Slide sem t

1
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)

2
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.
3
- PLANETARY RING SYSTEM GIANT PLANETS
- Giant Planets Origin and age of the rings. -
Saturn (lt 108) Collisions, fragmentations and
bombardments - Jupiter (lt103) 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
4
(No Transcript)
5
(No Transcript)
6

• 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 meteoroids
  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
  Earths 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.

7

• 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.

8

• 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).

9
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).
10
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)
11
Figure 2.c Variation of the Eccentricity of the
particle with I.C of eP 0.32.
Figure 2.e Variation of the Inclination of the
particle with I.C of iP 22.
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
indicating the collision point (rP lt rE) with the
Earth.
12
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.

13

• 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 gt 5years.
• In the next simulations the oblateness of the
  planet will be included.

14
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..
15
Figure 3.c Variation of the eccentricity of the
particle with I.C eP 0.32.
Figure 3.e Variation of the inclination of the
particle with I.C iP 220.
Figure 3.d Variation of the Orbital radius (km)
of the particle indicating the collision point
with the Earth.
16
Figure 3.e Position (x,y,z) of the particle.

• The particle collide with the planet after a
  period of approximately 166 days.
• Reduction of the particles survival time of
  approximately 80 .
• Increase on the variation of orbital radius of
  the particles.

17
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
(without J2).
Figure 4.b Initial semimajor axis aP 11968 km
(with J2).
Figure 5.a Initial semimajor axis aP 12468 km
(without J2).
Figure 5.b Initial semimajor axis aP 12468 km
(with J2).
18
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 between 0
to 0.5 (?e 0.01).
19
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).
20
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).
21
Figure 6d Stable region of the particles
between 6378 km ? aP ?100000 km (?a 50 km) and
eccentricity between 0 ? eP ? 0.5 (?e 0.01).
22
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).
23
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.
24

• 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.

25
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).
26
Figure 7.b Position (x,y,z) of the particle.
Initial conditions ap 9350 km, ep 0.05 and ip
25.19.
27
Figure 7.c Position (x,y,z) of the particle.
28
Figure 7.d Position (x,y,z) of the particle.
29
Figure 7.c Position (x,y,z) of the particle and
Phobos orbit.
30

• 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

31

• 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. 185-202, 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 impact-generated 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 planets.
  Lunar and Planet. Instit. Contribution 740, pag.
  49.

32
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.