The Kepler KOI 730 System
Kepler is a NASA space mission designed to detect extrasolar
planets by measuring slight decreases in a star's magnitude as a
planet passes in front of it. A paper by Jack Lissauer et al.,
published 25 Feb 2011, includes discussions about the results of the
first 4 months of Kepler's observations. "Objects of Interest" number
730 is a system in which 4 planets have been detected, of which 2
appear to be in one-to-one resonance - i.e. in the same orbit.
Lissauer's Paper:
http://arxiv.org/ftp/arxiv/papers/1102/1102.0291.pdf
It is quite common for small objects to be in one-to-one resonance
with a planet (E.g. Jupiter's Trojan Asteroids) but in this case we have two full-size
planets, each several times the mass of Earth, in the same orbit. It
is interesting to speculate how such a configuration could survive. We must
remember that KOI objects have not yet been fully researched and we
only have approximate information about their masses and orbits. I
have set up the integration assuming circular orbits and masses based
on the mass/radius relationship used by Lissauer (Equation 1 in his
paper).
The integration shown above is running slowly and you can see how
the two planets are chasing each other around their orbits. If you
speed it up a bit you will see that the orbits begin to separate
slightly - each adopting a small amount of eccentricity. Running the
integration fast it is clearly quite shaky - but it survives. Plotting
(see below) their progress for 5000 years we see how semimajor axis
and eccentricity vibrate rapidly but do not appear to have any long
term damaging trend.
An alternative way of looking at the system is to adopt
rotating coordinates so that we can see how 703.02 and 703.03 are
moving relative to each other. This view is shown
here.
The integration is run using the Yoshida 6th Order
method, variable integration steps based on 1/40th of the shortest
collision time and including adjustment for relativity.
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