**DDA 33rd Meeting, Mt. Hood, OR, April 2002**

*Session 9. Other Solar Systems*

Tuesday, April 23, 2002, 10:50am-12:10pm
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## [9.04] Techniques for Fitting Strongly-Interacting Multiple-Planet Systems

*A.C. McDaniel (U.C Santa Cruz)*

Ongoing radial velocity surveys have revealed the existence
of multiple planet systems such as GJ876. Such systems are
proving to be both a great challenge and a great opportunity
to those who study them. Traditional independent Keplerian
fitting techniques are insufficient to model the strong
planet-planet interactions that are present in resonant
systems. We analyze the performance of a fully
self-consistent method for determining the orbital
parameters of a multi-planet system which, while
computationally challenging, breaks the M*sin(i) degeneracy
of Keplerian fitting. The code is a Levenberg-Marquardt
minimization routine which drives a Bulirsch-Stoer
integrator. Initial orbital elements are fed to the
integrator which produces a radial velocity curve that is
compared to the data. The minimization routine attempts to
find minima in the Chi-Squared space defined by the set of
all possible initial conditions.

The space that must be searched for the correct orbital
solution is very complex and is littered with false minima
and perhaps more interesting statistically equivalent, but
dynamically separate minima. This complexity is due to
several factors including the complicated coupling between
different orbital elements, the non-zero error in the data,
and possible aliasing effects due to the sampling of the
data. Given these complications, the multidimensional
minimization technique must be given a reasonably good
initial guess in order to find an acceptable solution. We
describe ways of determining initial guesses for our
algorithm that include 1) understanding the shape of the
Chi-Squared space and 2) maximizing the amount of
information extracted from the Periodogram. As the baseline
and accuracy of radial velocity surveys grow more
multi-planet systems are sure to be found. As they are, the
development of efficient, self-consistent fitting techniques
will become increasingly important in understanding the
data.

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Bulletin of the American Astronomical Society, **34**, #3

© 2002. The American Astronomical Society.