Solar System Wave Function

5 Pluto, Ceres and all planets of solar system except Neptune, with a high approximation, follow a 6 law called Titius-Bode law (TBL) or Bode law, which can by no means be considered as a 7 stochastic event. This law shows that the distance of the planets from the sun in Solar system is 8 regulated. Here, we prove that the existence of a standing and cosine wave packet in solar system, 9 with the wavelength λ = 0.6 𝐴𝑈 ( 𝐴𝑈 represents the distance of earth from the sun) and the phase 10 constant ∅ 0 = 𝜋 6 , is the reason for TBL. Moreover, we prove that this huge wave packet belongs 11 to the sun. In the first part of the article we will obtain the equation of this wave packet empirically; 12 and in the second part we will prove that this equation is exactly in the form of the real part of the 13 solution of the Schrodinger equation and that's why we can attribute it to an object like the sun 14 (Certainly the presence of a standing wave in space is not without a origin). Finally in this article 15 we will prove that without solar system wave function, it is not possible to reach to the TBL from 16 the protoplanetary disk of solar system.


Introduction
The planets of solar system move around the sun in elliptical orbits such that the sun is in one of 21 the focal points of these ellipses. These ellipses are very close to the circle, and in fact the 22 orbits of the planets of solar system are concentric circles. Pluto, Ceres and all planets of Solar 23 system except Neptune, with a high approximation follow a law known as Bode law or 24 Titius-Bode law (TBL). According to this law, the distance of each planet from the sun is equal 25 to = 0.4 + 0.3 × 2 , where 0.4 is the distance of Mercury from the sun (or more 26 precisely the length of the semi-major axis of Mercury's orbit) and = 0,1,2,3, …. [1]. Table. 1 27 shows the high accuracy of the Bode law. If this law was only true for three or four planets, then 28 we could call it a coincidence, but when it is true for seven planets, plus Ceres and Pluto, there is 29 definitely a reason for it. It was historically based on this law that Ceres was discovered in 1801 30 [1]. In this article, we will find the reason for the existence of the TBL. In fact, we will prove that 31 the presence of a cosine and standing wave packet in solar system is the reason for existence of 32 TBL; and moreover, we will prove that this wave packet belongs to the sun. In this article we prove 33 that the Schrodinger equation is valid at the astronomical scale and is not limited to subatomic 34 particles. TBL does not predict the distance of Neptune from the sun but, this article is able to give 35 us the distance of Neptune. In this paper and in the section "Elliptical orbits and Isotropic Asteroid 36 Belt", we prove that nebular theory, which explains the formation of the solar system, without 37 considering the solar system wave function (SSWF) is incomplete and wrong. We will prove that 38 without solar system wave packet, it is not possible to reach to the TBL from the protoplanetary 39 disk.

43
Consider a standing and cosine wave function with a wavelength = 0.6 in solar system; if 44 we assume that the first node of this wave is at a distance of 0. ) and then we will show that our choice is correct (δ is a constant 100 number that we will derive its value). Since solar system has a certain size and is not infinitely 101 wide, its wave function must be localized (a wave packet). If we consider an expression in the 102 form − 2 (which is a Gaussian function and plays the role of a wave envelope) in the final 103 function of solar system, in such a case, the final equation is a localized wave or a wave packet 1 .

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The value of γ, which is a positive number, will be obtained in the following. Thus, the primary 105 form of the wave function of solar system is as follows (equation 1) and the planets are on the 106 nodes of this wave function ( Fig. 1): In equation 1, γ, C and δ are constant values and we obtain their values in this article. This is an 109 empirical equation which we will obtain it from mathematic methods in the next section.

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The value of (0,0) equals √3 2 ⁄ . This diagram is drawn by a certain value of , and γ in equation 1, which we 113 will obtain their value in this article. As you can see, the planets are on the nodes of the wave function. Jupiter, Saturn,

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Uranus, Neptune, and Pluto are on the nodes farther from the sun. The reason why there is no planet in some nodes 115 will explained in the section 6: ''Elliptical orbits and Isotropic Asteroid Belt''. This is due to the unbalanced mass 116 distribution in the protoplanetary disk of solar system. In figure 1, the wave oscillates along the axis over time. But the nodes and the anti-nodes do not 118 move relative to each other along the x-axis. This does not mean that the wave packet is stationary 119 in the space; it is just like passengers sitting on a train who do not move relative to each other but 120 the train is moving relative to the rails. In the same way, solar system wave packet (Fig. 1) is a 121 standing wave that rotates, along with solar system, around the center of the galaxy.

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As you observed, function 1 could easily predicts the position of planets. In the continuation of the 123 article, we will prove that this function is in the form of the real part of a solution of the Schrodinger    But when their experiments were performed in the real world, they concluded that the velocity of 141 light is independent of the velocity of observer and source. As another example, before the advent 142 of particle accelerators, it was thought that an object could be propelled at any velocity, even 143 beyond the speed of light. But particle accelerators showed us that we could not go beyond the  In the next section, we will obtain equation 1 mathematically and we will show that the equation   In this equation, the larger the α is, the more the width of wave packet, along the x-axis. We drew for subatomic particles, and here we attributed the wave nature to celestial objects. Neither of these 260 two actions is strange. Rather, they are truths that we must become accustomed to.

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In this section we will show that the nebular theory without our wave function theory is an 291 incomplete theory and our wave function model must be attached to the nebular theory in order to 292 explain the formation of the solar system.

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The equation 14 in cylindrical coordinate is: 16, the amplitude of the wave gradually decreases while we move away from the -axis. 301 As you can see in Fig. 1 and Fig. 2, because of symmetry of equation 1, the orbits, created by the 302 solar system wave function, are circle. But the real orbits of the planets are elliptic. The reason for 303 this is the existence of the inverse_square gravitational force of the sun 6 . As you know, the sun 304 formed earlier than the planets [10][11] [12]. Simultaneously with the formation of the sun, about 305 4.6 billion years ago [11], its wave function was also formed 7 , and the oscillation of this wave 306 function arranged and collected the gas and dust particles of the Protoplanetary disk in regular 307 orbits (Titius-Bode orbit). Just like the standing wave patterns on the kettledrum head ( Fig. 3) As 308 you can observe in Fig.3, by a mechanical oscillator at the upper left of the photograph, the powder 309 collects at the nodes [13]. As the same way, because of oscillation of solar system wave function, 310 in some nodes of the wave function the gas and dust grains of protoplanetary disk agglomerated 311 in the circular nodes (like figure 3) and then compressed due to collisions with each other 8 and 312 formed larger grains, Planetesimals, Protoplanets and finally planets 9 . At the same time, the 313 inverse_square force of the sun was at work, and changed the circular orbits to elliptical orbits.

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Don't you see resemblance between the powder ring in Figure 3 and the asteroid belt? The mass 315 distribution in the asteroid belt is uniform and isotropic, just like the powder ring in Figure 3, and 316 this is another confirmation for our wave theory (In asteroid belt, Planet formation has stopped at 317 the Planetesimals stage; And because of orbital resonances with Jupiter Protoplanet and planet was 318 not formed [15]). Can a theory other than our wave theory explain the uniform and isotropic 319 distribution of Planetesimals in the asteroid belt? 320 If solar system wave function did not exist; the planets might have been formed around the sun but 321 the distance of planets from the sun was random and irregular. Without solar system wave packet, 322 it is not possible to reach to the TBL from the protoplanetary disk. Thus, it seems that the existence 323 of a standing wave in the solar system is undeniable. Therefore, the nebular theory becomes more 324 complete by our wave function theory.

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The reason why there is no planet in some nodes in figure 1 and 2 is due to the unbalanced mass 326 distribution in the protoplanetary disk of solar system.  8 "Collisions" were more like gentle touches. The particles were far too small to attract each other gravitationally at this point, they were able to stick together through electrostatic forces-the same "static electricity" that makes hair stick to a comb [14]. 9 Since the mass distribution in the Protoplanetary disk had not been uniform. During formation of the planets, in some nodes of the solar system wave function, less dusts were collected and in some nodes, more dusts were placed next to each other. Therefore, in some nodes a planet had been formed and in others it had not been formed.   Unfortunately, many of the theories that we will review are "theories" and "Laws" in large part 372 due to assumptions or arguments of possibility rather than by calculations that predict definite and 373 unambiguous results . . . Too often the Titius-Bode Law has been discussed in terms of some 374 mechanism which could conceivably produce the Law if all other physical effects could be 375 ignored. Sad to say, that is not the type of physical universe with which we are dealing. Thus, one 376 should be aware of the fact that any claim that a particular theory of the solar system is correct 377 since it explains the Titius-Bode Law is not valid because, as of yet, no theory has properly 378 explained this Rule. What can be said of some theories is that they are compatible with and 379 indicative of a Titius-Bode Law, but not very much more. )) [20]. For example, In his three article, 380 Hannes Alfven hypothesized that if he consider the original solar dipole moment 100000 times 381 larger than at present and ignore the angular momentum in the early solar system [21] He could to the growing Planetesimals via radiation pressure) [22]. But in our article is not any simplification 387 or assumption. Our paper, without eliminating the physical parameters of solar system, justifies has been advanced that has found general acceptance.'' [23] 398

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In addition, some calculations and attempts were made which showed that TBL was a matter of 399 chance. But in 2003, Professor Peter Lynch denied that it was a coincidence: '' . . . this conclusion is unsafe, and that the possibility that the observed regularity in the patterns of the planetary and 401 satellite systems has some physical explanation is still open.'' [23].

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In this article we proved that almost there is no doubt about the existence of a wave function in 404 the solar system. In this article we proved that the nebular theory without our wave function theory 405 is an incomplete theory and our wave function model must be attached to the nebular theory in 406 order to explain the formation of the solar system. Without the solar system wave packet, it is not 407 possible to reach to the TBL from the protoplanetary disk. Can a theory other than wave theory 408 explain the uniform and Isotropic distribution of mass in the asteroid belt? De Broglie considered 409 the wave nature for subatomic particles, and here we attributed the wave nature to celestial objects.

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Neither of these two actions is strange. Rather, they are truths that we must become accustomed 411 to. In this article we proved that the Schrodinger equation is also valid for celestial objects and in 412 astronomical scale we need a larger Planck constant instead of present Planck constant.

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Based on this article, the associated wave packet of an object (such as electron, proton or sun) is Here, we proved that the word of '' thought experiment '' is meaningless and an experiment must 417 be done in the real world so that we can talk about its results.