Fifth giant ex-planet of the outer Solar System: characteristics and remnants

Fifth giant ex-planet of the outer Solar System: characteristics and remnants Yury I. Rogozin Abstract. In the past, the outer Solar System likely could have more planets than now. Using the new relations, we have found the orbital and physical characteristics of the icy giant explanet, which orbited the Sun about in the halfway between Saturn and Uranus. Validity of the obtained results is supported by the feasibility of these relations to other objects of the outer Solar System. Possible connection of the existing now mysterious objects of the outer Solar System such as the Saturn s rings and the irregular moons Triton and Phoebe with this destroyed planet is briefly discussed. Keywords: Solar System: planets and satellites; individuals: fifth giant ex-planet, Neptune, Triton, Phoebe, Saturn s rings 1. Introduction According to the existing representations on the formation of the Solar System its planetary structure persists unchanged during approximately 4.5 billion years. Such static situation of the things has found the reflection, particularly, as offered in 1766 Titius-Bode s rule of the orbital distances for known in that time the seven planets since Mercury up to Uranus. As is known, the conformity to this rule for discovered subsequently planets Neptune and Pluto has appeared much worse than for before known seven planets. However, the essential departures of the real orbital distances for these two planets from this rule till now has not obtained any acceptable justifying within the framework of such conservative sight on a structure of the Solar System. However, recently in such sights on the Solar System was planned the certain progress. Accordingly to the results of a recent computer simulation (Batygin et al 2012) the Solar System at a stage of its early dynamic evolution could have five outer planets (two gas giants and three icy giants). However, it is noteworthy that the orbital and physical characteristics of this former fifth giant planet in rather recent epoch yet were not determined and its possible remnants in the Solar System remain unrecognized. Here, we state our method to solve this problem and by that we try to give a key to unveiling the some astronomical mysteries of the outer Solar System. In years of the planetary researches of the Solar System by the ground-based telescopes and space missions Voyager and Cassini a number of outstanding questions has amassed on which as yet evidently there are no enough convincing answers. As is known, the present-day planetary science has no an rather acceptable explanation for some astronomical facts, in particular, an origin of the rings and irregular satellites of the giant planets, e. g., the largest retrograde satellite of the Solar System Triton. To shed new light on this situation, in our opinion, the hypothesis on existence in the past one more foregoing outer giant planet could. Veda LLC, Moscow, Russia, e-mail: yrogozin@gmail.com 1

2. Orbital characteristics of the fifth giant ex-planet Possible existence in the past the fifth planet of the outer Solar System first was informed in our before published the book (Yu. I. Rogozin "From numerical harmony to elementary astronomy", 2004, Moscow, Geos, ISBN 5-89118-359-5). As an more adequate rule for the orbital distances of planets from the Sun than Titius-Bode s rule, which, as is known, gives for Neptune and Pluto an error accordingly 29 % and 95 % compared to observable quantities we have found a new empirical rule for these distances. In doing so, a part of this rule relating to the outer planets being express a dependence of the value a semi-major axis of an orbit of these planets R n from serial numbers of a planet n is given by: R n /R o = (n + 2) 2 / Φ 1/Φ 2 (1) where R n, as usually, is expressed in astronomical units AU (R o = 1AU = 149.6 x 10 6 km - distance from the Earth up to the Sun), Φ = 1.618 factor of golden section", and n = 1, 2 6 accordingly for Jupiter, Saturn etc., including Pluto. In case of replacement of (n + 2) in eq. (1) by n with simultaneous change the former order of numbering by n = 3, 4 8 accordingly for Jupiter, Saturn etc. this formula without considering the correction 1/Φ 2 show up similar to the formula of electronic orbits in Bohr atomic model: R n ~ R no n 2, where R no = R o /Φ. In doing so, the qualitative analogy of a structure, at least, of the outer Solar System and atomic structure is observed. For the purpose of illustration the similarity and distinctions with an available now picture of an arrangement of planets of the outer Solar System (including Pluto that until recently was considered as one of outer planets) in the Table 1 the calculated by eq. (1) and observed semimajor axes of these planets are given. To this it is possible to add, that the orbital speed of the fifth giant ex-planet was equal to 7.674 km s -1, and orbital period was equal to 58.5 years. Table 1: Calculated and observed semi-major axes of the five giant planets and Pluto Planet number, n R n (calculated), AU R n (observed), AU Jupiter Saturn Deposs Uranus Neptune Pluto 1 5.18 5.20 2 9.51 9.54 3 15.07-4 21.87 19.19 5 29.90 30.06 6 39.17 39.48 Data of this table testify to an expected improvement of fit between calculated and observed values of semi-majors axes of Neptune and Pluto compared to Titius-Bode s rule. Also has appeared, that compared to earlier known rules of such type this rule gives two completely new results, which are as follows. First, in the past between planets Saturn and Uranus one more outer planet appropriate to number 3 in the Table 1, named here by planet Deposs (reduced from "destroyed planet of the outer Solar System") could in existence. Secondly, during an existence of planet Deposs the orbit of Uranus should be much further from the Sun than in the present epoch. On our sight, it would be logical to believe, that the reason of the occurred change of the orbital distance of Uranus of the Sun, accompanied by the strong tilt of its axis, could be cardinal realignment of gravitational interaction of nearby planets of the outer Solar System, as a result of a disappearance the planet Deposs, if its mass was comparable with their masses. The reality of 2

an existence in the past such planet Deposs, as a result of which destruction in its direction Uranus by the gravitational fields of Saturn and Jupiter was pull at, apparently, it is possible to confirm only by determining its physical characteristics and their comparison with the appropriate characteristics of other planets of the outer Solar System. 3. Determining the physical characteristics of giant ex-planet Deposs In the context of present-day astrophysics a determining the physical characteristics of now more not existing planet presents an intractable problem. Nevertheless, we could find the appropriate method. Its first step was a determining the density of planet Deposs. In one of our former papers (The journal "The natural and engineering sciences", Moscow, # 1, pp. 49-51, 2006, ISSN 1684-2626) based on an analysis of the orbital data and physical characteristics of known planets of the Solar System we have revealed a fact the existence of the orbital parameters - density behavior for these planets. It is displayed by the semi-major axis R- dependence of the product of the density of planet ρ by square of its orbital speed v 2, which has dimensions of pressure (named the orbital pressure). Using the known data of planets of the outer Solar System, the behavior of this dependence is visible in the lower line of the Table 2. Table 2: Orbital pressure data of the outer planets of the Solar System Jupiter Saturn Uranus Neptune Pluto Semi-major axis, R n (AU) Mean orbital speed, v (km s -1 ) Mean density, ρ (g cm -3 ) Orbital pressure*, ρv 2 (g cm -3 ) (km s -1 ) 5.2028 13.06 1.326 227 9.5388 9.6455 0.687 64.0 19.1914 6.80 1.29 59.65 30.0611 5.4334 1.638 48.34 39.4813 4.666 2.03 44.20 *Note: unit of the orbital pressure 1(g cm -3 ) (km s -1 ) 2 = 10 9 Pa Based on a decreasing behavior of this function F (R) =ρ v 2 with increasing R the most suitable type of approximation of this function was chosen by: F (R) = ρv 2 = a R b e Rc, (2) where a > 0 and at least one of factors b or c < 0. Using tabulated data for the planets Saturn, Uranus (on old orbit) and Neptune (R is equal to respectively 9.5388 AU, 21.87 AU, and 30.0611 AU; v is equal to respectively 9.6455 km s -1, 6.37 km s -1, and 5.4334 km s -1 ; ρ is equal to respectively 0.687 g cm -3, 1.29 g cm -3, and 1.638 g cm -3 ), when solving this system from three equations the following values of the factors were received: a = 108.2, b = - 0.22912, and c = - 0.00078. Substituting into eq. (2) these factors at the above-stated value of semi-major axis of this planet R = 15.07 AU and appropriate orbital speed v = 7.674 km s -1 gives the density of planet Deposs, which is equal to 0.974 g cm -3 (that is close enough to the density of water ice 0.94 g cm -3 ). For the purpose to check for correctness of the found value of the density of planet Deposs we have applied this method to nearby of Neptune heavenly bodies Pluto and Charon using the above-stated values of factors a, b, and c. Thus, we have calculated the values of the 3

Pluto s and Charon s density at their primary orbital distances (before the capture Charon), determined respectively as R is equal to 39.17 AU (Table 1) and 36.22 AU (Rogozin 2012) and v = 4.76 km s -1 and 4.95 km s -1, respectively. They have appeared equal to 2.048 g cm -3 and 1.886 g cm -3, respectively, that well agrees to the earlier found values 2.046 g cm -3 and 1.89 g cm -3 (Rogozin 2012). In absence of any evidences for the sizes of this planet the following step should be determining its mass. On the basis of the assumption about a primary harmony of Nature in general and the Solar System in particular, we have tried to reveal existence the functional dependence the mass of the outer planets of their distance from the Sun. It has appeared, that similarly to the law of orbital pressure (2) for the outer planets Jupiter, Saturn, and Uranus (on its old orbit) exists the law of orbital dependence of the angular momentum (Neptune does not subject to this dependence), i.e. M v R = a R b e Rc (3) Using the known parameters of three above-stated planets (mass M equals respectively 317.8, 95.2, and 14.5 mass of the Earth; v equals respectively 13.06 km s -1, 9.6455 km s -1, and 6.37 km s -1, and R equals respectively 5.2028 AU, 9.5388 AU, and 21.87 AU) for function satisfying to eq. (3), such values of its coefficients were obtained: a = 1.908 х 10 5, b = - 1.22484, and c = - 0.03665. The substitution the orbital data of planet Deposs in the obtained equation gives its mass equal to 32.68 mass of the Earth. From the obtained values of its density and mass follows radius of this planet appears equals 36,301 km. In a result, the surface gravity of this planet could be equal to 9.88 m s -2. To evidently represent the found physical characteristics of planet Deposs by comparison with the tabulated data of two nearby planets in the Solar System they are given in the Table 3. Table 3: Comparative physical characteristics of planet Deposs and two nearby planets Planet Name Saturn Deposs Uranus Mean radius ( km) 58,232 36,301 25,362 Mass (10 24 kg) 568.319 195,068 86,810 Surface gravity Density (g cm -3) (m s -2 ) 0.687 10.44 0.974 9.88 1.29 8.87 From data of Table 3 follows the density and surface gravity of planet Deposs with a precision about 1.5 2 % were the arithmetical averages of the appropriate values for its nearby planets. It is possible, there is connected with similar behavior of the orbital distances of the outer planets, which as it is visible from data of Table 1, subject to the relation R n = (R n-1 + R n+1 ) /2 with accuracy 6.2 % for Saturn, 4.2 % for Deposs, 3.2 % for Uranus (on a former orbit) and 1.6 % for Neptune. It can easily be shown, that the foregoing relation also is true for a space configuration of Saturn s rings and the semi-major axes of the trans-neptunian dwarf planets. 4. Remnants of the destroyed ex-planet Deposs in the outer Solar System The destroyed fifth giant planet could not disappear not being left after itself any seen traces in space. They could become, in particular, such strange objects of the outer Solar System as rings of the giant planets and retrograde satellites of Neptune and Saturn. Below we shall try to 4

prove this assumption, having connected characteristics of these strange objects with characteristics of this fifth giant ex-planet of the outer Solar System. 4.1. On the origin of the rings of the outer giant planets Found here the orbital and physical characteristics of this destroyed planet, apparently, can have been directly concerned with the origin of rings Saturn, Uranus, and Neptune. In our opinion, it is necessary to search the origin of rings of Saturn connected with the origin of rings of Uranus, and Neptune. Actually, the available scenario of formation of Saturn s rings from the fragments of some destroyed Saturn s moon of a size about 100 km can be not extended on the origin of rings of two other giant planets, which are strongly distanced from so much small object. The collision some assumed Saturn s moon with any asteroid in the present configuration of the Solar System shows up an unbelievable event in view of the large remoteness of both asteroid belts from Saturn. As the history of fall Comet of Shoemaker-Levy on Jupiter has shown, the collision of comets with the moon of the giant planets even of such large sizes as Galilean moons too is not represented by the real possible reason of destruction of the so much small moon with formation of rings. The explanation of disappearance of a rock core of such moon after a possible loss of its icy envelope to fall on Saturn also is unimpressive, as with one exception (retrograde moon Triton) other satellites of the giant planets, as is known, do not show the consecutive trend to bring into proximity with its hosts. According to the value of its mean density it is possible to consider planet Deposs as basically icy planet. As Saturn s rings and those of other planets consist mainly of the particles of water ice and accordingly to the data of space mission Voyager for Saturn have young age, they could not be formed simultaneously with a planet. Thus, it is possible to assume, that they have appeared as a result of destruction of this ex-planet and subsequent drift of the fragments of this planet to orbits other planets, where they were captured by these planets. It is known that by results of space mission Voyager the Saturn s rings could be a mere 100 million years old. One of results of later mission Cassini (Hedman et al 2007) is that, as it was established, during the elapsed 25 years image of сenter of light of ringlet D72 in ring D has shifted inwards by over 200 km. It seems implies that the velocity of an approach of rings to Saturn makes up about 8 km/yr. In such case average distance between these planets 15.07 AU - 9.54 AU = 5.53 AU = 827.3 x 10 6 km some fragments of the destroyed ex-planet could overcome approximately in a time 103.4 х 10 6 years. Thus, in view of the significant size of this planet and possible wide scatter of its fragments in space the process to thrown them into the Saturn s orbit, probably, can last much thousands years, that probably is the reason of longest existence of these rings and basis of formation new before invisible faint Saturn s rings. 4.2. On the origin of the retrograde moons Triton and Phoebe Other mysterious object of the outer Solar System is the retrograde moon of Neptune Triton. It is generally agreed that it is captured heavenly body. As Triton is retrograde satellite it could be captured only on opposing motion with reference to the Neptune s orbiting the Sun. Based on almost all heavenly bodies in the Solar System are orbiting in the same direction, for to have a retrograde motion Triton should be at one time to gain a head-on impulse. In view of the abovestated reasoning on negligible probability of collision of such heavenly bodies as moons of planets to other large heavenly bodies, we have assumed that Triton could gain head-on impulse 5

only in structure of the large destroyed icy planet Deposs. Considering its true spherical shape the only opportunity for Triton to preserve an intact surface at collision with other heavenly body could be its position only inside this planet in moment of its collision. The symmetric spherical shape of Triton allows assume that it could be the core of planet Deposs. One of reasons for the benefit of such assumption is the negligible surface age of Triton (Schenk et al 2007). Other basis for such assumption is the relation between Triton s the present-day density 2.061g cm -3 and above-stated mean density of Deposs 0.974 g cm -3 that equals 2.116. This value is close to 2.139 that, as we believe, is general for relation between the core density and the mean density of planets of the Solar System (at least, it is observed for terrestrial planets the Earth and Venus). Alongside with earlier known mathematical constants π (3.14159), Φ (1.61803) and e (2.71828) constant symbolized here as θ = 2.139, also is a mathematical constant, which satisfies to identity π x Φ x θ = 4 e. In this connection it is possible to specify that based on data of density of the internal and outer cores of the Earth (Anderson 1989) in whole the density of the core of the Earth ρ c is possible to estimate approximately equal to 11.91 g cm -3. The ratio of this value ρ c to the mean density of the Earth ρ o = 5.515 g cm -3 makes up 2.1595 different from θ only 1 %. As to Venus, condition ρ c = 2.139 ρ o is carried out at its core mass and radius respectively 20 % of total mass of the planet and 2755 km. These numbers agrees broadly with the present estimates of these parameters of Venus core. Use of this relation with reference to the destroyed planet Deposs gives the density of its core 2.0834 g cm -3 as primary density of Triton. Under condition of constant mass of Triton the lowering its density to present-day value 2.061 g cm -3 elapsed about 100 million years means its expansion in a diameter by 10 km. The reason for such expansion of Triton, obviously, is the action of forces of internal pressure, which, as the former core of a planet, was released from pressure on it almost all mass of planet 195 х 10 24 kg. It, apparently, explains also presence on its surface a uniform picture of cratering of a nonimpact origin, presence cantaloupe terrain on the investigated part of its surface and nitrogen ice geysers reaching heights of 8 km. Using 3-rd Kepler s law, from eq. (2) results ρ ~ R 1+b. Thus, the evolution of Triton s orbit mostly could be a consequence of the building up gas drag owing to foregoing increase its diameter induced by above-stated reduction of its density. Here, we will present a crude estimate of possible orbit evolution time of Triton. Using ratio for left and right parts of eq. (2), in view of foregoing proportion between ρ and R 1+b [if for simplicity to neglect for exponential multiplier in right part of eq. (2)], we have: (1+b) ln (R 1 /R 2 ) = ln (ρ 1 /ρ 2), (4) where ρ 1 is 2.0834 g cm -3 and ρ 2 is 2.061 g cm -3 are the initial and present-day densities of Triton, R 2 = 354,760 km its present-day semi-major axis, both R 1 its semi-major axis in a moment its capture by Neptune. Supposing, in particular, b = - 0.55 we have R 1 some 363,460 km. In view of present-day semi-major axis and foregoing elapsed time since a moment of capture of Triton 103.4 million years the orbital evolution velocity of Triton equals about 0.084 m/yr. As Neptune-Triton system s Roche limit is approximately 55,000 km it can be assumed, that some 3.57 billion years from now destruction of Triton will possible as a result of its passing within this limit. This duration agrees with a former estimate 3.6 billion years from now (Chiba et al 1989). The described origin of Triton as core of ex-planet Deposs, apparently, can explain also a record low average temperature of its surface 38 K whereas average temperature of Neptune s surface makes 72 K. 6

We do not can know the true reason for destruction of planet Deposs. It is possible only to assume that such reason became its collision with one of large comets. It can specify existence strange retrograde Saturn s moon Phoebe. Its unusual fragmentary shape, which can be seen on snapshots obtained by space mission Cassini, is not similar to other moons of Saturn, which are taking place in hydrostatic equilibrium, and is more in the nature a fragment knocked out from some heavenly body. For the benefit of this assumption the traces of comet origin found out on its surface testify. Speed of this comet likely could comprise 12.01 km s -1 as a sum of orbital speed of planet Deposs (7.674 km s -1 ) and initial speed of Triton orbited Neptune (4.336 km s -1 ). Furthermore, this allows the rotation velocity of Phoebe as some part within planet Deposs to be found (2.625 km s -1 ) as difference between foregoing speed of comet and sum of orbital speed of planet Deposs and that of Phoebe (1.711 km s -1 ). In view of mass of planet Deposs 195 x 10 24 kg the position of Phoebe as some part of this planet could be at distance 18,883 km from its center. With consideration for a possible compression as the result of the comet impact, the mean density of Phoebe 1.634 g cm -3 can be reasonably expected as intermediate that between the density of core of planet Deposs 2.0834 g cm -3 and its mean density 0.974 g cm -3. 5. Summary In this work we have tried to prove real existence of the fifth giant outer ex-planet not only in early Solar System, as was shown recently (Batigin 2011), but in rather recent epoch about 100 million years ago. Its calculated characteristics are in harmonic line with those of existing planetary objects of the outer Solar System. Based on the proved here existence in the past such icy giant planet we have offered also the new hypothesis of an origin of the some strange objects of the outer Solar System as its retained remnants. References Anderson, D. L. 1989. Theory of the Earth. Boston Blackwell Publications, 68. Batygin, K., Brown, M. E., and Betts, H. 2012. ApJ, 744, L3 Chyba, C.F., Jankowski, D.G,, & Nicholson, P.D. 1989, Astronomy & Astrophysics, 219 (1-2), L23 Hedman, M. M., Burns, J. A., Showalter, M., R., Porco, C. C., Nicholson, P. D. et al 2007, Icarus, 188 (1), 89 Rogozin, Yu. I. 2012, arxiv: 1210.3052 v1 [astro-ph. EP] Schenk, P. M., and Zanhle, K. 2007, Icarus, 192 (1), 135 7