Kozai Mechanism
In 1962 Yoshihide Kozai published a
paper describing how a small body, with a high orbital inclination
relative to a large body, could undergo long term variations of
eccentricity and inclination. The theory indicates that the body must
have an inclination more than 39.2 degrees. In 1979 an asteroid with
an inclination of 47 degrees was discovered and named 3040 Kozai.
3040 Kozai
In this integration I attempt to show the Kozai mechanism in
action. As it is a long term effect do not expect anything dramatic.
Watch the orbit of the asteroid (green). A rapid rate of precession is
clear quite quickly. The variation of eccentricity is less easy to
see. Use the rotate and tilt controls to try and gain an impression of
how the asteroid's orbit compares to Earth and Mars. Up to ~10000
years its orbit seems to become more circular and is all beyond Mars.
Then it starts to get more eccentric and by 30000 has become quite
eccentric passing into the region between Earth and Mars.
This integration includes Earth, Mars, Jupiter and Saturn (no orbit
drawn) and 3040 Kozai. Mercury and Venus and the outer planets are
excluded to maximise running speed as they would make little
difference to the effect. The integration step is fixed at 2 days and
the display step 1000 days. The method is Yoshida 6th order. The speed
of the integration will depend very much on the speed of your
computer. I am getting about 8000 years per minute on a 2.4Gh machine.
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