[meteorite-list] Orbital Evolution of Asteroid Itokawa
From: Ron Baalke <baalke_at_meteoritecentral.com>
Date: Wed Oct 26 12:44:09 2005
Orbital Evolution of Asteroid Itokawa
Japan Aerospace Exploration Agency (JAXA)
October 26, 2005
What orbit did the asteroid Itokawa follow in the past? Where will it
go? We have studied the orbital evolution of Itokawa. This study will
give some useful information, when we explain the observation results by
1. Orbit of Itokawa
The present orbit of Itokawa is shown in Fig.1. Its orbit looks like to
cross the orbits of the Earth and Mars. Actually the orbital inclination
of Itokawa is small so its orbital plane is quite near to that of the
Earth (=Ecliptic plane). Therefore, Itokawa approaches the Earth and
Mars frequently. In Fig.1, the positions of asteroids whose orbit are
determined are plotted. The asteroids plotted inside of the Mars orbit
are members of Near Earth Objects (NEO) and they may approach the Earth
closely. Itokawa is one of them.
If an asteroid is in an orbit that approach planets, its orbital
evolution becomes chaotic. This means that the negligibly small
difference in the initial condition will become very large quite soon.
There is error in the determined orbit, and by this error we cannot
predict its future orbit if the orbital evolution is chaotic. Asteroid
Itokawa is indeed in such situation.
Fig.1 Orbit of Itokawa.
The thick line is the orbit of Itokawa, and other lines are those of
Mercury, Venus, Earth, Mars, from inside to outside. The positions of
asteroids on 1 September 2005 are also plotted.
2. Orbital evolution of Itokawa
When we study orbital evolution of celestial bodies in chaotic state, it
is not enough to calculate their orbital motion simply. For example, in
the case of Itokawa, the small error in the initial condition grows very
rapidly, and after the calculation of about 200 years, the error becomes
as large as the scale of the orbit itself. In order to know the orbital
evolution for the chaotic motion, we consider many hypothesis objects
("clone"), whose initial orbits are slightly different from the nominal
orbit. Then those orbits are calculated and studied by statistical methods.
At first, we studied the orbital evolution of Itokawa in the past by
statistical methods. As the results, it is found that Itokawa possibly
existed near the present orbit at 5000 years ago.
We can estimate origin of Itokawa by using an steady state model of
orbital evolution of near earth objects. The detail things are omitted
here, but it is found that Itokawa probably came to the present orbit
from a region where a certain kind of resonance occurs or the region
where the orbit crosses Mars orbit. Thus we can say the origin of
Itokawa may be near the inner part in the asteroid belt. However, it is
difficult to know when the orbit of Itokawa became current one. The
typical time scale of such orbital change is about several million
years. Maybe we can get some clues from the observation by Hayabusa.
Next, we studied the orbital evolution of Itokawa about 100 million
years in the future, and we found that the fate of Itokawa ends most
probably by a collision with the sun or planets (Mercury, Venus, Earth,
Mars). Only in a small probability, it collides to Jupiter, or it is
thrown away farther than Saturn, or it is still alive orbiting in the
near earth region. The probability of colliding with the earth is about
once in one million years. The collision frequency of about Itokawa-size
objects (about 500m) is said to be about once in several hundred
thousand years, so the collision probability of Itokawa is rather high
as only one object.
Fig.2 shows the orbital changes of two cases ("clones"), which finally
collide to the earth. Especially for the case of long periods, the orbit
is changing very largely. This shows chaotic motion straightforwardly.
(You do not have to worry about the earth collision of Itokawa in near
Fig.2 The orbital changes of two "clones" that collide to the earth.
These figures show the orbital changes in arbitral time span for the
case of the earth collision in about 60,000 years (left) and about 13
million years (right). The orbits in blue lines are those of Mercury,
Venus, Earth, and Mars, from inner to outer.
The orbital evolution of Itokawa is as follows:
Itokawa existed in the inner part in the asteroid belt, and it was in a
certain resonant state or in the region where the orbit crosses that of
Itokawa is in an orbit that approaches the earth and Mars. The orbit
motion is strongly chaotic and we can trace its orbit only for about 200
Itokawa most probably collides to Sun or planets (Mercury, Venus, Earth,
Mars). In a small probability, it remains alive more than 100 million
years, or its orbit becomes larger than that of Jupiter. The probability
of the collision to the earth is about once in one million years.
As the summary, Itokawa has evolved to the current orbit from the inner
part of the asteroid belt, and it will collide to the sun or the planets
(Mercury, Venus, Earth, Mars). This is the typical evolution of near
earth objects. This means that the information that HAYABUSA gets from
Itokawa is important for spaceguard as well as the studies of asteroid
origin and asteroid-meteorite relationship.
Received on Wed 26 Oct 2005 12:42:44 PM PDT