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A generalized framework for the collinear restricted four-body problem with a central dominant mass
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Journal Article
A generalized framework for the collinear restricted four-body problem with a central dominant mass
2025
Overview
This study extends the classical circular restricted three-body problem (CR3BP) by introducing a dominant central primary, forming a collinear restricted four-body problem (CR4BP) that better reflects the dynamics of real planetary systems. The model remains dynamically consistent and non-degenerate when the central mass parameter
μ
0
lies in (½, 1) and the peripheral mass
μ
satisfies 0 <
μ
< ½ (1 –
μ
0
). It generalizes to the CR3BP by setting
μ
0
= 0, recovering classical results. The system exhibits six libration points: four collinear and two symmetric non-collinear points forming an isosceles triangle with the peripheral primaries. Non-collinear points emerge via a saddle-node bifurcation at a critical
μ
=
μ
c
and as
μ
increases further within the range
μ
c
<
μ
< ½ (1 –
μ
0
), these points move away from the
x
-axis and gradually align closer to the
y
-axis, while remaining symmetric with respect to the
x
-axis. The stability analysis reveals that collinear libration points
L
1
,
L
3
and
L
4
are linearly unstable under all conditions while
L
2
is stable in the interval 0 <
μ
<
μ
*
where
μ
*
is a critical threshold for
L
2
. The non-collinear points are linearly stable within a defined interval
μ
c
<
μ
<
μ
c
1
. Finally, these results are applied to the Saturn–Janus–Epimetheus system to illustrate the model’s practical relevance.
Publisher
Nature Publishing Group UK,Nature Publishing Group,Nature Portfolio
