John Pazmino
 NYSkies Astronomy Inc
 2008 August 31 
    The NYSkies Seminar of 3 June 2008 highlighted asteroids. The 
theme was limited to asteroids inside of Jupiter's orbit, omitting 
those in the outer solar system. This was merely a simplicity to help 
organize the discussion. 
    As part of that session I hacked a table from Internet of asteroid 
groups. The original was incomplete. I filled in missing data from 
various websites and print references. There are still holes in the 
table, but it's fleshed out to be useful in understanding and 
discussing asteroids of the inner solar system.
    For the Earth-threat asteroids I give the perihelion 'q' or 
aphelion 'Q' as well. The dashes are data that are not applicable in 
the group definition or have yet to be narrowed in my inquiries. 
Readers are invited to fill in the missing data. 
Groups and families
    When the number of known asteroid grew large enough, it became 
evident that they bunched around certain combinations of orbital 
elements. An 'asteroid group'  is a set of asteroids sharing common 
elements. Groups were revealed several decades ago, when asteroids 
were still mere pinpoints on photographs with almost no physical 
characteristics. They were studied for their dynamical behavior under 
gravity of the planets, notably Jupiter. 
    In the late 1990s we started to examine asteroids via radar, 
spectrometry, and colorimetry. These methods gave us physical 
properties of asteroids, leading to the establishment of families. An 
'asteroid family' is a set of asteroid sharing common physical 
properties, as sussed out by their spectrum, color, and radargram. 
    Some groups later were found also to be families, so they show up 
in dialog about both categories. There could be situations where 
pieces from one larger asteroid broke off, forming a family of the 
fragments. These may continue to travel in similar orbits, forming a 
    In this article I discuss only groups, the dynamical category of 
    The orbital elements of an asteroid are unlike those of the major 
planets. Asteroids, being infinitesimally small compared with a 
planet, are disturbed easily by gravity. This disturbance shows up in 
mutable orbit elements, such that a given set turns more and more 
stale within a decade. Hence, in a planetarium program, you must 
obtain current elements to faithfully plot the path of an asteroid. 
Using old elements will plot wrong paths, however neat and pretty they 
    Asteroid elements are 
Epoch - a given date, usually in Julian Day number at even 400th days, 
for which the elements are valid. The elements are valid for the next 
few hundred days, until the next epoch. Elements from a several epochs 
ago should be tagged for only historical use. 
Mean anomaly - the angular revolution of the asteroid in its orbit 
completed at the epoch date. This is NOT the 'longitude' of the 
asteroid relative to the Sun! It's a uniform-flowing angular motion 
from which, by computation, the actual longitude is derived. It starts 
at 0 at the perihelion of the orbit and runs thru 360 degrees back at 
perihelion after one lap around the orbit. 
Semimajor axis - the mean between the perihelion and aphelion distance 
of the asteroid from the Sun. Because asteroid orbits can be strongly 
excentric, it is not wise to equate semimajor axis with a 'mean orbit 
radius' like for a major planet. 
Excentricity - the degree of ellipse in the shape of the orbit, like 
for a periodic comet. 0 is a circular orbit. 1 is a parabola, for 
which no asteroid so far qualifies. Perhaps a dead comet in a 
parabolic orbit could be called an asteroid? Asteroids have closed 
orbits, unlike most comets. Comets can have parabolic orbits, allowing 
only a single round of the Sun. Excentricities between 0 and 1 are 
ellipses, the shape for an asteroid orbit. 
Inclination - the tilt of the orbit plane relative to the Earth's 
orbit, or ecliptic. Once in a while this is stated relative to 
Jupiter's orbit or to a combined plane of all the planets. For 
statistical purposes, it doesn't matter much which inclination is 
used, as long as you know which it is and don't mix them among 
asteroids. Inclinations from 0 to 90 degrees are direct or prograde 
orbits. 90 to 180 are for retrograde asteroids, of which there are 
apparently very few. 
Longitude of ascending node - the heliocentric longitude of the south-
to-north intercept of the asteroid orbit with the Earth's orbit. The 
other intercept is the descending node, 180 degrees away. 
Argument of perihelion - The angular distance around the orbit from 
the ascending node to the perihelion point. This is measured along the 
orbit, not in the ecliptic plane. For low inclination orbits, the 
error is small. For inclinations greater than about 5 to 8 degrees, 
the error is too severe to ignore and you must use the proper 
measurement method. 
longitude of perihelion - not a usual parameter, this is the sum of 
the longitude of ascending node and argument of perihelion This 
element is used in some statistical studies but is not a  basic 
dynamical property of the asteroid. The sum is a pure arithmetic one 
along two paths, the ecliptic and then the orbit. 
Mean daily motion - Not really necessary, but handy in computations, 
it's the angular change of mean anomaly per Earth day. It can be 
calculated from the semimajor axis with Kepler's laws, so it's not 
really an independent element. Alternatively, it's 360 degrees divided 
by the orbit period in Earth days. 
Perihelion date - The date, in either decimal or in Julian Day number, 
when the asteroid passes thru the perihelion point in its orbit. This 
is often missed out for an asteroid because it repeatedly rounds 
perihelion every few years. A comet may round perihelion once, for a 
parabola orbit, or only at long intervals. At the moment of perihelion 
pass the mean anomaly is 0. 
Perihelion distance - Not an independent element because it can be 
calculated from the semimajor axis and excentricity. It is the 
distance from the Sun to the perihelion point on the orbit. 
Aphelion distance - Not an independent element because it can be 
calculated from the semimajor axis and excentricity. It is the 
distance from the Sun to the aphelion point on the orbit. 
The big three 
    Dynamical studies of asteroids involve all of the orbital 
elements. however, for many purposes, examining just three can yield 
extremely good insight to the behavior of an asteroid. These are the 
semimajor axis, inclination, and excentricity. Their symbols are 'a', 
'i', and 'e' in charts, tables, formulae. Sometimes the Greek letters 
alpha, iota, and epsilon are used for one or an other of them. 
    Asteroid groups are defined principally by these three elements, 
with the action of any others offering supplemental qualification. 
    Several parameters are interrelated, being computed from each 
other. Additional, somewhat trivial, interrelations are permutations 
of the ones here. 
Semimajor axis = ((perihelion) + (aphelion)) / (2) 
               = (perihelion) / ((1) - (excentricity)) 
Perihelion = (semimajor axis) * ((1) - (excentricity)) 
Aphelion = (semimajor axis) * ((1) + (excentricity)) 
Excentricity = (1) - ((perihelion) / (semimajor axis)) 
Osculating elements 
    The orbital elements of asteroids mutate quickly, typicly over 
decades. Osculating elements are the instantaneous values of the 
elements for a given moment. they are valid for only a short time, 
within the current lap of the orbit. It is wise to use in most 
planetarium programs the osculating elements valid for an epoch close 
to the period of simulation. 
    The files of asteroid elements available from planetarium author 
and the Minor Planet Center wwbsites are the osculating elements and 
must be replaced every couple years. 
Mean elements
    Mean elements are those elements smoothed out to simulate an 
asteroid for many decades. The are cleared of shortterm deviations 
from the planets circulating around the Sun and tugging at the 
asteroid from all directions. However, to use them properly, a true 
dynamical model of the solar system is required. It moves the asteroid 
under gravity from the planets and will yield at a given moment the 
osculating elements. 
Proper elements
    For studies of asteroids over geologic or astronomic time, a 
refined set of elements is required. They account for the longterm 
changes in the planet orbits. For the larger asteroids, the proper 
elements are close to mean elements. However, they can be quite 
different from values of the osculating elements for a given moment. 
    The intent of the proper elements is to give elements for an 
asteroid as if it was in a pure two-body dynamical situation just it 
and the Sun without the other planets. To this end they are artificial 
and do not directly relate to the current behavior of the asteroid. 
    Because there is no generally agreed method for deriving proper 
elements, sources will offer different sets. Articles in astronomy 
journals present new or alternative approaches for obtaining proper 
elements, with comparison with existing sets. 
    Proper elements can be used only by a high-powered dynamical 
model, not the level commonly run on home computers. hence, they 
should NOT be the input to a planetarium or dynamic model; the 
resulting trajectory and ephemeris will be entirely wrong. 
    Proper elements are about as good a 'book' set of elements there 
is, without having to issue now ones like for mean or osculating 
elements. Thus, they are handy for statistical analyses of asteroids 
and the detection of groups. 
    Usually only the semimajor axis, inclination, and excentricity are 
computed as proper elements. The proper elements remain constant in 
the sense that they can begin a simulation at any point of time, 
backward or forward many millions of years. They will modify into the 
osculating elements at any given moment during the simulation. 
Names of groups
    A group is named for a prototype member in that group. This may be 
the most important, best studied, brightest, largest, or first 
discovered. There is no rule for picking a prototype, the name 
settling in by general consensus among astronomers. In rare cases, the 
group name doesn't come from an actual asteroid of that name, due to 
historical quirk. 
Kirkwood gaps
    In 1874 Kirkwood discovered that there were certain distances from 
the Sun where there were no or very few asteroids. Asteroids seem to 
avoid these specific distances and bunch up away from them. It's a bit 
of amazement that he figured this out with the only 200ish asteroids 
known is his day. In fact, he recognized that certain other gaps were 
possible but there were not enough asteroids to show them up. 
    Kirkwood explained the avoided distances as those having simple 
ratios of orbital period with Jupiter, like 2/5 or 1/3. For the 1/3 
case, the asteroid period is 1/3 Jupiter year, so every third 
revolution of the asteroid finds it in conjunction with Jupiter at the 
same longitude around the Sun. Thus, every third lap, Jupiter's tug of 
gravity pulls it a bit farther away from the Sun, out of the orbit at 
the 1/3 distance. 
    This tug is cumulative, where tugs in other directions tend to net 
out over a revolution of the asteroid and Jupiter. After a few rounds, 
the asteroid is deposited in a new orbit at such distance that disrupts 
the simple ratio. The 1/3 place is in time sweeped clear of asteroids, 
forming one of the Kirkwood gaps. 
    In the table below, some groups appear to sit in or very close to 
a Kirkwood gap. However, this is misleading from just the semimajor 
axis. Semimajor axis for asteroids can be a distance from the Sun 
rarely occupied by the asteroid during its rounds. In fact, such 
asteroids 'in a Kirkwood gap' have high excentricity so they are 
carried in and out of the gap, messing up the chances of always being 
tugged by Jupiter at each conjunction. Any low excentricity asteroids 
that once were in the gap were, yes, eventually sweeped away. 
    The ratio of one planet period to that of an other creates a 
resonance situation. When the one planet is extremely small compared 
to the other, like an asteroid against a Jupiter, the little body can 
suffer badly under the resonance mechanism. 
    Resonance is cited in four[!] ways, which can be hideously 
confusing if not clearly explained. Two are based on rounds of the 
bodies's orbit and two are based on the bodies's periods. In all four 
cases, the resonance may be written as a fraction or a proportion. So, 
there are in all EIGHT ways you may see, in different articles, the 
one and same resonance case. 
    To give the resonance by laps we state the laps of the one body 
versus the laps of the other. If an asteroid makes three rounds of its 
orbit while Jupiter makes two in its own, we say the asteroid is in a 
3/2 or 3:2 resonance with Jupiter. The first number applies to the 
asteroid; the second, Jupiter. 
    Some authors bank off of Jupiter and say the asteroid is in a 2/3 
or 2:3 resonance. All four of these statements are valid, provided you 
are explicit about which you are using. 
    Similar reasoning applies to the method of periods. The asteroid, 
by comparing period of revolution, is in a 2/3, 2:3, 3/2, 3:2 
resonance with Jupiter.
    To sort out things, we have 
                    Jupiter     asteroid 
                    viewpoint   viewpoint 
                    ---------   ----------
        fraction       2/3         3/2 
        proportn       2:3         3:2 
        fraction       3/2         2/3 
        proportn       3:2         2:3 
Jupiter the sweeper 
    Jupiter, being the most massive of the planets, more than every 
other solar system body combined (except, of course, the Sun), exerts 
a strong gravity influence over a wide sector around him. Woe be to 
the comet who wanders within 2 AU of Jupiter. Asteroids are more 
resistent to Jupiter's gravity by running in more or less stable 
orbits around the Sun in the asteroid belt. The pull of Jupiter comes 
from the whole 360 degree circle around the asteroid and from varying 
distances. The pulls net out in the short term, leaving minor 
oscillations of the asteroid's orbital elements. A comet pulled by 
Jupiter has no chance to 'undo' the distortion by a future pass within 
a few months or years, so its orbit is permanently changed. There are 
exceptions for short-period comets, like Oterma and Helin-Roman-
Crockett, whose orbits are radicly altered several times by Jupiter 
within decades. 
    When asteroids are caught in a resonance situation, in or near the 
Kirkwood gaps, they can suffer major orbit distortion. On each 
occurrence of conjunction with Jupiter the asteroid suffers an 
unbalanced extra pull, both in direction and strength. The 
accumulation of these tugs draws the asteroid out of the resonant 
orbit into one where the resonance is broken, there no longer being a 
simple ratio of the two periods or laps. 
    The result is that the Kirkwood gaps are sweeped clean of 
asteroids, save for those that pass thru in severely excentric orbits 
and do not repeatedly suffer the resonant pulls. 
    Beyond 4.05 AU Jupiter's gravity is so strong that no stable 
asteroid circular or low-excentricity orbit is possible. This region 
of the solar system (plus a similar one beyond Jupiter) is devoid of 
permanent residents. Thule, the only known asteroid to inhabit this 
'forbidden zone', is in an unstable orbit that will decay within a few 
decades or a century. The asteroid will eventually drop lower into the 
main belt or be veered outward beyond Jupiter, depending on the exact 
dynamical simulation you rely on. 
Earth & Mars resonance 
    Besides Jupiter, both Earth and Mars can create resonance with 
asteroids in the inner region of the asteroid belt. These are far 
weaker than Jupiter resonances, but given enough time, they are 
effective in shifting asteroids away from certain radii from the Sun.
Earth coorbiters
    Several asteroids have orbits almost coincident with Earth's but I 
found no generally agreed name for this group. Here I call it the 
Cruithne group, after perhaps the most famous of its members. There is 
likely no danger of collision, except if the orbit is disturbed by an 
other planet, because a Cruithne asteroid never actually gets too 
close to Earth. 
    A Cruithne asteroid may start in an orbit just larger than 
Earth's, say with a period of 366.25 days versus Earth's 365.25. If we 
start with the two bodies in superior conjunction, the asteroid seems 
from Earth's eye to plod slowly thru the stars, falling behind in the 
stars by about 1 degree of heliocentric longitude per year. 
Eventually, after some 180 Earth years, the asteroid is a few million 
kilometers ahead of earth, with Earth still gaining on it. 
    Earth's gravity than pulls the asteroid back, slowing it and 
making it fall into a lower heliocentric orbit, within that of 
Earth's. The asteroid now has a period of, say, 364.25 days. It pulls 
ahead of earth, 1 degree per year, to migrate away, round the Sun to 
superior conjunction, continue round to chase Earth from behind. 
    When it gets within hailing distance of Earth, Earth's gravity 
pulls the asteroid forward, speeding it and shifting it to a slightly 
higher orbit. This has the 366.25 day orbit, and the see-saw motion 
    A solar system plot of such an asteroid resembles a C-shape toilet 
seat, with the cutout at Earth! The asteroid runs faster than Earth 
along the inner edge of the toilet seat, loops around the cutout, runs 
slower than Earth along the outer edge, loops around the opposite side 
of the cutout, and so on. Some folk, for politeness sake, call this a 
horseshoe orbit, altho it hardly looks like any shoe a respectable 
horde will kindly wear. 
    The usual solar system diagram and descriptions are really tricky 
to interpret correctly. You really should simulate a Cruithne asteroid 
with a solar system dynamics program. No, you can not use a 'trolley 
track' model, even if using current elements. The resulting path over 
even a few years will be totally wrong.
    In fact, the asteroid makes this round and back motion ONLY as 
viewed from Earth. it DOES NOT shift back and forth relative to the 
Sun. What the Sun sees is a normal prograde asteroid that indexes 
between one, faster-than-Earth, orbit and an other, slower=than=Earth, 
orbit, but always moving prograde thru the zodiac. 
    If an asteroid's orbit can graze or cross that of Earth, that 
asteroid can be a threat to Earth by collision. This is true even if 
there is a substantial inclination so the asteroid usually passes 
north or south of Earth when crossing Earth's orbit. That's because 
the inclination can be shifted by perturbations from other planets, 
including Earth itself, such that on a future round, we could suffer 
the collision.
    There are four cases of threat: Apohele, Aten, Apollo, and Amor. 
The last three are named for actual members of their groups. The 
Apohele asteroid group is named for an asteroid that was not confirmed 
after discovery. For several years, there were no other members of the 
Apohele group. By now, 2008, there are five or six members, but none 
are actually named Apohele. 
    The Apohele asteroid orbits entirely within Earth's orbit with its 
aphelion at Earth's perihelion. That is, when an Apohele is farthest 
from the Sun, it COULD meet Earth when Earth is at perihelion. The two 
orbits are tangent, altho it will be some long while before both 
bodies are simultaneously at the common point. 
    It is extremely tough to find and track an Apohele because it, in 
Earth's sky, are for the most part of their orbit in daylight or 
strong twilight. Their greatest elongation from the Sun is 90 degrees, 
at which point the asteroid is REALLY close to us. 
    They also are seen only in partial phase, no greater than half-
full. This, with the highly textures surface, makes an Apohele among 
the faintest of asteroids. 
    An Aten asteroid has a semimajor axis less than Earth's but an 
aphelion greater than Earth's. This may be hard to visualize at first: 
How can an asteroid with a smaller orbit than Earth's cross Earth's 
orbit? The trick is in the excentricity, shown by a made-up example. 
    Suppose an Aten has an SMA of 0.8 AU, against Earth's 1.0 AU. Also 
allow that its excentricity is such that the perihelion distance of 
the asteroid is 0.3 AU. Such an asteroid would have an excentricity of 
    Adding twice the SMA to the perihelion gives the aphelion, so we 
have ((2)*(0.8))+(0.3) = 1.1 AU. This example asteroid can ride 0.1 
AU, about 15 million kilometers, beyond Earth, It could strike us on 
the outward rise to aphelion or on the inward fall from there. 
    An Apollo asteroid has SMA greater than Earth's and crosses her 
orbit. This is the easy situation to visualize. The meet can be at 
either the inward or outward segment of the Apollo trajectory. 
    an Amor asteroid has SMA greater than Earth's and its perihelion 
at Earth's aphelion. The orbits are tangent  This is the inversion of 
the Apohele case, but there are a lot of members in the Amor group. 
The Earth collision can occur when an Amor rounds its perihelion. 
SMA and period
    An equivalent definition of the Earth-threat asteroids is based on 
orbital period. Since the period is a direct relation to the semimajor 
axis, the two definitions are commutable. For period in Earth year's 
and semimajor axis in AU, the two are related by 
    (period) = (semimajor axis)^(3/2) 
    (smeimajor axis) = (period)^(2/3) 
Thus the Atens and Apoheles have periods less than Earth's, less than 
one year, while the Apollos and Amors have periods more than one year. 
Parameter limits
    The range of the orbit elements defining a group differs among 
authors because they are not truly hard and sharp frontiers. The best 
agreed boundaries are those of semimajor axis. Plots of asteroids 
generally show firm delimitation between groups along SMA, making 
vertical banding in the graphs (SMA on horizontal axis).
    The borders for excentricity and inclination are more diffuse. 
Authors may take as a limit the extreme values, a value enclosing some 
greater percent of group members, a statistical average, and so on. 
    You may find else where limits for excentricity and inclination 
that appear to disagree with the ones in the table here. 
    This group of asteroids hovers near 4 AU from the Sun in strongly 
excentric orbits. Any that were in a low-excentricity orbit were 
sweeped away long ago. The Hilda asteroid survives because its orbit 
adjusted to put the aphelion far from Jupiter, where it would 
otherwise put it within a fractional AU from the planet for a certain 
    The aphelia of the Hilda group are at 60, 180, and 300 degree 
longitudinal separation around the Sun from Jupiter. The perihelia are 
at 0, 120, 240 degrees. The 0 degree perihelion is close to Jupiter 
but the asteroid is moving fast enough to get away to a safe distance 
    The Hilda group is a good example of an asteroid orbit that is 
hardly static at all. Old elements of a Hilda will produce 
utterly wrong trajectories. The entire orbit migrates in step with 
Jupiter to keep the line of apsides, joining perihelion and aphelion, 
at the stated separations from Jupiter. 
    A given Hilda has an orbit aligned to ONE of the three longitude 
displacements and that orbit slews around the Sun pacing Jupiter. 
Collectively, the Hilda group sorted itself out into the three sets of 
    The 60-degree and 300-degree aphelia of a Hilda touches the inner 
edge of the Trojans, but there is no chance of either group losing 
members to the other. A Trojan moves too quickly to drop down into a 
Hilda orbit and a Hilda moves too slowly to be caught up with the 
Trojans. The members of both groups, altho mixed together at about 4.8 
AU from the Sun, bypass each other without interaction. 
    Stricta ments the Trojan group is uniquely associated with 
Jupiter. However, the name is applied to similar dynamical groups 
attached to other planets. Only the Jupiter Trojans have members named 
for participants of the Trojan War. 
    A loose descriptions of a Trojan is that they sit 60 degrees ahead 
and behind Jupiter in the planet's orbit. These points are also 
defined as the Lagrange libration points L4 (ahead) and L5 (behind). 
    This is false in the general case because no planet has a true 
circular orbit. The definition is the equilateral triangle 
configurations of asteroid, planet, Sun, regardless of where the 
asteroid point of the triangle is relative to the orbit of the planet. 
There are two triangles, one with its asteroids lagging the planet; 
the other, leading. The L4 and L5 points are at the points of the 
    In the case of a strongly excentric planet orbit, the Trojans may 
be an unstable group because the gravity regime around them is in 
constant flux. 
    Among the planets in 2007, Jupiter, Mars, and Neptune have Trojan 
asteroids. Earth is suspected to have Trojans but none as yet have 
been found. 
Table of asteroid groups
    The table here is arranged in ascending order of semimajor axis. 
Mind well that the limits for the parameters may differ from those 
cited by other authors. 
 group    | SMA (AU) | exc   | inc   | prototype    | remarks 
 Vulanoid | Q<0.4    | N/A   | ---   | none yet     | within Mercury 
 Apohele  | <1, Q=.98| ---   | ~0    | 1998-DK36    | Earth grazer 
 Aten     | <1, Q>.98| ---   | ~0    | 2062 Aten    | Earth crosser 
 Cruithne | 1        | 0     | ~0    | 3753 Cruithne| Earth coorbiter
 Earth Tj | 1        | ~0    | ~0    | none yet     | At L4 & L5 
 Amor     |>1, q=1.02| ---   | ~0    | 1221 Amor    | Earth grazer 
 Apollo   |>1, q<1.02| ---   | ~0    | 1862 Apollo  | Earth crosser  
 Mars Tj  | 1.52     | ~0    | ~0    | 5261 Eureka  | At L4 & L5 
 Hungaria | 1.78-2   | <.18  | 16-34 | 434 Hungaria | 9:2 resonance 
 Kirkwood | 1.9      | ---   | ---   | gap          | 9:2 resonance 
 Kirkwood | 2.06     | ---   | ---   | gap          | 4:1 resonance 
 Flora    | 2.15-2.35|.03-.23|1.5-8.0| 8 Flora      | 4:9 Mars res
 Kirkwood | 2.25     | ---   | ---   | gap          | 7:2 resonance
 Phocaea  | 2.25-2.5 | >.10  | 18-32 | 25 Phocaea   | 
 Nysa     | 2.41-2.5 |.12-.21|1.5-4.3| 44 Nysa      | AKA Hertha
 Kirkwood | 2.50     | ---   | ---   | gap          | 3:1 resonance  
 Alinda   | 2.5      | .4-.65| ---   | 887 Alinda   | 1:4 Earth res
 Maria    | 2.5-2.71 | ---   | 12-17 | 170 Maria    |
 Eunomia  | 2.53-2.72|.08-.22| 11-16 | 15 Eunomia   | family?
 Adeona   | 2.66-2.69| <.18  | 0-21  | 145 Adonia   | family?
 Pallas   | 2.7-2.82 | ---   | 33-38 | 2 Pallas     | 
 Kirkwood | 2.71     | ---   | ---   | gap          | 8:3 resonance
 Dora     | 2.76-2.81| <.2   | 0-14  | 668 Dora     | family?
 Kirkwood | 2.82     | ---   | ---   | gap          | 5:2 resonance
 Koronis  | 2.83-2.91| 0-.11 | 0-3.5 | 158 Koronis  | family?
 Kirkwood | 2.95     | ---   | ---   | gap          | 7:3 resonance  
 Eos      | 2.99-3.03|.01-.13| 8-12  | 221 Eos      | family?
 Themis   | 3.08-3.24|.09-.22| 0-3   | 24 Themis    | family?
 Griqua   | 3.1-3.27 | >.35  | >20   | 1362 Griqua  |
 Hygiea   | 3.06-3.24|.09-.19|3.5-6.8| 10 Hygiea    | family?
 Kirkwood | 3.27     | ---   | ---   | gap          | 2:1 resonance
 Cybele   | 3.27-3.7 | <.3   | 0-25  | 55 Cybele    | 7:4 resonance 
 Kirkwood | 3.7      | ---   | ---   | gap          | 5:3 resonance
 Hilda    | 3.7-4.2  | >.07  | 0-20  | 153 Hilda    | 3:2 resonance  
 forbidden| 4.05-5.0 | ---   | ---   | gap          | empty
 Thule    | 4.2      | ---   | ---   | 279 Thule    | unstable 4:3 res
 Trojan   | 5.05-5.4 | ~0    | ---   | 588 Achilles | At L4 & L5