On Some General Regularities of Formation of the Planetary Systems

Transcription

1 Volume 10 (2014) PROGRESS IN PHYSICS Issue 1 (January) On Some General Regularities o Formation o the Planetary Systems Anatoly V. Belyakov belyakov.lih@gmail.com J. Wheeler s geometrodynamic concept has been used, in which space continuum is considered as a topologically non-unitary coherent surace admitting the existence o transitions o the input-output kind between distant regions o the space in an additional dimension. This model assumes the existence o closed structures (micro- and macrocontours) ormed due to the balance between main interactions: gravitational, electric, magnetic, and inertial orces. It is such macrocontours that have been demonstrated to orm independently o their material basis the essential structure o objects at various levels o organization o matter. On the basis o this concept in this paper basic regularities acting during ormation planetary systems have been obtained. The existence o two sharply dierent types o planetary systems has been determined. The dependencies linking the masses o the planets, the diameters o the planets, the orbital radii o the planet, and the mass o the central body have been deduced. The possibility o ormation o Earth-like planets near brown dwars has been grounded. The minimum mass o the planet, which may arise in the planetary system, has been deined. 1 Introduction Wheeler s geometrodynamic concept, in which microparticles are considered as vortical oscillating deormations on a non-unitary coherent surace and the idea about transitions between distant regions o space in the orm o Wheeler s wormholes, made it possible to substantiate the existence o closed structures (micro- and macrocontours) acting at various levels o organization o matter [1 3]. These contours are material, based on the balance between main interactions: electrical, magnetic, gravitational, and inertial orces. They are not associated to the speciic properties o the medium; they determine the important properties o objects and allow using analogies between objects o various scales. Such approach allows using a model that best are independent o the properties o an object or medium. In this paper the concept is used to establish some o the basic laws o the ormation o planetary systems. Here, as in paper [2], there is no need to consider the nature o the cosmological medium, i.e. protoplanetary nebula, rom which the planets ormed, and other speciic eatures o the process. Idea o the planetary system consisting o some amount o macrocontours, rom which planets ormed, and the contours o a higher order integrating the planets and a central body was enough to get the general regularities. 2 Initial assumptions As was shown earlier [1], rom the purely mechanistic point o view the so-called charge only maniests the degree o the nonequilibrium state o physical vacuum; it is proportional to the momentum o physical vacuum in its motion along the contour o the vortical current tube. Respectively, the spin is proportional to the angular momentum o the physical vacuum with respect to the longitudinal axis o the contour, while the magnetic interaction o the conductors is analogous to the orces acting among the current tubes. It is given that the elementary unit o such tubes is a unit with the radius and mass equal to those o a classical electron (r e and m e ). It should be noted that in [1, 2] the expressions or the electrical and magnetic orces are written in a Coulombless orm with charge replaced by electron limiting momentum. In this case, the electrical and magnetic constants (ε 0 and µ 0 ) are expressed as ollows: ε 0 = m e /r e = kg/m, (1) µ 0 = 1/ε 0 c 2 = N 1, (2) where c is the velocity o light. Thus, the electric constant ε 0 makes sense the linear density o the vortex tube current, and the magnetic constant µ 0 makes sense the reciprocal value o the interaction orce between two elementary charges. In [2] the relative comparison o various interactions have been carried out and the basic relationships were obtained, some o which are necessary or the understanding o this article. 1. The balance o electric and magnetic orces gives a geometric mean a characteristic linear parameter that is independent o the direction o the vortex tubes and the number o charges: R s = (r 0 L) 1/2 = (2π) 1/2 c [sec] = m (3) a magnitude close to the Sun radius and the sizes o typical stars, where r 0, and L are the rotary radius or the distance between the vortex tubes (thread) and their length. 28 Anatoly V. Belyakov. On Some General Regularities o Formation o the Planetary Systems

2 Issue 1 (January) PROGRESS IN PHYSICS Volume 10 (2014) 2. The balance o gravitational and inertial (centriugal) orces gives the maximum gravitational mass o the object satisying the condition (3): M m = R sc 2 = R s ε 0 = kg. (4) γ 3. The balance o magnetic and gravitational orces also results in a geometrical mean: ( ) 1/2 ε (r 0 L) 1/2 = R s, (5) where the ratio o the products ε = (z g1 z g2 )/(z e1 z e2 ) is an evolutionary parameter, which characterizes the state o the medium and its changes, as the mass carriers become predominant over the electrical ones and, as a matter o act, shows how the material medium diers rom vacuum. Here z e and z g are the relative values o charge and mass in the parameters o electron charge and mass, is the ratio o electrical-to-gravitational orces, which under the given conditions is expressed as ollows: = c2 ε 0 γ = , (6) where γ is the gravitational constant. In the general case, expression (5) gives a amily o lengthy contours consisting o contra-directional closed vortex tubes (mg-contours). 4. The vortex tubes can consist, in their turn, o a number o parallel unidirectional vortex threads, whose stability is ensured by the balance o magnetic and inertial orces orming mi-zones. 5. Structurizations o the primary medium, where there is more than one pair o balanced orces, results in complication an originally unstructured mass by orming in it local mi-zones. In particular, the number o mi-zones in the object o arbitrary mass M i will be: ( ) 1/4 Mm z i =. (7) 3 Planetary systems Let us assume there is a cloud o the originally protoplanetary material having an evolutionary parameter ε, in which a planetary system with a central mass M 0 and planets with a mass m p on a radius r p, with a rotary velocity v 0 is being ormed. Let us assume that the central body is a point-like mass, and the mass o the planet is ormed o contours o total number z p and axis sizes d p l p. Then the mass o the planet can be expressed as the total mass o contours: M i m p = z p εε 0 l p. (8) The characteristic size o the mg-contour by analogy to (5): ( ) ( ) 1/2 1/2 ε lp d p = R s. (9) Suppose the number o mg-contours constituting the mass o the planet is proportional to the distance to the central body, i.e. a planet contour is a structural unit or the contour o higher order that integrates planet with the central body: z p = r p d p. (10) This is true or a lat homogeneous disk o the initial nebula, where the mg-contour is one-dimensional, but in general, density o medium may be dierent and, o course, decrease toward the periphery. The protoplanetary disk may have a local rareaction or condensation, i.e. have sleeves or be latspiral. Thereore, in general, we have: ( ) n rp z p =, (11) where the coeicient n relects the packaging o contours in the model object (planet). The orbital velocity o the planet can be expressed rom the balance o centriugal and gravitational orces: ( ) 1/2 γm0 v 0 =. (12) d p r p On the other hand, we can use the analogy o the Bohr atom, where in the proton-electron system the orbital velocity o the electron at the radius o r i is equal to ( ) 1/2 re v 0 = c. (13) Then or the contour integrating the planet with the central body, taking the parameter l p as the unit o length, an analogous relation can be written: ( ) 1/2 lp v 0 = c. (14) The number o mg-contour z 0 or the stable state o the object, as given in [2], should be taken equal to the number o mizones: ( ) 1/4 Mm z p = z i =. (15) Share urther the dimensionless parameter: M = M 0 /M m, m = m p /M m, v = v 0 /c, r = r p /R s, l = l p /R s, d = d p /R s, and z = m 1/4. Taking into account (8-15), ater transormations we obtain expressions describing the dependence o the planet mass on its orbit radius and mass o the central body: r i r p m p m = ( rm 2) 4n/(5n 1), (16) Anatoly V. Belyakov. On Some General Regularities o Formation o the Planetary Systems 29

3 Volume 10 (2014) PROGRESS IN PHYSICS Issue 1 (January) Fig. 1: Dependence o the mass o Type I planets on their orbital radius at M 1 s.m. 1 HD10180, 2 HD125612, 3 HD134606, 4 HD160691, 5 HD204313, 6 HD75732, 7 HD95128, 8 HD31527, 9, 10 KOI. Fig. 2: Dependence o the mass o Type I planets on their orbital radius at M 0.7 s.m. 1 HD20794, 2 HD40307, 3 GJ676A, 4 HD10700, 5 HD181433, 6 KOI 701, 7 HIP proportions o mg-contour and the value o the evolutionary parameter d = m5/4 M 2, (17) l = M, (18) ε = m5/4 M. (19) However, this model also admits a second case o orientation o mg-contour according to another to its axis. In this case an expression or z p analogous to (11) can be written: z p = ( rp l p ) k ; (20) Fig. 3: Dependence o the mass o Type I planets on their orbital radius at M s.m. 1 GJ, 2 Gliese, 3 OGLE. then relation m(r) taking into account (15), (18), (20) will look as ollows: ( M ) 4k m =. (21) r In this variant the emerging masses o planets quickly decrease to the periphery o the protoplanetary disk, and it can be assumed that such initial nebulae are lenticular in nature. We call planets corresponding relations o (16) and (20) as Type I planets and Type II planets, accordingly. The actual data relating to the planets in extrasolar planetary systems having three or more planets plotted on diagrams in the coordinates o r m, where r the size o the major semiaxis, (Fig. 1-3). The results o the site have been used. The numbers in the igures correspond to the position o the experimental points and point to the sections o the catalog o extrasolar planets. The calculated dependencies m(r) according with ormula (16) converted to coordinates expressed in the masses o Jupiter and astronomical units by multiplying m by M m / and r by R s / These dependencies correspond to the period o planet ormation, but several isolines n are shown, because the conditions o ormation o the planets and their urther evolution is unknown. A large scatter in the values is present on this and others diagrams; in this case it is inevitable. However, the dependence o the masses o extrasolar planets on their orbital radii and on the masses o central stars is revealed quite clearly in agreement with the expression (16). These regularities, i.e. increase in the mass o planets with increasing distance to the central star and with increasing the mass o central stars, also conirmed in [4 7] and others. Types II planets do not it into this pattern. In (Fig. 1-3) they would be located near the dashed line. They have masses o the order o the mass o Jupiter and greater than one and are in orbits close to the central star (hot Jupiters). 30 Anatoly V. Belyakov. On Some General Regularities o Formation o the Planetary Systems

4 Issue 1 (January) PROGRESS IN PHYSICS Volume 10 (2014) Fig. 4: Dependence o the mass o Type II planets on their orbital radius at M 1 s.m. 1 CoRoT, 2 HAT-P, 3 WASP, 4 TrES, 5 XO, 6 OGLE, 7 HD. Fig. 5: The calculated dependence m(r) on the background o distribution o all known extrasolar planets in the semimajor axis-mass parameter spaces. Triangles represent the planets o the system GJ 221. Masses are expressed in the masses o the Earth. Figure 4 shows the actual data on extrasolar Type II planets, which are in agreement with the expression (21) at a coeicient k, whose value diers very little rom 1/3. When comparing (11) and (20), given that k 1/3, one comes to the conclusion that in this case mg-contour is a three-dimensional element. With decreasing the density o medium towards the periphery o the disc the dimension o mg-contour can be reduced. These planets are mainly ound in single-planet systems. The existence o systems o this type was unexpected or astrophysicists. It is supposed that their ormation or dynamical history occurred in another way when the planets were ormed on the periphery o the initial disc and then migrated to closer orbits [8]. In the ramework o the proposed model the existence o such planetary systems is natural. More- Fig. 6: Dependence o the mass o the solar system planets on their orbital radius. over, this situation by Type II occurs in systems o planetary satellites, such as the Earth-Moon, Neptune-Triton, and Pluto-Charon. Figure 5, taken rom the article [9], shows a large array o data on extrasolar planets in the coordinates r m (star masses are dierent). In order to conirm these regularities isolines m(r) by (16) and (21) at M = 1 s.m. superimposed on the diagram; they just pass through areas, where the planets are at the most grouped. Moreover, the model allows us to explain the presence o the large number o massive planets and indicate the area, where they are concentrated. In paper [2] it is shown that or the central star there is a period o evolution when the number o mg-contours is equal to the number o mi-zones, which should correspond to the most stable or balanced state. It is this period is most avorable or the ormation o the most massive planets. In this case, the evolutionary parameter ε receives the expression: Then, as it ollows rom (19) and (22), ε = M 11/12. (22) m = M 23/15. (23) For the mass o the Sun M = Then m p = ( ) 23/15 M m or kg, which is almost exactly the mass o Jupiter. Depending on the type o planetary system this mass can arise in orbit size o au (hot Jupiters), or 2.3 au (cold Jupiter), (Fig. 5). More massive stars give rise greater mass o the planet. Figure 6 shows the dependencies o m(r) by (16) at dierent n and by (21) at k = 1/3 as well as the position o the planets in the solar system. Decrease in the value o index n with increasing radius and decreasing density o protoplanetary disk is interpreted by expression n (n 0.4)r/50, assuming that the disk was limited o radius 50 au wherein n was reduced to a value 0.4 at the periphery. Anatoly V. Belyakov. On Some General Regularities o Formation o the Planetary Systems 31

5 Volume 10 (2014) PROGRESS IN PHYSICS Issue 1 (January) the authors by solving the equation o state, which describes the relationship between density, pressure, and temperature or the substance under conditions o thermodynamic equilibrium. The position o the terrestrial planets corresponds exactly to the general trend and conirms the assumption that these planets were ormed by Type I near the Sun. During evolution irst planets were ormed when the orbital angular momentum o the planet is compared to the rotational angular momentum o the central body. Let us compare the corresponding expression: to the central body derived in [2] and, reerring to (10), (12), (17), (19), at n = 1, analogous one to the planet: M ε M mcr s = M 7/10 ( ε ) 6/5 M m cr s. (25) Fig. 7: Dependence o the diameter o the planets on their mass or Type I planets. The squares marked planets o the system Kepler- 11. Rectangle roughly bounded region o massive Type II planets at M 1. Dash-dot line shows the boundary o the minimum planetary masses, determined rom the condition r p = R s at n = 1. In general, the initial protoplanetary cloud o the solar system would it the lat model at n 1 i it is assumed that the small planets were ormed close to the Sun, but later moved to a more distant orbit under the inluence o massive planets that were ormed later. Detection o Earth-like planets that are very close to the central star [10, 16] conirms this assumption. It is also possible that the initial cloud had a low density on the orbits where small planets have been ormed. 4 On the parameters o planets For Type I planets calculations show that d l, i.e. a mgcontour is actually a one-dimensional structure and when packaging it in a volume ratio o its linear dimensions, i.e. ratio o the diameters o planets averaged over density, taking into account (17), must meet the relationship: D = d 1/3 = m 5/12 M 2/3. (24) These parameters are here dimensionless and can be expressed as, or example, the parameters o Jupiter and the Sun. Figure 7 shows the dimensionless dependence D(m) by (24) or Type I planets reduced to the parameters o Jupiter and mass o the Sun. The planets o the solar system are located along a solid line. It also shows the position o the six planets o the sistem Kepler-11 having an intermediate density [11], which generally corresponds to the calculated dependence. It is interesting to note that the expression (24) obtained solely on the basis o general provisions and being adequate to a wide range or Type I planets, in act, coincides with the analogous dimensionless dependence derived by the authors in the paper [7]. However, this dependence was obtained by As ollows rom (25): and then one can obtain: ε = M 3/2, (26) m = M 2, (27) r = 1, (28) Radius r p = R s is the natural limit or the minimum masses o Type I planets. The outer planets, whose mass is greater, have the orbital angular momentum greater than the rotational angular momentum o the central star. With M = 1 s.m. m p min = M m = kg, which just corresponds to the average mass o the terrestrial planets. Thus, in this model the existence o Earth-like planets near the central star is natural. The size o the planets o type II can be estimated by the value o the orbital radius, having on a mg-contour, r/z. Keeping in mind the ormula (20) at k = 1/3, and expressing r rom (21), we obtain: D M, (29) m1/2 There is a need additionally to take account the act that the unit mg-contour is in this case not one-dimensional, and the mass o the model object is proportional to the parameter ε, ormula (8). Thus, the relation (29) should be supplemented. Using (19) and moving rom the mass ratio to the ratio o linear sizes the inal expression gets the ollowing orms: in the case o a three-dimensional mg-contour D = M ( m 5/4 M 1) 1/3 M 2/3 = ; (30) m 1/2 m1/12 or the less dense medium, in the case o two-dimensional mg-contour, ormula (30) takes the orm: D = M ( m 5/4 M 1) 1/2 M 1/2 = m 1/2 m ; 1/8 (30a) 32 Anatoly V. Belyakov. On Some General Regularities o Formation o the Planetary Systems

6 Issue 1 (January) PROGRESS IN PHYSICS Volume 10 (2014) The obtained dimensionless relationships are generally in agreement with the actual laws. Figure 8 shows the dependence o D(M), and Figure 9 shows the dependence o D(m) calculated rom ormulas (30) and (30a) at dierent M, which are or illustrative purposes superimposed on the chart taken rom the article [12]. In particular, it becomes clear both the existence o planets with similar sizes but sharply diering masses and having the same mass at various sizes. Planets with a relatively small mass, or example, GJ 1214b [13], Kepler-87c (they are shown in Figure 8 and 9), and others, ormed probably by type II; their diameters varied greatly and correspond to the values, which are calculated by the option (30a). The densities o Type I and Type II planets through their mass and the mass o a star in dimensionless units (in units o the Jupiter s mass and the Sun s mass), having in mind that ρ md 3, have radically dierent character and can be expressed as ollows: ρ 1 = m 1/4 M 2, (31) Fig. 8: Dependence o the diameter o the planets on the mass o the central star (masses o the planets are dierent). 1 CoRoT, 2 HAT-P, 3 WASP, 4 KOI, 5 XO, 6 TrES, 7 OGLE, 8 GJ. ρ 2 = m 5/4 M 2, (32) ρ 2a = m 5/8 M 3/2. (32a) O course, obtained dependences are not precise or deinitive. They only relect the general trends uniting the diameter o the planet to its mass and the mass o stars in the period o the ormation o planetary systems. By equating the orbital angular momentum o the planet and the rotational angular momentum o the central body one can obtain the relations similar to (25-28) or Type II planets at k = 1/3: M ( ) ( ) 1/2 ε ε M m cr s = M 3/2 M m cr s, (33) ε = M, (34) m = M 8/5, (35) r = M 1/5, (36) which determine their speciic mass and orbital radius. At M = 1 s.m. m p = M m = kg or 0.4 Jupiter s masses, r p = 13.8 R s = m or 0.07 au. The inner planets with a greater mass have angular momentum that is less than that o the central star. As ollows rom (21) and (32) Type II planet masses decrease with increasing distance rom the central star as well as their density decreases. This is illustrated by the planet Kepler 87c having a very low density with its orbital radius o 136 R s or 0.68 au. Formation o the planets in more remote orbits it is unlikely, where the less oten they exist, the more massive major planet [8]. Low-mass rocky planets o type II can not be ormed near Sun s mass stars and having greater masses, but, as ollows rom (32), their ormation is possible in the system o Fig. 9: The calculated dependences D(m) o Type II planet on the background o distribution o known transit extrasolar planets in the planet mass-radius spaces. Squares shows the planets in the solar system. Dotted lines are lines o equal density 0.1, 0.3, 0.9, 3.0, 9.0, 25.0, and 100 g/cm 3. Dash-dotted line limits the maximum masses o the planets, k = 1/3. dwar stars when M < 1 s.m. Indeed, another test o the correctness o the presented model may serve determination the masses o stars, at which planets with masses and sizes like the Earth can be ormed. Let their mass is in the range rom Jupiter s mass and the density is Jupiter s density. Then or the Type I planets ormula (31) gives: M = s.m. and or Type II planets ormulas (32) and (32a) give: M = and M = s.m. The irst solution is obvious and corresponds to the stars Anatoly V. Belyakov. On Some General Regularities o Formation o the Planetary Systems 33

7 Volume 10 (2014) PROGRESS IN PHYSICS Issue 1 (January) Fig. 10: Dependence o the mass o the planets on their orbital radius at l = d. with a mass close to the mass o the Sun and the second solutions just correspond to the very low-mass stars brown dwars. This prediction proved to be correct. Indeed, recent observations have shown that is quite possible the ormation o Earth-like planets around o brown dwars and there may be created suitable conditions or emergence o lie [14]. These types o planetary systems even more preerable since no need planets to migrate to more distant (as in the case o the Earth) and the suitable masses o the brown dwars vary within a more wide range. The question arises whether there are conditions under which the ormation o planets in the evolution o both types is equally probable? It is logical to assume that in the initial period there had been rareied initial spherical cloud around the central body, which is then transormed into or latspiral disk, or lenticular in shape, rom which Type I planets or Type II planets, respectively, have been ormed. Hypothetically, this would correspond to the initial state o complete equality o conditions o planets ormation in both types, i.e. l = d = M, n = k, masses o planets by (16) and (21) are equal. Having in mind (16), (17), (21), we ind: lg ( rm 2) n = k = 0.2 lg (M/r) + 1, (37) m = M 12/5. (38) Thus, this mass depending on the coeicient n may occur at any orbit (Fig. 10). The size o the planet in this case is uncertain since dependences (24) and (30) are here incorrect. One can speciy the maximum size o an object i mg-counters are packaged in a linear structure, D max = zl. Since z = m 1/4 and l = M, using (38), we obtain: D max = M 2/5. (39) Convergence coeicient values o n and k indicate a decrease ormally in the density o medium in any variant evolution that, obviously, corresponds to the moust low mass. The average value o the coeicient equal to 0.5 at M = 1 s.m. corresponds to the orbital radius o 0.07 au, which coincides with the speciic radius or Type II planets. For the mass o the Sun, m p lim = M m = = kg, D p max = R s = m. It is unknown whether such planets orm in reality. In any case, in the solar system there are no regular planet s masses less than m p lim, except Pluto having a similar mass o kg, the status o which is uncertain. The same can be said o the satellite systems o the major planets. Masses less settlement not observed to date also among extrasolar planets. The existence o lowest masses or the planets ormed and, accordingly, their lowest diameters explains act o rapid decrease o the planets having a small radius as well as existence o a maximum o the planetary radii speciied in [15]. 5 Conclusion Planetary systems can be quite diverse as their structure depends on the initial composition o the protoplanetary cloud, mass and type o stars, ormation history o the planetary system, and the random actors. Nevertheless, there are some general patterns. There are two types o planetary systems. In the system o the irst type planets are ormed rom latspiral protoplanetary cloud. Masses o Type I planets increase to the periphery passing through their maximum (cold Jupiters) that occur in the distance rom the center in the local condensations o the medium (the sleeves, spirals), supposedly, in later periods o the evolution. Earth-like planets are ormed near the central star and maybe can migrate to the more remote orbits. In the second type o planetary systems planets are ormed rom a protoplanetary cloud lenticular or elliptical type. The masses and densities o Type II planets decrease to the periphery o the disc. Massive planets (hot Jupiters) are ormed in condensations near the central star; the ormation o other planets in more distant orbits is unlikely. Low-mass rocky planets in these systems can be ormed only at low-mass stars (brown dwars). The possibility o the ormation o Earth-like planets in the planetary systems o brown dwars has been predicted. The regularities among the masses, sizes, orbital radii o the planets and masses o the central stars have been obtained. Reerences Submitted on: July 03, 2013 / Accepted on: July 21, Belyakov A. V. Charge o the electron, and the constants o radiation according to J.A.Wheeler s geometrodynamic model. Progress in Physics, 2010, v. 4, Belyakov A. V. Evolution o Stellar Objects According to J. Wheeler s Geometrodynamic Concept. Progress in Physics, 2013, v. 1, Anatoly V. Belyakov. On Some General Regularities o Formation o the Planetary Systems

8 Issue 1 (January) PROGRESS IN PHYSICS Volume 10 (2014) 3. Belyakov A. V. On the independent determination o the ultimate density o physical vacuum. Progress in Physics, 2011, v. 2, Stephane Udry. Geneva University, Debra Fischer. San Francisco State University, Didier Queloz. Geneva University. A Decade o Radial- Velocity Discoveries in the Exoplanet Domain. 5. Montet B. T., Crepp J. R. et al. The trends high-contrast imaging survey. iv. the occurrence rate o giant planets around m-dwars. 24 July 2013, arxiv: astro-ph/ v1. 6. Jones M. I., Jenkins J. S. et al. Study o the impact o the post-ms evolution o the host star on the orbits o close-in planets. A giant planet in a close-in orbit around the RGB star HIP June 2013, arxiv: astro-ph/ v1. 7. Seager S., Kuchner M., Hier-Majumder C., Militzer B. Mass-Radius Relationships or Solid Exoplanets. 19 Jul 2007, arxiv: Steen J. H., Ragozzine D. et al. Kepler constraints on planets near hot Jupiters. 10 May 2012, arxiv: astro-ph.ep/ v1. 9. Arriagada P., Anglada-Escud G. et al. Two planetary companions around the K7 dwar GJ 221: a hot super-earth and a candidate in the sub-saturn desert range. 9 May 2013, arxiv: astro-ph/ v Sanchis-Ojeda R., Rappaport S. et al. Transits and occultations o an earth-sized planet in an 8.5-hour orbit. 17 May 2013, arxiv: astroph/ v Lissauer J. J., Jonto-Hutter D. et al. All Six Planets Known to Orbit Kepler-11 Have Low Densities. 14 Jun 2013, arxiv: astroph/ v Sato B., Hartman J. D. et al. HAT-P-38b: A Saturn-Mass Planet Transiting a Late G Star. 24 Jan 2012, arxiv: astro-ph/ v Charbonneau D., Berta Z. K. et al. A super-earth transiting a nearby low-mass star. Nature Ricci L., Testi L., Natta A., Scholz A., Gregorio-Monsalvo L. Alma observations o ρ-oph 102: grain growth and molecular gas in the disk around a young brown dwar. 28 Nov 2012, arxiv: astro-ph.sr/ v Morton T. D., Swit J. The radius distribution o small planets around cool stars. 14 Mar 2013, arxiv: astro-ph/ v Charpinet S., Fontaine G. et al. A compact system o small planets around a ormer red-giant star. 22 Dec 2011, Nature, 480, Anatoly V. Belyakov. On Some General Regularities o Formation o the Planetary Systems 35