Issue |
A&A
Volume 400, Number 3, March IV 2003
|
|
---|---|---|
Page(s) | 1085 - 1094 | |
Section | Planets and planetary systems | |
DOI | https://doi.org/10.1051/0004-6361:20021811 | |
Published online | 07 March 2003 |
Stability limits in double stars
A study of inclined planetary orbits
Institute for Astronomy, University of Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria
Corresponding author: E. Pilat-Lohinger, lohinger@astro.univie.ac.at
Received:
25
July
2002
Accepted:
12
November
2002
We treat the problem of the stability of planetary orbits in double stars with
the aid of numerical studies in the model of the elliptic restricted
three–body problem. Many investigations exist for the limits of the
stability of the S-type planetary motion (i.e. the motion around one
component of the binary). In this paper we present a numerical investigation of
the so-called P-type orbits which are defined as orbits of the planet
around both primary masses. The growing interest of such stability studies
is due to the discovery of the numerous extra-solar planets, where five
of them move in double star systems.
Two different methods are used; in a first study the stability was
investigated systematically
for different initial conditions of the planet, which is regarded to be
massless. We vary
the initial starting distance from the barycenter (always with velocities
corresponding to circular orbits at the beginning), the angle to the
connecting line of the binary and the starting position of the primaries
(peri-astron and apo-astron); the primaries' masses are considered to be
equal.
The numerical stability criterion is set to the condition that during the
whole integration time (50 000 periods of the primaries) the planet should not
suffer from a close encounter to one of the primaries.
The binary's eccentricity (e) is increased form 0 to 0.5 with
, and the initial distance (
)
to the barycenter is taken of the range from 1.8 to
(for
)
or to
(for
) with
.
For the first time, we study inclined P-type orbits
(
with a step of
) for which we analyse
the border line of the stable zone.
Additionally we also record the escape times for all orbits.
In the second part of our study we apply the Fast Lyapunov Indicator (FLI)
to distinguish between the differnt types of motion, taking the same
initial
conditions, only the grid for the initial distance to the barycenter was
finer (
). Since the FLI is known to be a fast chaos indicator
we reduced the integration time to 104 periods of the primaries.
A comparison of the results of the two studies show that they are in
good agreement.
It turned out that the inclination does not influence the stability
significantly. The stability limit itself varies
between
(for
and
) and
(for
and
).
Key words: stars: binaries: general / stars: planetary systems
© ESO, 2003
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