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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: [email protected]
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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 Rn from serial numbers of a planet n is given by:
Rn/Ro = (n + 2)2/ Φ – 1/Φ2
(1)
where Rn, as usually, is expressed in astronomical units AU (Ro = 1AU = 149.6 x 106 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/Φ2 show up similar to the
formula of electronic orbits in Bohr atomic model: Rn ~ Rno n2, where Rno = Ro /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
Rn(calculated), AU
Rn(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
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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 Rdependence of the product of the density of planet ρ by square of its orbital speed v2, 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
Semi-major axis, Rn
(AU)
Mean orbital speed, v
(km s-1)
Mean density, ρ
(g cm-3)
Orbital pressure*, ρv2
(g cm-3) (km s-1)
Jupiter
Saturn
Uranus
Neptune
Pluto
5.2028
9.5388
19.1914
30.0611
39.4813
13.06
9.6455
6.80
5.4334
4.666
1.326
0.687
1.29
1.638
2.03
227
64.0
59.65
48.34
44.20
*Note: unit of the orbital pressure 1(g cm-3) (km s-1)2 = 109 Pa
Based on a decreasing behavior of this function F (R) =ρ v2 with increasing R the most
suitable type of approximation of this function was chosen by:
F (R) = ρv 2 = a Rbe 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
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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 RbeRc
(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 105, 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
(1024 kg)
568.319
195,068
86,810
Density
(g cm-3)
0.687
0.974
1.29
Surface gravity
(m s-2)
10.44
9.88
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 Rn = (Rn-1 + Rn+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
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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 106 km some fragments of the destroyed ex-planet could overcome approximately in a
time 103.4 х 106 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 ρc is possible to estimate approximately equal to 11.91 g cm-3. The ratio of this value ρc
to the mean density of the Earth ρo = 5.515 g cm-3 makes up 2.1595 different from θ only 1 %.
As to Venus, condition ρc = 2.139 ρo 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 1024 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 ~ R1+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 R1+b [if for simplicity to neglect
for exponential multiplier in right part of eq. (2)], we have:
(1+b) ln (R1/R2) = ln (ρ1/ρ2),
(4)
where ρ1 is 2.0834 g cm-3 and ρ2 is 2.061 g cm-3 are the initial and present-day densities of
Triton, R2 = 354,760 km its present-day semi-major axis, both R1 – its semi-major axis in a
moment its capture by Neptune. Supposing, in particular, b = - 0.55 we have R1 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.
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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 1024 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
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