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inner and outer planets), 2 e.g., the 2:1 resonant systems: GJ 876, HD 82943
and HD 128311 (see Table 1), and hierachical systems with P 1 /P 2
5:1,
for example, HD 168443 and HD 38529. In addition, we point out that the
above mentioned planets all bear the mass of Jupiter. Due to the limita-
tion of the ground-based observation, the much smaller planets (e.g., the
terrestrial planets) cannot be detected at the present. Hence, a direct ques-
tion is that whether there exist Earth-like planets or terrestrial planets, or
other small bodies in these multi-planet systems, just as the situation in
our solar system. Because, on the base of planetary formation theory, it is
now believed that µ m-size dust grains in the planetary debris disks where
most of the gas has been dissipated, are presumably accreted to form km-
size rocks or planetesimals from physical collisions, then these planetesimals
can further grow up to larger bodies as 10 3 km-size planetary embryos by
gravity focusing, and finally form the planets.
To study the possibility of the existence of the Earth-like planets in the
multi-planet systems, we carried out a systematic numerical explorations
of the dynamical structure in several systems. However, herein we mainly
concentrate on the investigation of the 47 UMa planetary system (see also
Ref. 6), because this system is usually considered to be a close analog of
the solar system, for example, the mass ratio of the two giant companions
in 47 UMa is
2.62 (see Table 1), as compared to that of Jupiter-Saturn of
3.34; and the ratios of two orbital periods are close to each other. Several
pioneer works 7 - 10 were concentrated on the structure of the system and pre-
sented a preliminary understanding of this issue according to some earlier
solutions, 11 where the dynamical model was treated as a restricted multi-
body problem. Nevertheless, as the terrestrial planets possess significant
masses, they can interact with the two giant planets by mutual gravitation,
which may result in secular effects for the planetary system. Accordingly,
we should take into account the masses of terrestrial bodies in the model
when exploring the dynamical architecture. In this paper, we performed
extensive simulations to examine the dynamical architecture in both the
HZ and extended areas, for Earth-like planets (with masses from 0.1 M
to 10 M ) of 47 UMa with stable coplanar planetary configuration, based
on the best-fit orbital parameters given by Paper I. On the other hand, in
the extended study, we also explored such low-mass planets in the region
0 . 05 AU
a< 0 . 4 AU and we found that the secular resonance arising
from the inner giant planet can render the eccentricity excitations for the
Earth-like planets.
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