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in Paper I that can describe the exact motions for the two giant planets.
Hence, a comparative run was carried out to examine this, again we ran
630 simulations for 10 Myr but with the earlier orbital elements for the two
massive planets to reproduce the previous results at the 3:1 resonance. Our
results with the earlier data show that most of the Earth-mass planets about
3:1 resonance are unstable for the investigated time, and their eccentricities
canbepumpedupto
∼
1 through resonance; besides, the inclinations are
excited to high values ranging 90
◦
-180
◦
, indicating that the orbits of the
Earth-mass planets become retrograde in the dynamical evolution and cross
those of the prograde giant planets before they terminate their dynamical
lifetimes. Thus, we may safely conclude that the stability of the terrestrial
planets depends on the initial planetary configuration.
In Fig. 3, a narrow unstable stripe appears at the 5:2 MMR at
1
.
13 AU,
although several of them can be luckily left behind, most of the Earth-size
planets are removed within 1 Myr due to the perturbation of 47 UMa b, and
in this sense it is analogous to the situation in the solar system. However,
a wider area between 3:1 and 5:2 MMR is assumed to be a qualified candi-
date habitable environment where the Earth-mass planet will not encounter
the problem of dynamical stability. This is also almost true for the region
(1.13 AU and 1.30 AU) with
e
∼
0
.
1, except several unstable islands near
7:3 MMR at 1.18 AU. The smaller eccentricity (near-circular orbits) may
not cause dramatic variations of temperature on the planet's surface, so
favoring habitability. Therefore, in a dynamical sense, if the 47 UMa sys-
tem can be adopted as a candidate target for SIM, it is also possible to
detect other Earths with stable orbits about 1 AU.
≤
2.1.4. 1
.
3
AU
≤
a
≤
1
.
6
AU
We performed 651 simulations for 10 Myr, and found the dynamical struc-
ture in this regime to be quite complicated: 14% of them can finally survive
for this time span, and 86% are lost by ejection into hyperbolic trajec-
tories, indicating the chaotic nature for these bodies. In Fig. 4, we can
notice that the 2:1 MMR region is at
1
.
31 AU and also close to the
outer edge of HZ, and the orbits with 0
.
0
<e<
0
.
10 are unstable, while
for 0
.
10
∼
0
.
20, there are stable islands where fictitious planets can
remain in bounded motions in the final system. We observe that the 2:1
resonance marks out a remarkable boundary between chaotic and regular
orbits, indicating that orbits with
a<
1
.
31 AU can have much larger surviv-
ing rates than those of
a>
1
.
31 AU. However, there are wider stable region
≤
e
≤
