Astron. Astrophys. 329, 1145-1151 (1998)

2. Dynamical analysis

The three observed objects have been integrated a first time with the same code used to build the First General Page of the Atlas of Dynamical Evolution of Short-Period Comets (Carusi et al., 1995). Initial orbital parameters of these objects have been derived from the Bowell (1996) catalogue of asteroid orbital data. The integration of the orbits, over a time interval of 821.4 years centered on 1996 (1585-2406), has been performed using the Everhart's routine RADAU to the 15^th order (Everhart, 1985), taking into account the gravitational influence of the Sun and all planets. All passages of minor bodies within a sphere of a given radius d around each planet have been recorded as described in Carusi and Dotto (1996) and in Carusi et al. (1985a,b).

Tables 1, 2 and 3 summarize, for each object, the results obtained by the Atlas orbital integration. These Tables contain: i) the listing of the orbital parameters at the starting point of the integration (first line) and every 50 000 days, from JD 2 300 000.5 to JD 2 600 000.5. The Epoch and the time of perihelion passage T are given, according to the Gregorian Calendar, in year, month and day. The other columns report the semi-major axis of the orbit a (in AU), its eccentricity e, the argument of perihelion , the longitude of the ascending node , the inclination i and the longitude and latitude of the perihelion (L and B). All angular elements are in degrees and their fractions, and are referred to the mean equinox and ecliptic of 2 000.0; ii) the epochs and the minimum distances of all encounters within a distance d from the planets; iii) all possible librations about mean motion resonances with the giant planets, detected by an automatic procedure among a list of 53 possible mean-motion resonances.

Table 1. Dynamical evolution over a time span of 821.4 years of (6042) 1990 WW₂ : (top) orbital parameters at the starting point of the integration (first line) and every 50 000 days, from JD 2 300 000.5 to JD 2 600 000.5; (middle) close encounters with planets; (bottom) possible librations about mean motion resonances with the giant planets.

Table 2. Dynamical evolution over a time span of 821.4 years of (6144) 1994 EQ₃ : (top) orbital parameters at the starting point of the integration (first line) and every 50 000 days, from JD 2 300 000.5 to JD 2 600 000.5; (middle) close encounters with planets; (bottom) possible librations about mean-motion resonances with the giant planets.

Table 3. Dynamical evolution over a time span of 821.4 years of 1995 QY₂ : (top) orbital parameters at the starting point of the integration (first line) and every 50 000 days, from JD 2 300 000.5 to JD 2 600 000.5; (middle) close encounters with planets; (bottom) possible librations about mean-motion resonances with the giant planets.

Figs. 1, 2 and 3 show, for each object, the obtained evolution of dynamical parameters, as in the Second General Page of the Atlas of Dynamical Evolution of Short-Period Comets (Carusi et al., 1995). Plots have the time in abscissa from 1 500 to 2 500 AD and represent: i) the energy diagram, since the ordinate is proportional to the orbital energy. A vertical arrow on the abscissa, close to the year 2 000, indicates the epoch 1.0 January 1993. On the right side some of the 53 resonance levels with Jupiter, taken into account in the search for librations, are indicated; ii) the diagram of the latitude and longitude of the perihelion (B and L); iii) the diagram of the Tisserand parameter (T) with respect to Jupiter; iv) the inclination i and the aphelion and perihelion distances diagrams (Q and q, respectively).

Fig. 1. Evolution of dynamical parameters of (6042) 1990 WW2 . For the description see the text.

Fig. 2. Evolution of dynamical parameters of (6144) 1994 EQ3 . For the description see the text.

Fig. 3. Evolution of dynamical parameters of 1995 QY2 . For the description see the text.

(6042) 1990 WW₂ has an high inclination orbit, which seems to have a typical asteroidal behavior with very small variations of the semi-major axis and of the aphelion and perihelion distances; (6144) 1994 EQ₃ is on a Jupiter-crossing orbit and, as a consequence, the semimajor axis varies chaotically due to repeated close encounters with Jupiter, while 1995 QY₂ is a Mars crosser and librates about the 15/7 resonance with Jupiter.

To investigate in more detail the dynamical evolution of the last two objects [(6144) 1994 EQ₃ and 1995 QY₂ ], we have integrated for a long-time span a sample of 15 "clone" orbits for each object. The clones were obtained by changing the last digit of the current orbital elements. The orbital integration, performed with the Everhart's routine RADAU, includes all planets.

The clones of (6144) 1994 EQ₃ have been integrated backwards for 1 yr to look for a possible connection with the Edgeworth-Kuiper Belt or with the Trojan swarms (as it will be shown below, the asteroid very probably belongs to the D-class). 3 over 15 of the analyzed clones were temporarily trapped for short intervals of time, of the order of 10 000 yr, in the 1/1 resonance with Jupiter on horseshoe orbits and one was trapped on a more stable orbit for more than 20 000 yr. Due to the high degree of chaos of the orbit, it is not possible to discriminate between the two sources only from a dynamical point of view. However, the orbital integrations show that this object could have spent in the past some time in a Jupiter's horseshoe orbit, as a significant percentage of fragments, generated in a family forming event occurred in the Trojan clouds, does.

The 15 clones of 1995 QY₂ have been integrated forwards in time for 1.2 yr. 9 over 15 of the clones show a moderate chaotic behavior and jump on different Jovian mean-motion resonances (15:7, 9:4, 11:5), while Mars crossers; some of them become also Earth crossers before the end of the integration. The growth of the eccentricity causes 6 of the clones to become Jupiter crossers, behaving like Jupiter-family comets and being ejected from the Solar System over timescale of the order of yr. From a dynamical point of view, we conclude that 1995 QY₂, classified at present as an asteroid, has a 40% chance to make a transition from asteroidal to cometary orbit over a timescale of about 3-5 yr.

© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997
helpdesk.link@springer.de