A STUDY OF THE ORBITAL DYNAMICS OF THE ASTEROID 2001 SN263.

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1 O.C.Winter,2, R.A.N.Araujo, A.F.B.A.Prado, A.Sukhanov INPE- National Institute for Space Research, São José dos Campos,Brazil. 2 Sao Paulo State University, Guaratinguetá, Brazil. Abstract: The asteroid 200SN263 was revealed in February 2008 as the first known near-earth triple asteroidal system []. Using preliminary information about the orbit and the physical composition of such asteroid [2], we have performed numerical integrations in order to study the orbital dynamics of the system, and the effects of the gravitational perturbations of the planets Mars, Earth and Jupiter on such system. We discuss the evolution of each body when only the three asteroids are considered (mutual perturbation), and the effects due to Jupiter and Mars, and also due close-approaches between the triple asteroid and the Earth. Then, we consider a system composed by seven bodies: Sun, triple asteroid system, Mars, Earth and Jupiter, in order to analyze the perturbation on the triple system of asteroids. Keywords: asteroids, triple system, 200 SN263.. INTRODUCTION In the present work we deal with the Near Earth triple asteroid system named 200SN263. Composed by 3 asteroids, here called A (central body), A 2 and A 3 (satellites). See Table for orbital and physical details of the bodies. The orbit of this system cross the orbit of Mars and approach the orbit of the Earth. It belongs to the class Amor. The goal of the work is to study the orbital dynamics of the triple system 200 SN263 and the effects of the gravitational perturbations of the planets Mars, Earth and Jupiter on such system. The methodology adopted here is the numerical integration of the N-body problems. We used the Gauss- Radau integrator [3] with time of integration of 00,000 years. Table - Physical and Orbital datas. Asteroid Orbits a e I Period Radius Mass 2 A Sun.99 UA º ~ 2.8 years.4 km A 2 A 7 km * * ~ 47 hours 0.5 km A 3 A 4 km * * ~ 46 hours 0.2 km M 3 =.5x0 kg 2 2 M 7.9x0 M 3 3 M 5.7x0 M * Not determined yet. Nolan, M.C. [4] 2 Calculated for density equal to.0 g/cm 3. Estimated to be between.3±0.6 g/cm 3 [2] 2. RESULTS The results are divided according to the dynamical system considered in the simulation and they are presented in terms of the time evolution of the orbital elements. Results from the integrations considering only the three asteroids are presented in Figures to 6. We analyze the variation of the orbital elements of the satellites A 2 and A 3 with respect to A, due to their mutual perturbation. Serra Negra, SP - ISSN

2 O.C.Winter, R.A.N.Araujo, A.F.B.A.Prado, A.Sukhanov Fig. : A 2 -Variation of about 0.9 km in the semi-major axis due to its gravitational interaction with the other bodies. Fig. 2: A 3 - Variation of about 0.02 km in the semi-major axis due to its gravitational interaction with the other bodies. Fig. 3: A 2 - Variation of about 0.06 in the eccentricity due to its gravitational interaction with the other bodies. Fig. 4: A 3 - Variation of about 0.02 in the eccentricity due to its gravitational interaction with the other bodies. In short period its possible to see a periodic variation. Fig. 5a: The argument of pericentre of A 2 is circulating, but in short period we see it librating. Fig. 5b: In long period the argument of pericentre of A 3 is circulating. In short period we see it also librating. Fig. 6: Inclination of A 2 and A 3. The mutual perturbation between the bodies causes no significant variation on their inclinations. 2 Serra Negra, SP - ISSN

3 Following we present the results from the individual perturbations due to Sun,Earth, Mars and Jupiter. The semi-major axis and the eccentricity of A, and of the satellites do not present significant variation when the Sun, or the planets Earth, Mars are separately included in the system. The inclinations of A 2 and A 3 present a variation with amplitude of about 4 degrees when the Sun is considered. The planets Earth and Mars do not change these orbital elements. The planet Jupiter causes variation in the semimajor axis, eccentricity and inclination of A (Fig.7), but it does not affect the orbits of A 2 and A 3. Fig 7 Variation in the semi-major axis, eccentricity and inclination of A due to the influence of Jupiter. Fig 8: Variation in the semi-major axis (AU) of A when the Sun and the planets Mars, Earth and Jupiter are considered. The two major jumps in semi-major axis correspond to encounters with the Earth, as shown on graphs on the right. They show the distance A -Earth. The green circle points out the closest encounters. 3 Serra Negra, SP - ISSN

4 O.C.Winter, R.A.N.Araujo, A.F.B.A.Prado, A.Sukhanov Fig. 9: Variation in the eccentricity, inclination, argument of pericentre and longitude of ascending node of the A due perturbation of Earth, Mars and Jupiter. The semi-major axis of A 2 suffers a small variation at t~3490yrs and t~3690yrs. The semi-major axis of A 2 suffers a more significant variation when t>70000yrs (see Fig.0(a)). In a appropriate scale of time, we see that there were two significant variations, at t~74380yrs and t~74900yrs (Fig.0b). Taking a look at Figure 8 we see that they correspond to moments for which close encounters with the Earth happen. The same behavior is observed on the variation of the semi-major of the A3, due to the encounters with the Earth. Fig. 0: Variation in the semi-major axis of A 2 due to the close encounter with the Earth 4 Serra Negra, SP - ISSN

5 3. CONCLUSION We conclude that for a period of 00,000 years: a) When the planets are considered separately : i) The planet Mars and Earth have no significant influence. ii) The planet Jupiter changes the orbit of A, but do not influence the orbits of the satellites A 2 and A 3. b) When we consider a system composed by the three asteroids, the Sun, and the planets Earth, Mars and Jupiter together: The planet Earth influences the system in close encounters, especially in two moments, which change the orbital elements of the satellites as shown in Table 2. REFERENCES [] Nolan, M.C. et al., Arecibo radar imaging of 200 SN263: a near-earth triple asteroid system. Asteroids, Comets, Meteors, nº 8258, [2] Becker, T. Howell, E.S., Nolan, M.C., Magri, C. Physical Modeling of Triple Near-Earth Asteroid 5359 (200 SN263). American Astronomical Society, DPS meeting #40, #28.06; Bulletin of the American Astronomical Society, Vol. 40, p.437 [3] Everhart, E. An efficient integrator that uses Gauss- Radau spacings. In Dynamics of comets: Their origin and evolution, Eds. A. Carusi Carusi and G. B. Valsecchi, D. Reidel Publishing Company (Holanda), p , 985. [4] Nolan, Presentation in the Astronomical Institute of the Academy of Science of the Czech Republic. [5] http: //ssd.jpl.nasa.gov/?orbits 5 Serra Negra, SP - ISSN