The Kepler 11 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. On 2 Feb 2011 NASA announced the discovery of a multi-planet system
called Kepler 11 based on data from this mission. Details of the
discovery are in a paper by Jack Lissauer et al.
NASA Announcement:
http://www.nasa.gov/mission_pages/kepler/news/new_planetary_system.html
Lissauer's Paper:
http://arxiv.org/ftp/arxiv/papers/1102/1102.0291.pdf
The remarkable thing about this system is that the six planets are
all located within 0.5AU of the star. One would expect that the
gravitational interactions of planets so close together would make the
system unstable. However, the authors of the paper have run a model of
the system for 250 million years and it seems stable.
The integration shown above runs quite slowly as the planet's
periods are short. You can see quite a bit of movement in the orbits
but I have run this for 50,000 years without any instability
setting in. My integration uses the Yoshida 6th Order method with a variable
integration step of 1/50th of the closest collision time.
The outer planet is not subject to any danger of instability but
the inner 5 planets present an interesting study. From my integration
I plotted their eccentricity and semi-major axis at 1000-year
intervals. The eccentricities show cyclic oscillations while the
semi-major axes seem rock solid.
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