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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) COROT/NATAL 2004 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. COROT/NATAL 2004 - 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 COROT/NATAL 2004 Jupiter Saturn Uranus Neptune COROT/NATAL 2004 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 1-610-6 10-3 mm cm – 5 m 10 cm – 10 m 1011 - 1016 1021 – 1022 1018 - 1019 COROT/NATAL 2004 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. COROT/NATAL 2004 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. COROT/NATAL 2004 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). COROT/NATAL 2004 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). COROT/NATAL 2004 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) COROT/NATAL 2004 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 2004 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. COROT/NATAL 2004 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. COROT/NATAL 2004 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.. COROT/NATAL 2004 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 2004 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. COROT/NATAL 2004 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 COROT/NATAL 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 COROT/NATAL 2004 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). COROT/NATAL 2004 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). COROT/NATAL 2004 Figure 6d – Stable region of particles between 6378 km 100000 km (a = 50 km) eccentricity between 0 eP 0.5 = 0.01). COROT/NATAL 2004 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). COROT/NATAL 2004 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. COROT/NATAL 2004 -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. COROT/NATAL 2004 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). COROT/NATAL 2004 Figure 7.b – Position (x,y,z) of the particle. Initial conditions: ap= 9350 km, ep = 0.05 and ip = 25.19°. COROT/NATAL 2004 Figure 7.c – Position (x,y,z) of the particle. COROT/NATAL 2004 Figure 7.d – Position (x,y,z) of the particle. COROT/NATAL 2004 Figure 7.c – Position (x,y,z) of the particle and Phobos’ orbit. COROT/NATAL 2004 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 COROT/NATAL 2004 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 COROT/NATAL 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. COROT/NATAL 2004