Asteroids in the surroundings of 5:2 resonance

8 real asteroids and their 32 close clones (da = 10-7 AU), orbital elements from the Bowell's astorb.dat, planetary ephemeris DE405 (4 outer planets only), without Yarkovsky, numerical integration upto 500 Myr with dt = 36 days
  • (9631) - the first fall of a clone into the 5:2 after 50 Myr
  • (9990) - stays ABOVE the "chaotic zone" for more than 200 Myr
  • 1988 DX1, 1989 TT3 - initially inside the 5:2 resonance
  • 1988 RY5, 1996 TE - initially in the chaotic zone, median lifetime \approx 101 Myr
  • 1992 DH3 - mean elements below the resonance
  • 1992 RF5 - stays for 100 Myr BELOW the chaotic zone and above the 5:2 resonance

  • images of individual particles, detail of first 67 Myr (a(t) graph)
(9631)
(9990)
1988 DX1
1988 RY5
1996 TE
1989 TT3
1992 DH3
1992 RF5

Run 2953-8b - the same initial conditions as in the previous case 2953-8a, but with Yarkovsky switched on. We are assuming regolith covered bodies with obliquity \approx 135°, asteroids' radii are estimated from their absolute magnitudes and expected albedos 0.12 (except for 1993 TE, where A = 0.2)

The lifetimes before the fall into the 5:2 resonance (see tab. 1) are 10× shorter, especially for asteroids initially placed outside the strongly chaotic region. Notice that time scale on x-axis is only 100 Myr (shorter than in the previous figure).

The analysis of both runs are presented in following tables. One could see median lifetimes of asteroids (everyone has got 4 close clones) in tab. 1. If any asteroid or its clone stayed outside the 5:2 resonance for the whole time span of integration, it is noticed in the column "limit".

2953-8a 2953-8b
median interval limit
(9631) 268445>500 30 26
(9990) 395302>500 22 13
1988 DX1 0.20 0.26 0.20 0.13
1988 RY5 47344 11 72
1996 TE 14 91 22 61
1989 TT3 0.09 0.02 0.09 0.02
1992 DH3 239443>500100 0>100
1992 RF5 116212 11 10

Tab. 1 - Lifetime medians and difference of extreme values, comparison between runs 2953-8a and 2953-8b.

"Proper" orbital elements are presented in tab. 2 - mean elements are averaged over first 5 Myr and group of 5 asteroids (except one clone of 1989 TT3, which was rejected from the integration just before t = 5 Myr). Asteroids initially placed inside the 5:2 resonance (ie. 1988 DX1 and 1989 TT3) have high averaged eccetricities. Additionaly, asteroids orbiting in the strongly chaotic region (1998 RY5, 1996 TE) have higher differences between proper elements of individual clones (da > 5×10-4 AU).

a [AU] e [] i [°] da [AU]
(9631) 2.82730 0.0502 2.4806 2.4e-07
(9990) 2.82959 0.0662 2.4250 2.6e-06
1988 DX1 2.82475 0.5185 11.2328 4.1e-03
1988 RY5 2.82825 0.0600 2.6025 5.5e-04
1996 TE 2.82617 0.0635 2.4120 7.0e-03
1989 TT3 2.82422 0.4497 2.5528 2.5e-03
1992 DH3 2.81215 0.1992 7.6540 1.4e-04
1992 RF5 2.82671 0.0432 2.4715 1.1e-04

Tab. 2 - Averaged (proper) elements - first 5 Myr, 5 clones each. See orbital elements of individual particles.
Another 7 real asteroids from the Bowell's astorb.dat in this region (only sufficently precise orbits with CEU < 1 were selected), 28 close clones (da = 10-7 AU), numerical integration spanning 47 Myr (planned upto 100 Myr) with dt = 36 days
  • (8279), (8361), (10907), (12893), (12936) - initially ABOVE the chaotic zone, stable orbits
  • (6814), 2000 GQ6 - initially in the chaotic zone, median lifetime > ~50 Myr
(6814)
(8279)
(8361)
(10907)
(12893)
(12936)
2000 GQ6

Miroslav Broz, miroslav.broz@email.cz, Jun 7th 2000