Geoscience Reference
In-Depth Information
Fig. 2.
Case for 0.4 AU
≤ a<
1
.
0AU for 5Myr. The
e
of the orbits with 0.70 AU
<a<
0
.
78 AU can be excited and in the 2:9 MMR at
∼
0
.
76 AU,
e
can reach
∼
0
.
90.
pumped up and may reach
0
.
76 AU, indicat-
ing that there may exist a gap near this resonance. Most of the Earth-like
planets about 1:4 MMR at
∼
0
.
90 in the 2:9 MMR at
∼
0
.
82 AU move stably in bounded motions with
low-eccentricity trajectories, except for two cases where the eccentricities
eventually grow to high values. Paper II pointed out that the secular reso-
nance
b
ν
2
arising from the outer companion (similar to
ν
6
for Saturn) can
remove the test bodies. Would the
ν
2
also influence the Earth-like planets
in this system? Nevertheless, we did not find this mechanism at work at
about
∼
0
.
85 AU (see Paper II) when we examined the results, because the
terrestrial planets under study that all bear finite masses that may change
the strength of this resonance; on the other hand, the location of the secular
resonance is changed due to the orbital variation of the outer companion.
For a terrestrial planet with a mass of 10 M
⊕
, the region for
ν
2
secular
resonance is now shifted to
∼
0
.
70 AU, where two eigenfrequencies for the
terrestrial body and outer giant planet given by the Laplace-Lagrange secu-
lar theory are, respectively, 211
.
37/yr and 225
.
48/yr. This indicates that
both planets almost have the same secular apsidal precession rates in their
motion. At the new location, the
ν
2
resonance, together with the mean
motion resonance, can work at clearing up the planetesimals in the disk
∼
b
This means two bodies may bear almost the same precession frequencies in secular
orbital motion, Bois
et al.
15
suggested to use the item “apsidal synchronous precession”.