Fig. 5.

Summary of the behavior of Pluto’s argument of perihelion ω over 2 Gy, as a function of the solar oblateness, J₂, in the modified restricted three-body model. In the dark red zone, ω rotates (in a retrograde sense in the small-J₂ regime, and in a prograde sense in the large-J₂ regime). In the orange zone, ω exhibits chaotic behavior with intermittent rotations and librations, and it librates steadily in the green zone. The red hatched zones indicate the fuzzy boundaries between the neighboring zones. The blue vertical line indicates the value 1,574.1 of the total effective J₂ estimated for the orbit-averaged combined quadrupolar effect of the inner three giant planets, Jupiter, Saturn, and Neptune (Table 1). Note that the horizontal scale in Upper is logarithmic from $J_2=$ 1 to 10,000, whereas, in Lower, it is linear from $J_2=$ 600 to 3,000.