Table of contents

 

Last updated 2009 July 1

 

ASTEROIDS (AND DWARF PLANETS) - WHERE ARE THEY ?

 

1.0       Introduction

 

Groups of asteroids can be found in many locations in the Solar System ie;

Near Earth Objects

Main Belt Asteroids

Trojans

Centaurs

Edgeworth-Kuiper Belt Objects

Scattered Disk Objects

Extended Scattered Disk Objects

 

Lists and definitions of these groups can be found on various websites eg;

Description of the System of Asteroids - Gerard Faure with English translation by Richard Miles

Minor Planet Groups/Families - Bill Gray

Lists and Plots - Minor Planet Center

Asteroid and Comet Groups - Petr Scheirich. This is an excellent site with many diagrams and animations. 

 

The XXVIth General Assembly of the International Astronomical Union was held in Prague 14th to 25th August 2006. Two resolutions were passed, but not without considerable discussion, relating to planets, asteroids and comets. The outcome of these resolutions is that the Solar System is now made up of Planets, Dwarf Planets and Small Solar System Bodies (ie; asteroids and comets). For further details see ‘New Definitions for Solar System bodies’.

 

2.0       Orbits

 

2.1       Introduction

 

This section introduces and explains the terms used to describe an orbit. If you are of a mathematical bent and want to dig in to the depths of the subject then try one or more of these books;

 

Orbital Motion by A E Roy, published by the Institute of Physics

Solar System Dynamics by C D Murray and S F Dermott, published by Cambridge University Press

Fundamentals of Celestial Mechanics by J M A Darby, published by Willman-Bell

 

2.2       Orbital Elements – a definition

 

The path followed by an asteroid round the Sun (or that of any body around another), its orbit, can be described by the following six numbers plus the date (epoch) for which they are valid;

 

Name

Symbol

MPC notation

Description

Mean anomaly

M

M

Although the true definition is a little more complicated this is essentially the current angular distance from perihelion to the present position of the asteroid measured in the direction of motion

Semi-major axis

a

a

(Half ) the length of the long axis of the ellipse

Eccentricity

e

e

A measure of the deviation of the orbit from a circle (all asteroid orbits are ellipses).e = c/a

Inclination

i

Incl

The angle between the plane of the orbit of the asteroid and the ecliptic

Longitude of the ascending node

Node

The direction in space of the line where the orbital plane intersects the plane of the ecliptic. It is measured eastwards (increasing RA) from the Vernal Equinox (First Point of Aries)

Argument of perihelion

w

Peri

Defines how the major axis of the orbit is oriented in the orbital plane and is the angle between the ascending node and the perihelion point measured in the direction of motion

Epoch

 

Epoch

The date for which the values of the above elements are valid.

 

 

The orbital elements listed in the table above are shown in the diagram below.

 

Distance of perihelion from the Sun, q = a(1-e). Distance of aphelion from the Sun, Q = a(1+e).

 

2.3       Orbital elements – an example        

 

The orbital elements for 1997 XF11, downloaded from the Minor Planet Centre are shown below.

 

---------------------------------

Minor Planet Ephemeris Service: Query Results

Below are the results of your request from the Minor Planet Center's Minor Planet Ephemeris Service. Ephemeredes are for observatory code 940.


(35396) 1997 XF11

Epoch 2002 Nov. 22.0 TT = JDT 2452600.5                 MPC
M  41.47384              (2000.0)            P               Q
n   0.56889082     Peri.  102.64552     +0.72558616     +0.68697184
a   1.4425031      Node   213.98824     -0.65582495     +0.67278524
e   0.4841203      Incl.    4.09603     -0.20837072     +0.27464471
P   1.73           H   16.9           G   0.15           U   2

 

 

---------------------------------

 

The data that would need to be entered into an application such as Megastar to enable the track of the asteroid to be plotted is shown in red above. H is the absolute magnitude (the magnitude of an asteroid if it were 1 AU from both the Sun and the Earth) and G is the slope parameter (the slope of the graph of magnitude vs Solar Phase angle).         

 

Orbit diagrams (and other relevant data) can be viewed on the JPL Orbit Diagrams page. Once the orbit diagram is displayed it can be run forward or backwards, zoomed in and out and the viewpoint altered from edge-on to above. An example of such a diagram for 1997 XF11 is shown below with additional explanatory data added.

 

Referring to the diagram and table above and the orbital elements downloaded from the MPC;

 

Epoch

Date shown at bottom right corner of diagram

Mean anomaly (M)

Angle FSM

Semi-major axis (a)

Half the distance PSA (approximately the same as that for Mars)

Eccentricity (e)

((AP/2)-SP)/(AP/2)) or c/a in the diagram above

 

Looking at the diagram one can see that the major axis, AP, of the orbit of 1997 XF11 approximates to that of Mars (3.0 AU) and the perihelion distance, SP, to the radius of the orbit if Venus (0.7 AU). The inclination of the orbit of 1997 XF11 is small and can be ignored for this approximation. Therefore e (approx) = ((3.0/2 – 0.7)/(3.0/2)) = 0.5. Fairly close to the actual value of 0.48.

 

Argument of perihelion (Peri)

Angle NSP

Longitude of the ascending node (Node)

Angle FSN

Inclination (Incl)

To see this visit the JPL Orbit diagram page, call up the orbit for 1997 XF11 and adjust the view to ‘edge-on’ using the slider on the right side of the diagram. The position of the nodes can also be ascertained.

 

2.4          Orbit determination

 

As soon as it becomes possible the Minor Planet Centre will compute the orbital elements for newly discovered asteroids. These can be obtained by accessing the Minor Planet Ephemeris Service and an example is shown in section 3.0 above. However if you want to have a crack at this for yourself then Project Pluto, the producers of Guide, have provided a program, Find_Orb, for just this purpose.

 

How to use the software is described fully on the Project Pluto website however I will just mention how to use your own observations (thanks to Matt Dawson). A file of simulated observations, EXAMPLE.TXT, is provided with Find_Orb and is located in the Guide directory (after downloading and unzipping). Part of  the file is shown below;

 

    

J97Z99Z  C1997 04 21.12432 13 56 34.48 -09 11 06.7          13.5 V      413

J97Z99Z  C1997 04 21.16887 13 56 49.70 -09 11 08.1          13.5 V      413

J97Z99Z  C1997 04 21.21342 13 57 03.97 -09 11 16.6                      413

J97Z99Z  C1997 04 21.25797 13 57 16.44 -09 11 31.6                      413

J97Z99Z  C1997 04 21.30252 13 57 26.35 -09 11 51.4          13.4 V      413

J97Z99Z  C1997 04 21.34707 13 57 33.13 -09 12 14.3                      413

J96X01X  C1997 10 12.78968 00 39 05.00 +04 02 04.4          17.2        709

J96X01X  C1997 10 13.13317 00 38 36.63 +03 59 03.6          17.4        709

J96X01X  C1997 10 14.16365 00 37 10.15 +03 49 57.0                      709

       J96X01X  C1997 10 14.85064 00 36 12.34 +03 43 50.6                      709

       J96X01X  C1997 10 15.53762 00 35 13.77 +03 37 44.6          17.1        709

       J96X01X  C1997 10 16.91160 00 33 19.02 +03 25 30.9                      691

    

 

This is in the same format as that used to send ones observations to the MPC. To allow Find_Orb to access such observations simply copy them from your own file, in this case observations of 2002 NY40, and paste them in to EXAMPLE.TXT and then that file will look like;

 

        K02N40Y  C2002 08 12.99076 21 29 04.60 -03 07 29.0          14.4 V      940

         K02N40Y  C2002 08 12.99278 21 29 04.33 -03 07 26.0          14.4 V      940

         K02N40Y  C2002 08 12.99485 21 29 04.05 -03 07 22.9          14.4 V      940

         K02N40Y  C2002 08 12.99678 21 29 03.76 -03 07 19.9          14.5 V      940

         K02N40Y  C2002 08 12.99934 21 29 03.43 -03 07 16.0          14.4 V      940

         K02N40Y  C2002 08 13.00131 21 29 03.14 -03 07 12.8          14.5 V      940

         J97Z99Z  C1997 04 21.12432 13 56 34.48 -09 11 06.7          13.5 V      413

         J97Z99Z  C1997 04 21.16887 13 56 49.70 -09 11 08.1          13.5 V      413

         J97Z99Z  C1997 04 21.21342 13 57 03.97 -09 11 16.6                      413

         J97Z99Z  C1997 04 21.25797 13 57 16.44 -09 11 31.6                      413

         J97Z99Z  C1997 04 21.30252 13 57 26.35 -09 11 51.4          13.4 V      413

         J97Z99Z  C1997 04 21.34707 13 57 33.13 -09 12 14.3                      413

         J96X01X  C1997 10 12.78968 00 39 05.00 +04 02 04.4          17.2        709

         J96X01X  C1997 10 13.13317 00 38 36.63 +03 59 03.6          17.4        709

         J96X01X  C1997 10 14.16365 00 37 10.15 +03 49 57.0                      709

         J96X01X  C1997 10 14.85064 00 36 12.34 +03 43 50.6                      709

         J96X01X  C1997 10 15.53762 00 35 13.77 +03 37 44.6          17.1        709

         J96X01X  C1997 10 16.91160 00 33 19.02 +03 25 30.9                      691

 

On starting up Find_Orb and clicking on the Open button 2002NY40 (K02N40Y) will be listed along with the objects originally stored in the EXAMPLE file. To calculate the orbital elements and an ephemeris follow the instructions as mentioned above.

 

2.5          Resonances

 

Asteroid orbits are affected by the gravitational interaction of asteroids with planets most notably with the gas giants. This interaction, or mean motion resonance, is most obvious where the orbital periods of asteroid and planet are whole number ratios eg; 1:1, 2:1 and 3:2. Beyond 3.5 AU from the Sun resonances work to contain asteroids within the resonant orbits rather than eject them as is the case with the Kirkwood Gaps in the Main Belt. The reason for this is not fully understood.

 

Mean Motion Resonances are described in detail in  Tabare Gallardo’s website - Atlas of Mean Motion Resonances

 

2.6          Data sources

 

Orbital elements, data and orbit diagrams for specific asteroids can be obtained from several websites ie;

JPL Near Earth Object Program – Orbit Diagrams

Minor Planet Center Comet and Ephemeris Service

Near Earth Objects Dynamics (NEODyS) – Object List

Asteroids Dynamics (AstDys) – Object List

UK NEO Information Centre – Close Approaches

European Asteroid Research Node – The Near Earth Asteroids Database

 

3.0          Asteroid Groups

 

3.1          Near Earth Asteroids

 

Near Earth Asteroids fall in to three classes, Atens, Apollos and Amors, named after the first asteroid to be discovered in each of those classes ie;

 

2062, Aten, 1976 AA

Discovered on 7th January 1976 by E. F. Helin at Palomar and named after the Egyptian Sun god.

 

1862, Apollo, 1932 HA

Discovered on 24th April 1932 by K. Reinmuth at Heidelberg. Named after the god of the Sun, child of Zeus and Leto.

 

1221 Amor, 1932 EA1

Discovered on 12th March 1932 by E. Delporte at Uccle. Amor is the Latin name for the Greek Eros, the god of love.

 

3.1.1               Atens

 

Atens have a semi-major axis smaller than that of Earth (1 AU) and a aphelion distance of >0.9833 AU. The significance of these numbers is that at perihelion the Earth is 0.9833 AU from the Sun and at aphelion, 1.0167 AU. As can be seen from the diagram below (eccentricities exaggerated) Atens spend most of their time within the orbit of the Earth but can pass outside it.

 

 

There is a sub-set of Atens known as Inner Earth Objects (IEO’s) or Apoheles. All of the orbit of an IEO lies within that of the Earth and this makes them extremely difficult to detect. So not only must an IEO have a semi-major axis smaller than that of the Earth but both its aphelion (Q) and perihelion (q) distances must be less then the Earth’s perihelion distance (0.9833) as in the diagram below. However if the long axis of the orbits of the IEO and the Earth were to line up as shown in the diagram below the aphelion distance could be greater than 0.9833 but less than 1.0167 au.

 

Three IEO’s have been discovered to date (20th  December 2004); 2002 JX8, 2003CP20 and 2004 JG6. 1998 DK36 and 2005 G31 may also be IEO’s.

 

Arjunas are asteroids with Earth-like orbits ie; low eccentricity, low inclination and a semi-major axis close to 1 AU.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


3.1.2               Apollos  

 

Apollos have a semi-major axis greater than that of Earth (1 AU) and a perihelion distance of <1.0167 AU. As can be seen from the diagram below Apollos spend most of their time outside the orbit of the Earth but can pass inside it.

 

 

3.1.3       Amors

 

Amor orbits lie between Mars and Earth (a>1.0 AU, 1.017<q<1.3) and are therefore Earth-approaching rather than Earth-crossing asteroids as are Atens and Apollos.

 

 

3.2          Mars crossers

 

This definition is courtesy of the MPML and Dr Alan Harris.

 

Asteroids which cross only the orbit of Mars have a quite long collision lifetime (of the order of the age of the solar system), whereas those that actually cross the Earth's orbit have much shorter collision lifetimes, and also the time scales for major orbit modification (due to clse passes by the planets) are also much different. Thus on dynamical grounds it is important to distinguish between asteroids that cross only the orbit of Mars from those that cross the orbits of Earth and/or Venus. Therefore, in common usage, we usually do not include Amors (q < 1.3) or Apollos and Atens (which actually do cross the Earth's orbit, in two dimensions) as "Mars crossers", although most do actually cross the orbit of Mars as well. So in practical terms, objects that would be referred to as "Mars-crossers" would be those with 1.300 < q < 1.665. The dividing line between Mars-crossers and Amors is also arbitrary. The Amors don't become dynamically active members of the "Earth-crossing population"
until around q < 1.1.

Gérard Faure’s ‘Description of the system of asteroids as of May 20 2004’ lists 638 numbered out of a total of 3387. A paper on the subject ‘The Population of Mars-crossers – Classification and Dynamical Evolution’ can be viewed here

 

The first Mars-crosser to be so identified was 132 Aethra. It was discovered by James Craig Watson in 1873.

 

 

 

3.3          Main Belt Asteroids

 

3.3.1       Location

 

The Main Belt of asteroids lies between Mars and Jupiter and stretches from approximately 2.0 AU to 3.3 AU from the Sun. The first asteroid, and first Main Belt asteroid, to be discovered was 1 Ceres in 1801.

 

 

3.3.2       Gaps

 

Within the Main Belt there are gaps, where few asteroids are found, corresponding to various orbital period ratios with Jupiter ie; 4:1, 3:1, 5:2 and 2:1. The explanation for these was first given by Daniel Kirkwood hence they are known as Kirkwood Gaps.

 

The population of asteroids in the 2:1 mean motion resonance with Jupiter is described in a paper by Broz, Vokroughlicky, Roig, Nesvorny, Bottke and Morbidelli. Asteroids in this region are classified as unstable, marginally stable (Griquas such as 1999 VU218) or stable (Zhongguos such as 2003 AK88). The stable asteroids are those with a dynamical lifetime (ie; they stay where they are) of the order of the age of the Solar System, the marginally stable ones, several hundreds of millions of years and the unstable variety around 10 million years. The paper suggests that the loss of the unstable asteroids from the region is balanced by an inflow due to the Yarkovsky effect on asteroids outside the resonance zone. If you really want to know more about the Yarkovsky effect than my be good for your health then try here.

 

3.3.3       Groups

 

Groups of asteroids within the Main Belt have similar orbital elements. Such groups are often referred to as Hirayama families named after K. Hirayama who first noticed this in 1918. Each family may have originated from a single larger asteroid which was broken up by a collision in the distant past. A diagram of many of the groups can be seen here.

 

3.4          Trojans

 

Trojan asteroids occupy the same orbit as their parent planet but are located around the Lagrangian L4 and L5 points, as shown in the diagram below. The vast majority of Trojan asteroids are associated with Jupiter but Neptune also has a small number. The first Trojan, 588 Achilles (1906 TG), was discovered in 1906. In August 2006 the Minor Planet Center listed 2051 Jupiter and 4 Neptune Trojans (these links will take you to the latest listings).

 

 

The Trojans oscillate or librate around the Lagrangian points as shown in this animation.

 

3.5          Centaurs

 

Centaurs occupy the region of the Solar System between Jupiter and Neptune having semi-major axis between 5.5 and 29 AU. At times they behave like comets being surrounded by a small coma of gas and at others like a common or garden asteroid - completely inert. Due to their large size (100's of kilometers in diameter) and location they do pose a threat to life on Earth. They are subject to the gravitational influence of the giant planets and could have their orbits changed to such an extent that they are flung in to the inner Solar System (or, if we are lucky, out !). The orbit of the first Centaur to be discovered, 2060 Chiron in 1977, is shown in the diagram below.

 

 

A list of Centaurs can be found here and a diagram including them is shown here.

 

3.6          Edgeworth-Kuiper Belt Objects (EKBO's)

 

These objects (also known as Trans Neptunian Objects or TNO's) can be sub-divided into;

- Plutinos

- Classical EKBO's

- Scattered Disk Objects (SDO's)

- Extended SDO's

 

A diagram of the Solar System showing several different types of EKBO's can be seen here. Dave Jewitt's Kuiper belt web page is well worth a visit.

 

Plutinos are objects which have similar orbits to that of Pluto in that they have a semi-major axis between 39 and 40 AU, a perihelion distance (q) less than or equal to that of Neptune and are in a 3:2 resonance with that planet. The first such object discovered, except for Pluto itself, was 1993 RO.

 

Classical EKBO's have semi-major axis between 42 and 48 AU's and are sometimes referred to as Cubewanos, the first such object discovered being 1992 QB1 (15760). They occupy various resonances with Neptune ie; 5:3, 7:4 and 2:1.

 

SDO's , or Scattered Kuiper Belt Objects, are asteroids in highly eccentric orbits with semi major axis greater than 48 AU. 1996 TL66 (15874) was the first of these to be discovered. For more detail and interesting diagrams see here.

 

Extended SDO's, also known as Inner Oort Cloud or Scattered Extended Objects, of which 2003 VB12, 90377 Sedna was the first discovered, exist at great distances from the Sun and move in highly eccentric orbits.

 

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