Transcript Preliminary analysis of the hypothetical ring system in the inner

Preliminary Analysis of a Hypothetical Ring System in the
Inner Planets: Earth and Mars Cases.
Silvia Maria Giuliatti Winter2,1
Marcos Allan Ferreira Gonçalves1,2
1
Instituto Nacional de Pesquisas Espaciais - MCT
São José dos Campos (SP)
2Grupo
de Dinâmica Orbital e Planetologia - FEG/UNESP
Guaratinguetá (SP)
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Abstract
This work analyses the evolution of a hypothetical terrestrial ring that could be
responsible for the south polar cap in the past.
In Mars case, the possible evolution of the Phobos and Deimos fragmentation
will can to become on a ring system in the future. Our results show a transitory ring
particle with ‘necessity’ of a continuous fountain of material to furnish and maintain the
ring to Earth case.
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- PLANETARY RING SYSTEM : GIANT PLANETS
-
Giant Planets: Origin and age of the rings.
- Saturn (< 108): Collisions, fragmentations and bombardments;
- Jupiter (<103): Collisions, fragmentations and bombardments;
- Uranus, Neptune: Collisions and fragmentations.
-
Inner Planets
- Three satellites.
- The satellite failure in Mercury and Venus was caused by tidal evolution
(Burns, 1973; Ward and Reid, 1973; Harris and Kaula, 1975).
- The Earth was displayed by numerous bombardments of meteors in the
past. In this way, the planet can have periods with a transitory ring system.
- Mars: a possible ring due to Phobos’ fragmentation
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Jupiter
Saturn
Uranus
Neptune
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Thickness (km)
Optical depth
Particle size
Total mass (g)
Property of the Planetary Ring System
Jupiter
Saturn
Uranus
< 30
0.01 - 0.1
0.01 - 0.1
0.1 - 2
0.1 – 2.3
1-610-6
10-3 mm
cm – 5 m
10 cm – 10 m
1011 - 1016
1021 – 1022
1018 - 1019
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Neptune
30
0.1 - 0.4
cm - m
?
EARTH :
 The Earth was exposed by numerous impacts of comets and asteroids during all its
history. In the midst of example, we can cite the meteoroid’s craters in the Arizona.
The model suggestS a stratospheric cloud of debris that could reduce extremely the
solar action (Fawcett & Boslough, 2000). One of this mechanism suggests that one
impact could have generated a ring of debris circum-equatorial
The model establish a relation of opacity scale with the B ring of Saturn,
characterizing the ring with rmin= 1.53 R (planets radius) and rmax= 1.93 R. Scaling
these dimensions to Earth’s radius gives a rmin= 9.758 km and rmax= 12.310 km. The
edges of the ring would be 3.380 km and 5.932 km above the surface. The for a total
radial ring width of about 2.500 km.
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MARS:
 The semi-major axis of Phobos is contracting due tidal effects.
 Craterization and material ejection from Phobos and Deimos surface could
form a tenuous ring around Mars.
 Preliminary we analyse a dynamical behaviour of a particle in order to
stablish stable regions where the ring can be formed in the future.
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Results :
Initial conditions of the system:
= 23.5° (Earth obliquity)
Moon : aL = 384400 km ; eL = 0.05490 and iL = 5.1454°
(Murray & Dermott, 1999)
particle test : semi-major axis ranging from 9758 km to
12310 km, eccentricity from 0 to 0.5 and the inclination was
taken to be iP = 22°
J2 = 1083.0 X 10-6
Integrator: Radau (Everhart, 1985) modified by Fiorillo (2004).
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Figure 1 – Stability region of the particles between 9758 km to
12310 km (a = 50 km) and eccentricity from 0 to 0.5 (e = 0.01).
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Figure 2.a – Position (x,y,z) of the particle in
a geocentric orbit.
Figure 2.b – Semi major axis (in km)
versus time (in yrs) (particle initially
located at aP = 11468 km)
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Figure 2.c – Variation of the Eccentricity of the
particle with I.C of eP = 0.32.
Figure 2.e – Variation of the
particle with I.C of iP = 22°.
Inclination of the
Figures 2(a-f) show the behavior of a
particle in a geocentric orbit. The set of
initial conditions (I.C) are: semi-major
axis ap = 11468 Km, eccentricity ep = 3.2
 10-1 and ip = 22.0° to the particle test
and aL = 384400 Km, ep = 5.49  10-2 e
ip = 5.1454° to the Moon.
Figura 2.d – Orbital radius (km) of the particle
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indicating the collision point (rP < rE) with theCOROT/NATAL
Earth.
Figure 2.f – Position (x,y,z) of the particle.
 Variation on orbital radius of the particle and collision with the planet after a period of
approximately 1.261 days.
 The survive to a more or less period depends on the set of the orbital elements
assumed on simulation, do not ultrapassing more than 5 years (~ 1825 days).
 Work of Galeotti et al. (2004), whose model predict the redution of the solar action on
the planet.
 Oblateness insertion on model.
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 Collision with the planet after a period of approximately 1.261
days.
 The survival of the particles depends on the set of initial orbital
elements. The particles did not survive for a period > 5years.
 In the next simulations the oblateness of the planet will be
included.
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Figure 3.a – Position (x,y,z) of the particle
on geocentric orbit.
Figure 3.b – Initial semimajor axis aP =
11468 km from particle with J2 Inclusion..
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Figure 3.c – Variation of the eccentricity of the Figure 3.e – Variation of the inclination of the
particle with I.C eP = 0.32.
particle with I.C iP = 220.
Figure 3.d – Variation of the Orbital radius (km) of
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the particle indicating the collision point COROT/NATAL
with the
Earth.
Figure 3.e – Position (x,y,z) of the
particle.
o The particle collide with the planet after a period of approximately 166
days.
o Reduction of the particle’s survival time of approximately 80 %.
o Increase on the variation of orbital radius of the particles.
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Behavior of two particles which collide with the planet in a time less then 100 days.
Figure 4.a – Initial semimajor axis aP = 11968 km Figure 4.b –Initial semimajor axis aP = 11968 km
(without J2).
(with J2).
Figure 5.a – Initial semimajor axis aP = 12468
km Figure
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20045.b – Initial semimajor axis aP = 12468 km
(without J2).
(with J2).
Possible region for a Earth ring
 We investigated a possible region where a ring around the Earth could be stable. In
this region the particle has a semi-major axis ranging between 6378 km to 100000 km
and the values of the eccentricity are taken from 0 to 0.5.
Figure 6a – The three regions between 6378 km
to 100000 km (a = 50 km) and eccentricity
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between 0 to 0.5 (e = 0.01).
Collision
Figure 6b – Collision region of the particles
between 6378 km to 100000 km (a = 50 km)
and eccentricity between 0 to 0.5 (e = 0.01).
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Escape
Figure 6c – Escape region of the particles
between 6378 km to 100000 km (a = 50 km)
and eccentricity between 0 to 0.5 (e = 0.01).
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Figure 6d – Stable region of
particles between 6378 km 
100000 km (a = 50 km)
eccentricity between 0  eP  0.5
= 0.01).
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the
aP
and
(e
Figure 6e – The regions of the particles between 45000 km
to 50000 km (a = 50 km) and eccentricity between 0 to 0.1
(e = 0.01).
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Mars System
Phobos
Semi major axis: 9378 km
Diameter: 22.2 km (27 x 21.6 x 18.8)
Mass: 1.08e16 kg.
Deimos
Semi major axis: 23459 km
Diameter: 12.6 km (15 x 12.2 x 11).
Mass: 1.8e15 kg.
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-Mars case: Two possibilities
Ejection of particles from Phobos and Deimos:
Dust particles from Phobos and Deimos could form a tenuous ring
around Mars (Ishimoto, 1996; Hamilton, 1993,1996).
The ring can be provide by this means: Phobos and Deimos are
continuously bombarded for interplanetary meteor and the particles
escape from these satellites due to their powerless gravitational field.
Phobos’ fragmentation:
Phobos is on a synchronous radius. Therefore the gravitational
force decreaces its orbit (about 1,8 m to century)
It can collide with Mars in about 50 million years (Burns, 1979).
Phobos can enter in the Roche Limit in about 14 million years.
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Some preliminary results
Figure 7.a – The regions of the particles between
2300 km to 9350 km (a = 50 km) and eccentricity
between 0 to 0.5 (e = 0.01).
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Figure 7.b – Position (x,y,z) of the
particle. Initial conditions: ap= 9350 km,
ep = 0.05 and ip = 25.19°.
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Figure 7.c – Position (x,y,z) of the particle.
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Figure 7.d – Position (x,y,z) of the particle.
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Figure 7.c – Position (x,y,z) of the particle
and Phobos’ orbit.
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DISCUSSION
 The results indicate a transitory ring which particles surviving few orbital periods
 If the Earth had one or more episodes of a transitory circum-equatorial ring, the more
probable source was the impact which originated various bolides (Schultz & Gault,
1990; Rasmussen, 1991).
 Some experimental works suggest that events of big impacts are capable to eject some
fraction of material on space which could coalesce and give size to a provisory ring
formed from debris (Ida et al., 1997; Schultz & Gault, 1990).
 In some case, a possible terrestrial ring needs a continuous source to furnish material
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Marcos Allan Ferreira Gonçalves thanks CAPES for the financial support.
Bibliografia
 Everhart, E. (1985). An efficient integrator that uses Gauss-Radau spacings. In
Dynamics of Comets: Their origin and evolution (Carusi and Valsecchi, Eds.) pp. 185202, D. Reidel, Dordrecht.
Fawcett, P. J. & Boslough, M. B. E. (2002). Climatic effects of an impact-induced
equatorial debris ring. J. of Geoph. Res. 107, ACL 2 1-18.
 Fiorillo, C. (2003). Comunicação pessoal.
 Galeotti, S., Brinkhuis, H. & Huber, M. (2004). Records of post-Cretaceous-Tertiary
boundary millenial-scale cooling from the western Tethys: A smoking gun for the
impact-winter hypothesis?. Geological Society of America. v. 32, 6, 529-532.
Ida, S., Canup, R. M. and Stewart, G. R. (1997). Lunar accretion from an impactgenerated disk. Nature 389, 353-357.
 Murray, C. D. & Dermott, S. F. (1999). Solar system dynamics. Cambridge University
Press.
 Schultz, P. H. & Gault, D. E (1990). Decapted impactors in the laboratory and on the
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2004pag. 49.
planets. Lunar and Planet. Instit. Contribution
740,
Figura 6 – Região de estabilidade das partículas
entre 9758 km  aP  12310 km (a = 50 km) e da
excentricidade entre 0  eP  0.5 (e = 0.01), para
iP = 20°.
Figura 7 – Semi eixo maior (em km) das partículas
e o tempo de sua colisão com o planeta com as
condições iniciais descritas na figura 6.
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