −16 -10 −17 m.
Calculated concentration of Dions n D in the largest shell with the density ρ D ≅ 1.5 × 10 −21 kg/m 3 : shows that a distance between particles is around ~10 −5 m, which is much smaller than R W . Thus, the weak interaction between DMPs will provide integrity of DM shells.
It is worth noting that the critical density of the World in the present Epoch equals to [1] : ρ cr = 3ρ 0 Q −1 ≅ 8.9 × 10 −27 kg/m 3 which is about 5 orders of magnitude smaller than ρ D ( ρ 0 = h/c a 4 is a basic unit of density). Distance between particles in the Medium of the World is around ~10 −3 m that is larger than R W .

Beginning of the World. Dark Epoch. Rotational Fission. Light Epoch
Beginning of the World. Before the Beginning there was nothing but an Eternal Universe. About 14.2 billion years ago the World was started by a fluctuation in the Eternal Universe, and the Nucleus of the World, which is a fourdimensional 4-ball, was born. An extrapolated Nucleus radius at the Beginning was equal to that is chosen to fit the Age of the World. The 3D World is a hypersphere that is the surface of a 4-ball Nucleus. All points of the hypersphere are equivalent; there are no preferred centers or boundary of the World [1] [12] .
Expansion. The 4-ball is expanding in the Eternal Universe, and its surface, the hypersphere, is likewise expanding so that the radius of the Nucleus R is increasing with speed that is the gravitoelectrodynamic constant, for the absolute cosmological time from the Beginning and equals to = . The expansion of the Hypersphere World can be understood by the analogy with an expanding 3D balloon: imagine small enough "flat" observer residing in a curved flatland on the surface of a balloon; as the balloon is blown up, the distance between all neighboring points grows; the two-dimensional world grows but there is no preferred center [1] [12] .
Creation of Matter. The surface of the 4-ball is created in a process analogous to sublimation. It is a well-known endothermic process that occurs when surfaces are intrinsically more energetically favorable than the bulk of a material, and hence there is a driving force for surfaces to be created. Continuous creation of matter is the result of a similar process. Matter arises from the fourth spatial dimension. The Universe is responsible for the creation . The World at cosmological times less than 10 −18 s is best described by Quantum mechanics. The value of the parameter Q at that time was: Q q = α −2 ; a size of the World R q was a × α −2 = 2πa B ( a B is Bohr radius) and a total mass of the World: At time τ ≫ τ q density fluctuations could happen in the Medium of the World filled out with DMF1, DMF2, DIRACs, ELOPs, DMF3 and DMF4. The heaviest DMF1 with mass m DMF1 = m 0 α −2 could collect into a cloud of radius R cl with distance between them equals to R W = aQ 1/4 . As the result of the weak interaction, clumps of DMF1 will arise with density ρ cl = ρ 0 α −2 × Q −3/4 , volume V cl and mass M cl : Considering the analogy between electromagnetic and gravitoelectromagnetic fields [1] , we can write the following equation for the minimum product of objects masses to exert gravity on one another: The volume of a clump V cl then equals to V cl = 2α 4 a 3 × Q 7/4 and mass of a clump M cl is: A well-elaborated classical model can be introduced when the cosmological time was τ cl = t 0 α −8 ≅ 7 × 10 −6 s .
Taking the value of the parameter Q cl = α −8 we get At that time, mass M World and size R World of the World were Analogous calculations for DMF2 produce the following results for clump mass M ′ cl and density ρ ′ cl : we estimate the number of Supercluster Cores to be around ~10 3 . In our opinion, all Supercluster Cores had undergone rotational fission at approximately the same cosmological time.
Rotational Fission. Local Supercluster is a mass concentration of galaxies containing the Local Group, which in turn contains the Milky Way galaxy. At least 100 galaxy groups and clusters are located within its diameter of 110 million light-years.
Let's calculate the rotational angular momentum L LSC rot of Local Supercluster Core (LSC) before rotational fission based on the Equation (3.1) and parameters of Dion shell (see Table 2 Extrasolar system Cores can give birth to planet cores, and they can generate cores of moons by the same Rotational Fission mechanism (see next Section).
The mass-to-light ratio of the Local Supercluster is about 300 times larger than that of the Solar ratio. Similar ratios are obtained for other superclusters [16] . These facts support the rotational fission mechanism proposed above.
In 1933, Fritz Zwicky investigated the velocity dispersion of Coma cluster and found a surprisingly high mass-tolight ratio (~500). He concluded: if this would be confirmed, we would get the surprising result that dark matter is This is a description of Gravitational Bursts (GBs) analogous to the description of Gamma Ray Bursts (GRBs) and Fast Radio Bursts (FRBs) [11] . In frames of WUM, the repeating GBs can be explained the following way: ・ As the result of GB, the OC loses a small fraction of its mass and a large part of its rotational angular momentum; ・ After GB the Core absorb new DMPs increasing its mass ∝ τ 3/2 and growing up L rot much faster ∝ τ 2 until the next critical point of its stability at which it detonates again; ・ Afterglow of GBs is a result of processes developing in the Nuclei and shells after detonation. In case of Extrasolar systems, a star wind is the afterglow of star detonation: star Core absorbs new DMPs, increase its mass ∝ τ 3/2 and gets rid of extra L rot by star wind particles.
In frames of the developed Rotational Fission model it is easy to explain hyper-runaway stars unbound from the Milky Way with speeds of up to ~700 km/s [18] : they were launched by overspinning Core of the Large Magellanic Cloud with the speed higher than the escape velocity.
C. J. Clarke et al. observed CI Tau, a young 2 million years old star. CI Tau is located about 500 light years away in a highly-productive stellar 'nursery' region of the galaxy. They discovered that the Extrasolar System contains four gas giant planets that are only 2 million years old [19] , amount of time that is too short for formation of gas giants according to prevailing theories.
In frames of the developed Rotational Fission model, this discovery can be explained by Gravitational Burst of the overspinning Core of the Milky Way two million years ago, which gave birth to CI Tau system with all planets generated at the same time.
To summarize, ・ The rotational fission of macroobject cores is the most probable process that can generate satellite cores with large orbital momenta in a very short time; ・ Macrostructures of the World form from the top (superclusters) down to galaxies, extrasolar systems, planets, and moons; ・ Gravitational waves can be a product of rotational fission of overspinning Macroobject Cores; ・ Hypersphere World-Universe model can serve as a basis for Transient Gravitational Astrophysics.
In the next Section we discuss main characteristics of Solar System considering the developed mechanism of Rotational Fission. ・ Core that extends from the center to about 20% -25% of the solar radius, contains 34% of the Sun's mass with density ρ max = 1.5 × 10 5 kg/m 3 and ρ min = 2 × 10 4 kg/m 3 . It produces all Sun's energy;

Solar System
・ Radiative zone from the Core to about 70% of the solar radius with density ρ max = 2 × 10 4 kg/m 3 and ρ min = 2 × 10 2 kg/m 3 in which convection does not occur and energy transfer occurs by means of radiation; ・ Core and Radiative zone contain practically all Sun's mass [20] .
In our opinion, the Sun has an Inner Core (Nucleus made up of DMF1) whose radius is 20-25% of the solar radius, and an Outer Core-the Radiative zone. We then calculate the Solar Core rotational angular momentum L SC rot : L SC rot ≅ 8.9 × 10 43 J ⋅ s which is 2.8 times larger than the overall angular momentum of the Solar System (6.1).
Let's look at the structure of the Earth. According to the standard model it has: ・ An inner core and an outer core that extend from the center to about 45% of the Earth radius with density ρ max = 1.3 × 10 4 kg/m 3 and ρ min = 9.9 × 10 3 kg/m 3 ; ・ Lower mantle, spanning from the outer core to about 90% of the Earth radius (below 660 km) with density ρ max = 5.6 × 10 3 kg/m 3 and ρ min = 4.4 × 10 3 kg/m 3 ; ・ Inner core, outer core, and lower mantle contain practically all of the Earth's mass [21] .
Very little is known about the lower mantle apart from that it appears to be relatively seismically homogeneous.
In our opinion, lower mantle is a part of the Earth's core. It could be significantly different 4.6 billion years ago, since during this time it was gradually filled with all chemical elements produced by Earth's core due to DMF1 annihilation. Considering the Earth's core (EC) with radius R Earth core = 5.7 × 10 6 m ( θ 9.6 ≅ 2/3 and δ = 4.4/13.1 ), the rotational angular momentum equals to: L EC rot = 6.5 × 10 34 J ⋅ s which is 2.2 times larger than the orbital momentum of the Moon.
As for the Pluto-Charon pair, it is definitely a binary system. Charon was not generated by Pluto's core; instead, they are two independent objects that happened to be bounded together by gravity.
Earth's internal heat. According to the standard model, the Earth's internal heat is produced mostly through radioactive decay. The major heat-producing isotopes within Earth are K-40, U-238, and Th-232 with half-lives of Particles supply not only additional mass (∝τ 3/2 ), but also additional angular momentum (∝τ 2 ). Cores irradiate products of annihilation, which carry away excessive angular momentum. The Solar wind is the result of this mechanism.
WUM explanation. The internal heating of all gravitationally-rounded objects of the Solar system is due to DMPs annihilation in their Nuclei made up of Let us calculate deceleration a P at the distance r P ≫ R f due to additional mass of the structure M FS ∝ r  Above the chromosphere, in a thin (about 200 km) transition region, the temperature rises rapidly from around 20,000 K in the upper chromosphere to coronal temperatures closer to 1,000,000 K. The particle density decreases from 10 17 up to 10 16 -10 15 m −3 in the low corona.
In our opinion, this is a zero level of the fractal structure. The calculated density according to (6.3) is: (6.4) ρ f ≅ 2.3 × 10 − 9 kg / m 3 Corona is an aura of plasma that surrounds the Sun and other stars. The Sun's corona extends at least 8 million kilometers into outer space [48] and is most easily seen during a total solar eclipse. Spectroscopy measurements indicate strong ionization and plasma temperature in excess of 1,000,000 K [49] . The corona emits radiation mainly in the X-rays, observable only from space. The plasma is transparent to its own radiation and to that one coming from below, therefore we say that it is optically-thin. The gas, in fact, is very rarefied and the photon mean ・ The plasma is transparent to its own radiation and to that one coming from below; ・ The abundances of the solar corona are known to differ from those of the solar photosphere; ・ During the impulsive stage of Solar flares, radio waves, hard x-rays, and gamma rays with energy above 100 GeV are emitted (one photon emitted during the solar minimum had an energy as high as 467.7 GeV) [51] ; ・ Assuming the particle density in the low corona 10 15 m −3 and mass of DMF1: m D M F 1 = 2.3 × 10 − 24 kg we can find mass density ρ D M F 1 i n = 2.3 × 10 − 9 kg / m 3 that is equal to the density of the fractal structure (6.4); ・ A distance between particles DMF1 is about 10 −5 m that is much smaller than the range of the weak interaction of DMPs R W (4.1). It means that the Solar corona is a stable Shell around the Sun with density decreasing according to Equation (6.2) with inner radius about R i n ≅ 7 × 10 8 m and outer radius R o u t :  ・ Thermosphere: 80 to 700 km. The highly diluted gas in this layer can reach 2500˚C. The lower part of it, from 80 to 550 kilometers contains the ionosphere; external torque is zero. Angular momentum, like linear momentum, is also a property of the atoms and subatomic ・ Exosphere: 700 to 10,000 km. The top of exosphere merges into the solar wind.
The mesopause is the temperature minimum at the boundary between the mesosphere and the thermosphere. It ・ The X-rays from Venus and, to some extent, the Earth, are due to the fluorescence of solar X-rays striking the atmosphere; ・ Fluorescent X-rays from oxygen atoms in the Martian atmosphere probe heights similar to those on Venus. A huge Martian dust storm was in progress when the Chandra observations were made. Since the intensity of the Xrays did not change when the dust storm rotated out of view, astronomers were able to conclude that the dust storm did not affect Mars's upper atmosphere; ・ Jupiter has an environment capable of producing X-rays in a different manner because of its substantial magnetic field. X-rays are produced when high-energy particles from the Sun get trapped in its magnetic field and accelerated toward the polar regions where they collide with atoms in Jupiter's atmosphere. Chandra's image of Jupiter shows strong concentrations of X-rays near the north and south magnetic poles. The weak equatorial Xray emission is likely due to reflection of solar X-rays; ・ Like Jupiter, Saturn has a strong magnetic field, so it was expected that Saturn would also show a concentration of X-rays toward the poles. However, Chandra's observation revealed instead an increased X-ray brightness in the equatorial region. Furthermore, Saturn's X-ray spectrum, or the distribution of its X-rays according to energy, was found to be similar to that of X-rays from the Sun.
V. I. Shematovich and D. V. Bisikalo gave the following explanation of the planetary coronas [66] : The measurements reveal that planetary coronas contain both a fraction of thermal neutral particles with a mean kinetic energy corresponding to the exospheric temperature and a fraction of hot neutral particles with mean kinetic energy much higher than the exospheric temperature. These suprathermal (hot) atoms and molecules are a direct manifestation of the non-thermal processes taking place in the atmospheres. These hot particles lead to the atmospheric escape, determine the coronal structure, produce non-thermal emissions, and react with the ambient atmospheric gas triggering hot atom chemistry.
Let's summarize the obtained results for Geocorona and Planetary Coronas: ・ FUV radiation has been observed out to a distance of approximately 243,000 km from the Earth; ・ FUV radiation was observed in the wavelength range down to 52 nm; ・ X-rays were observed in the range of energies 0.08 -10 keV; ・ X-rays from Venus are due to the fluorescence of solar X-rays striking the atmosphere; ・ Fluorescent X-rays from oxygen atoms in the Martian atmosphere probe heights similar to those on Venus.
Dust storm did not affect Mars's upper atmosphere; ・ Jupiter's X-rays are produced when high-energy particles from the Sun get trapped in its magnetic field and accelerated toward the polar regions where they collide with atoms in Jupiter's atmosphere; ・ Saturn's X-ray spectrum was found to be similar to that of X-rays from the Sun; ・ Suprathermal (hot) atoms and molecules are a direct manifestation of the non-thermal processes taking place in the atmospheres. These hot particles produce non-thermal emissions.
In our opinion, the described picture of Geo and Planetary Coronas is similar to the picture of the Solar Corona: ・ The Earth thermosphere and exosphere composed of DMF1 explains the difference in the size of the Geocorona and the size of the Earth: The Sun and Solar corona have the same ratio of sizes; ・ At the distance of 243,000 km from the Earth, atoms and molecules are so far apart that they can travel hundreds of kilometers without colliding with one another. Thus, the exosphere no longer behaves like a gas, and the particles constantly escape into space. In our view, FUV radiation and X-rays are the consequence of DMF1 annihilation; ・ All planets and some observed satellites (Europa, Io, Io Plasma Torus, Titan) have X-rays in upper atmosphere of the planets, similar to the Solar Corona; ・ The calculated density of the Earth's fractal structure ρ f ≅ 2.5 × 10 − 7 kg / m 3 (6.3) is in good agreement with experimental results for atmosphere density at the lowest temperature (below −143˚C) at 100 km altitude, similar to that of the Solar Corona; ・ The most impressive result is that Saturn's X-ray spectrum is similar to that of X-rays of the Sun; We suppose that not only gravitationally-rounded objects in the Solar System have Coronas made up of Dark Matter particles, but so do all gravitationally-rounded Macroobjects of the World.

Conclusions
Dark Matter is abundant: ・ 2.4% of Light Matter is in Superclusters, Galaxies, Stars, Planets, etc.