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

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

1

INPE- National Institute for Space Research, São José dos Campos,Brazil.

2

Sao Paulo State University, Guaratinguetá, Brazil.

Abstract: The asteroid 2001SN263 was revealed in February 2008 as the first known near-Earth triple asteroidal system [1]. 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, 2001 SN263.

1. INTRODUCTION

In the present work we deal with the Near Earth triple asteroid system named 2001SN263. Composed by 3 asteroids, here called A1 (central body), A2 and A3 (satellites). See Table 1 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 2001 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 100,000 years.

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 1 to 6. We analyze the variation of the orbital elements of the satellites A₂ and A₃ with respect to A1, due to their mutual perturbation. Table 1- Physical and Orbital datas.

Asteroid Orbits a1 e1 I1 Period1 Radius1 Mass2

A1 Sun 1.99 UA 0.478 6.69º ~ 2.8 years 1.4 km M₁=1.15x10 kg13

A2 A1 17 km * * ~ 147 hours 0.5 km M2 ≈7.9x10−2M1

A3 A1 4 km * * ~ 46 hours 0.2 km M3 ≈5.7x10−3M1

* Not determined yet. 1

Nolan, M.C. [4] 2

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

O.C.Winter, R.A.N.Araujo, A.F.B.A.Prado, A.Sukhanov

Fig. 2: A3- Variation of about 0.02 km in the semi-major axis due to its gravitational interaction with the other bodies.

Fig. 1: A2 -Variation of about 0.9 km in the semi-major axis due to its gravitational interaction with the other bodies.

Fig. 5a: The argument of pericentre of A2 is circulating, but in short period we see it librating.

Fig. 5b: In long period the argument of pericentre of A3 is circulating. In short period we see it also librating.

Fig. 4: A3 - 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. 3: A2 - Variation of about 0.06 in the eccentricity due to its gravitational interaction with the other bodies.

Fig. 6: Inclination of A2 and A3. The mutual perturbation between the bodies causes no significant variation on their inclinations.

Following we present the results from the individual perturbations due to Sun ,Earth, Mars and Jupiter. The semi-major axis and the eccentricity of A1, 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 A2 and A3 present a variation with amplitude of about 14 degrees when the Sun is considered. The planets Earth and Mars do not change these orbital elements. The planet Jupiter causes variation in the semi-major axis, eccentricity and inclination of A1 (Fig.7), but it does not affect the orbits of A2 and A3.

Fig 7 – Variation in the semi-major axis, eccentricity and inclination of A1 due to the influence of Jupiter.

Fig 8: Variation in the semi-major axis (AU) of A1 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 A1-Earth. The green circle points out the closest encounters.

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

O.C.Winter, R.A.N.Araujo, A.F.B.A.Prado, A.Sukhanov

The semi-major axis of A2 suffers a small variation at t~31490yrs and t~36190yrs. The semi-major axis of A2 suffers a more significant variation when t>70000yrs (see Fig.10(a)). In a appropriate scale of time, we see that there were two significant variations, at t~74380yrs and t~74900yrs (Fig.10b). 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. 9: Variation in the eccentricity, inclination, argument of pericentre and longitude of ascending node of the A1 due perturbation of Earth, Mars and Jupiter.

3. CONCLUSION

We conclude that for a period of 100,000 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 A1, but do not influence the orbits of the satellites A2and A3

.

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

[1] Nolan, M.C. et al., Arecibo radar imaging of 2001 SN263: a near-earth triple asteroid system. Asteroids, Comets, Meteors, nº 8258, 2008.

[2] Becker, T. Howell, E.S., Nolan, M.C., Magri, C. Physical Modeling of Triple Near-Earth Asteroid 153591 (2001 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. 185-202, 1985. [4] Nolan, Presentation in the Astronomical Institute of the Academy of Science of the Czech Republic. http://www.asu.cas.cz/~asteroid/paris/add-ons.html.