Asteroid orbits have been grouped by orbit clusters.
Orbits were integrated to +4000 and -4000 years from J2000.
Perturbations are included from Mercury, Venus, Earth, Moon, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto. (Planetary states from JPL's DE441 Ephemeris)
Additionally perturbations from 20 of the largest asteroid were included. (1, 2, 3, 4, 6, 7, 10, 15, 16, 29, 31, 52, 65, 87, 88, 107, 190, 324, 511, 704)
The integration was done in a solar system barycentric frame with relativistic forces. Calculations were done with 80 bit floating point rather then the standard 64 bit to reduce roundofff accumulation.
A least squares fit was used to find the secular and principal periodic terms;
these were then grouped into the following orbit groups.
Group names were generally taken from either the first or largest asteroid in each group except for the main belts or where established from other work.
Dot extensions to the group name indicate planet crossing orbits.
Groups will likely be modified as more asteroids are processed.
Orbits were initially computed for +3000 and -3000 years; those are slowely being replaced with the new longer integrations.
This research has made use of data and/or services provided by the International Astronomical Union's Minor Planet Center.
GROUPS
******** Mercury 1:1 a = 0.38710 ******** ******** Venus 1:1 a = 0.72333 ******** Atira: Ra < 0.983 Aten: a < 0.992 ******** Earth 1:1 a = 1.00000 ******** Earth: 0.992 < a < 1.008 Eros: 1.008 < a < 1.520 ******** Mars 1:1 a = 1.52368 ******** Mars L5: 1.385 < a < 1.665 ; 280.0 %lt L < 310.0 ******** Earth 2:1 a = 1.58740 ******** Wright: 1.528 < a < 1.779 ******** Jupiter 1:5 a = 1.77877 ******** Amor: 1.779 < a < 1.997 ; i < 16.0 Hungaria: 1.779 < a < 1.997 ; i > 16.0 ******** Jupiter 1:4 a = 2.06408 ******** ******** Earth 3:1 a = 2.08008 ******** Medusa: 1.997 < a < 2.187 ******** Jupiter 3:11 a = 2.18735 ******** Flora: 2.187 < a < 2.256 ; i < 10.5 Atlantis: 2.187 < a < 2.256 ; e > 0.29 ******** Jupiter 2:7 a = 2.25625 ******** Melpomene: 2.256 < a < 2.331 ******** Jupiter 3:10 a = 2.33085 ******** I: 2.331 < a < 2.496 ; i < 18.0 Phocaea: 2.331 < a < 2.496 ; i > 18.0 ******** Jupiter 1:3 a = 2.50045 ******** Alinda: 2.496 < a < 2.504 IIa: 2.504 < a < 2.703 ******** Jupiter 3:8 a = 2.70471 ******** Yoshitsune: 2.703 < a < 2.705 IIb: 2.705 < a < 2.824 ; i < 22.0 Pallas: 2.705 < a < 2.824 ; i > 22.0 ******** Jupiter 2:5 a = 2.82362 ******** IIIa: 2.824 < a < 2.956 ******** Jupiter 3:7 a = 2.95653 ******** IIIb: 2.956 < a < 3.029 Eos: 3.0 < a < 3.02 ; 9.0 < i < 12.0 ; e < 0.13 ******** Jupiter 4:9 a = 3.02909 ******** IIIc: 3.029 < a < 3.275 ******** Jupiter 1:2 a = 3.27652 ******** Griqua: 3.275 < a < 3.280 Cybele: 3.280 < a < 3.515 ******** Jupiter 5:9 a = 3.51494 ******** Ulla: 3.515 < a < 3.582 ******** Jupiter 4:7 a = 3.58158 ******** Helga: 3.582 < a < 3.700 ******** Jupiter 3:5 a = 3.69999 ******** Oda: 3.700 < a < 3.802 ******** Jupiter 5:8 a = 3.80207 ******** Chicago: 3.89 < a < 3.94 Hilda: 3.94 < a < 4.01 ******** Jupiter 2:3 a = 3.96922 ******** ******** Jupiter 5:7 a = 4.15605 ******** Quixote: 4.01 < a < 4.24 Thule: 4.24 < a < 4.36 ******** Jupiter 3:4 a = 4.29346 ******** ******** Jupiter 4:5 a = 4.48222 ******** ******** Jupiter 1:1 a = 5.20260 ******** Jupiter.L4: 5.0 < a < 5.4 ; 79.0 < L < 109.0 Jupiter.L5: 5.0 < a < 5.4 ; 319.0 < L < 349.0 Hidalgo: 5.4 < a < 6.0 Centaur: 6.0 < a < 19.0 ******** Saturn 1:1 a = 9.55491 ******** ******** Uranus 1:1 a = 19.21845 ******** Nessus: 19.95 < a < 29.84 ******** Neptune 1:1 a = 30.11040 ******** Kuiper: 30.4 < a ******** Pluto 1:1 a = 39.47965 ******** Plutino: 38.5 < a < 40.5
In the plots the following symbols are used:
T = Time in Julian Millennia (365250 days) relative to J2000.0 (JD 2451545.0) a = Semimajor axis Ra = Aphelion Rp = Perihelion e = Eccentricity ϖ = Longitude of Perihelion = ω+Ω i = Inclination to the ecliptic Ω = Longitude of Rising Node L = Mean Longitude measured from Perihelion dL = Deviation of L from linear fit k = e·cos(ϖ) h = e·sin(ϖ) q = sin(i/2)·cos(Ω) p = sin(i/2)·sin(Ω)
For planet relative plots the asteroid is plotted in a rotating reference frame with the planet fixed along the positive x axis.
d is the distance from the planet in AU. S(f) is a sin function for a periodic term without the phase shown.