On SOHO comets
and
high inclination asteroids
E. M.
M. Pittich
Pittich and
and N.
N. A.
A. Solovaya
Solovaya
E.
Astronomical Institute, Slovak Academy of Sciences
High-inclination asteroids
• All known asteroids move in the prograde direction. Most of them have orbital inclination
less than 20◦. The largest inclination observed for an asteroids is 64◦ – asteroid 2102.
• The major asteroid survey are limited by low ecliptic latitude, which limits knowledge of
the high-inclination asteroids.
• It is possible to make assumptions about the existence of high-inclination asteroids.
Discovered SOHO comets support these assumptions.
• For the study of high-inclination asteroids we took model asteroids from main asteroid
belt, located at the boundary of the Hill stability criterion in the restricted three-body
problem.
• The initial values of the semimajor axis of the model asteroids were calculated from the
Jacobian integral for the value of the constant in the inner equilibrium point.
• The long-period evolution of orbits of the model asteroids was investigated by numerical
integration under the gravitational influence of all planets for the period of 200 k.y. The
behaviour of the osculating orbital elements is shown in following Figures for 20 k.y.
q [AU]
i [◦ ]
80
2.0
60
1.5
40
1.0
20
0.5
0.0
0
0
5000
10000
15000
t [yr]
e
rn [AU]
0.8
2.0
0.6
1.5
0.4
1.0
e
0.2
i [◦ ]
0
5000
10000
15000
t [yr]
0
5000
10000
15000
t [yr]
0.5
0.2 40 60 80
0.4 40 60 80
0.0
0.0
0
5000
10000
15000
t [yr]
Asteroids with prograde motion: e = 0.2 and 0.4 and i = 40◦, 60◦, and 60◦ .
q [AU]
i [◦ ]
170
2.0
150
1.5
130
1.0
110
0.5
0.0
90
0
5000
10000
15000
t [yr]
e
rn [AU]
0.8
2.0
0.6
1.5
0.4
1.0
e
0.2
i [◦ ]
0
5000
10000
15000
t [yr]
0
5000
10000
15000
t [yr]
0.5
0.2 100 120 140
0.4 100 120 140
0.0
0.0
0
5000
10000
15000
t [yr]
Asteroids with retrograde motion: e = 0.2 and 0.4 and i = 100◦, 120◦, and 140◦.
Sungrazing comets
• At present we know nearly two thousand sungrazing comet, most of them SOHO comets.
• Most of the SOHO comets have radius probably smaller as 100 m.
• Due to the small size, the SOHO comets are very faint objects. They are detectable only
when they become bright enough – when they are near the Sun, or close to the Earth.
• Orbits of the SOHO comets are determined imprecise due to the limited observation
period shortly before the perihelion passage. Their orbits have been calculated only in
the first approximation as parabolic ones.
• It is possible to make assumptions about their near-parabolic eccentricities. Sungrazers
discovered from the Earth with better determined orbits support these assumptions.
• The median of inclinations i of the SOHO comets with prograde orbits is about 60◦ , with
retrograde orbits about 145◦.
• The median of perihelion distances q of the SOHO comets is about 0.0055 AU.
• The equation of motion of model SOHO comets with near-parabolic eccentricities from
e = 0.9900 to e = 0.9993 and with the median values of i = 60◦ and 145◦ and q = 0.005
we numerically integrated within an interval of 200 k.y. The behaviour of the osculating
orbital elements is shown in following Figure for 20 k.y.
q [AU]
i [◦ ]
170
2.0
150
1.5
130
1.0
110
0.5
90
0.0
0
5000
10000
15000
t [yr]
0
e
rn [AU]
0.8
2.0
0.6
1.5
Mars
1.0
Earth
0.4
i = 145◦
q = 0.0055 AU
e = 0.9900, 0.9950, 0.9990,
0.9991, 0.9992, 0.9993.
0.2
5000
10000
15000
t [yr]
5000
10000
15000
t [yr]
Venus
0.5
0.0
Mercury
0.0
0
5000
10000
15000
t [yr]
0
SOHO comets with retrograde motion: i = 145◦, q = 0.055 AU, and
e = 0.9900, 0.9950, 0.9990, 0.9991, 0.9992, and 0.9993.
q [AU]
i [◦ ]
170
2.0
150
1.5
130
1.0
110
0.5
0.0
90
0
5000
10000
15000
t [yr]
e
rn [AU]
0.8
2.0
0.6
1.5
0.4
1.0
e
i [◦ ]
0.2 100 120 140
0.4 100 120 140
0.2
0.0
0
5000
i = 145◦
q = 0.0055 AU
e = 0.9900, 0.9950, 0.9990,
0.9991, 0.9992, 0.9993.
10000
15000
t [yr]
0
5000
10000
15000
t [yr]
0
5000
10000
15000
t [yr]
0.5
0.0
Asteroids and SOHO comets.
Conclusions
• Asteroids with high-inclination orbits can under the influence of the gravitational forces
of other planets, periodically changing their eccentricities and inclinations within a wide
range.
• The semimajor axes of their orbits change little, without any secular perturbations.
Because the perihelion distance is a function of the eccentricity and semi-major axis, the
perihelion distances change together with the eccentricities.
• The evolution of the orbits of the model SOHO comets is similar to the evolution of
orbits of high-inclination asteroids.
• The bodies migrate within whole region of the solar system, from the vicinity of the Sun
to the distant outer part of the solar system
• The bodies come periodically to the vicinity of the orbits of terrestrial planets, some of
them cross their orbits at nodes.
• At close encounters with the planets orbits of the bodies can change dramatically or the
bodies can be candidates for collisions.
Acknowledgements. This work was supported by the Slovak Academy of Sciences Grant
VEGA No. 2/4002/04. Authors are gratefull to the Organizing Committee of the JENAM
2004 for the grant.
References
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