Meeting on Asteroids and Comets in Europe Vienna, Austria, 12-14.05.2006 The stability of orbits of effective Mars Crossers Paweł Kankiewicz, Ireneusz Włodarczyk Astrophysics Division, Institute of Physics, Świętokrzyska Academy, Kielce, Poland E-mail: pawel.kankiewicz@pu.kielce.pl, ciupo@amu.edu.pl Astronomical Observatory of Chorzów Planetarium (MPC 553), Chorzów, Poland E-mail: astrobit@ka.onet.pl
The stability of Orbits of Effective Mars-Crossing Asteroids 1. Introduction: known facts about MC population, effective MC 2. Methods of calculation 3. Initial data selection 4. Dynamically interesting objects 5. Results: close approaches, resonances and stability of effective MC. 6. Conclusions
Introduction Mars Crossers (MC): asteroids satysfying the following criterion: 1.3 AU < q < 1.67 AU. Origin: Jupiter perturbations (MMR 3:1) and long-time migrations from Main Belt (timescale: 100 000 y). Possible future: the migration to NEA population (timescale: 10 mln y) due to gravitational influence of Mars. Effective Mars Crossers : asteroids approaching to Mars at a distance smaller than the Martian Hill Sphere Radius (approx. 0.0072 AU) The main aim of the project: the analysis of stability of orbits of effective MC (potentially hazardous to Mars or the future NEA reservoir).
Mars Crossers region 1000 Number of asteroids 100 10 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Perihelion distance [AU]
The e,a distribution of MC with low and high (i > 10) inclinations.
Methods of calculations In our numerical simulation of the motion of 4190 MC we used methods based on SWIFT (Duncan, Levison, Lee, 1998) and Mercury package (Chambers, 1999). Additional programs, useful for the estimation of stability and the analysis of close approaches and resonances have been written by the authors.
Initial data selection Orbital elements of 4190 MC (source: Lowell Observatory Database). Epoch: JD 2453200.5. Planetary initial ephemeris: JPL DE405/406 and DE405/WAW (Sitarski, 2002). Initial selection of effective MC was based on close approaches to Mars in the next 10 000 y. We found 655 MC approaching at d < 3 R Hill, but only 72 at d < R Hill.
Stability, predictability or trajectories and the dynamical lifetime of asteroids The Dynamical Lifetime ( T D ). The Time of Stability (TS). Lyapunov Characteristic Exponent/Indicator (LCE/LCI) and Lyapunov Time - LT.
Dynamically interesting objects 1. 1999 KN15 - the typical example of effective MC. 2. 2003 SC220 - temporary locked in MMR 1:1 with Mars. 3. 2003 SE41 - the closest approach to Mars.
1. 1999 KN15 - the typical example of effective MC In the first 5000 y in the future, the motion is dominated by 2:1 MMR with Mars (Fig a) and shows a regular, shallow encounters with this planet (Fig b). In the next 5000 y the influence of 2:1 MMR is smaller. The asteroid is in a different dynamical regime, with a smaller inclination (Fig c) and higher eccentricity (Fig d). Additionally, more frequent and deeper close approaches to Mars are present. Fig. a,b,c,d =>
1999 KN15 - the short time (10 4 y) orbital evolution
2. The Mars-crosser 2003 SC220 is temporary locked in MMR 1:1 with Mars. Frequent, regular close approaches of asteroid 2003 SC220 to Mars, are the cause of rapid changes of the semimajor axis. (Fig. a) The time of stability (TS) of this asteroid is about 9 000 years, so we can accurately predict the behavior of 2003 SC220 in this timespan (Fig. c). Fig. d shows the time evolution of the orbits of the asteroid in a reference frame which corotates with Mars. Each orbit is separated in time by 5 000 days i.e. about 137 years. After about 700 years the asteroid 2003 SC220 will become a temporary moon of Mars. A similar situation will occur after 1420 years and will be repeated regularly every 700 years. The orbital evolution of 2003 SC220: Fig. a,b,c,d => Orbital elements of 2003 SC220 (MPC, mean resid.=0.52 arc sec. from 62 resid.)
3. 2003 SE41 - the closest approach to Mars The 2003 SE41 asteroid exhibits the closest approach to Mars in our MC sample. The new orbit was determined by Sitarski from 35 observations (2003 Sep. 17-2003 Nov. 2) provided by MPC (Tab. 2). By integrating 1000 random 'clone orbits' located in the vicinity of the nominal orbit, the closest possible approach to Mars was found (Tab. 3).
The statistics of close approaches of 4190 MC to planets in the next 10 4 y
The correspondence between the frequency of encounter to Mars and LT value of 72 effective MC.
The presence of mean motion resonances for selected MC
The LT values vs semimajor axis for 45 MC in MMR and secular resonance.
Secular (nodal and apsidal) resonances in the motion of selected MC
The correspondence between the nodal/apsidal precession ratio and LT value of effective MC in secular resonances.
Conclusions The number of effective Mars Crossers is relatively low (72 objects, i.e. about 2% of observed MC population). Most of the determined Lyapunov Time values are of the order of 100 y and are in relationship with the mean approach frequency to Mars. Another source of chaoticity are MMR with Mars and SR with Saturn. SR with Mars and Earth are also present. We found the group of more chaotic MC orbit (LT < 100 y) existing in a different, more unstable dynamical regime. However, a typical effective MC has usually greater LT value than NEA. Most of orbital elements of studied MC have been determined with limited precision. In the future we expect the growth of the known effective MC population and the application of new observational results.