How do I calculate a gas giant's altered trajectory?

[PlutonianEmpire]

Eleven months ago, I posted a question about a rogue gas giant altering the Moon's orbit. Now I have a new question.

I have a new question about it.

Two years after this giant consumes Earth, it makes a close approach to Saturn. In Celestia, closest approach is 4,759,100 kilometers.

I've also modified the rogue a bit since the last post about it as well, and added more moons to it.

How do I determine the trajectories of both planets during and after the close approach?

Here's the new code for the planet:

Code: Select all

"Plutonium" "Sol" {
    Texture "gc_gasgt_04.jpg"
    BumpMap "gc_gasgt_04-bump.jpg"
    BumpHeight 1.16
    Radius 32584.3794
    Mass 34.667264  # 0.109 Jupiters
    Oblateness 0.02

SpecularTexture "gc_gasgt_04-spec.jpg"
    SpecularColor [ 1.00 1.00 0.75 ]
    SpecularPower 32.76

    Atmosphere {
        Height 320
        Lower [ 0.00 0.00 1.00 ]
        Upper [ 0.00 0.00 0.20 ]
        Sky [ 0.00 0.00 0.10 ]
        CloudHeight 32
        CloudSpeed 750
        CloudMap "gc_gasgt_04-clouds.png"
        Mie 0.001
        MieAssymetry -0.30
        Rayleigh [ 0.0005 0.001 0.007 ]
        MieScaleHeight 20
    }

    EllipticalOrbit
    {
    Period       1000703.800
    SemiMajorAxis  10000.000
    Eccentricity       0.999990
    Inclination        0.00325
    AscendingNode    180.000
    LongOfPericenter 121.29875
        LongitudeNode      0.000
    Epoch        2457888.5000
    }

    RotationPeriod          18.000
    Obliquity               26.000
    EquatorAscendingNode    85.3000
    RotationOffset        226.4925

    Albedo           0.430

    Rings {
        Inner   40032.60
        Outer   96771.53
        Texture "gc_rings_06.png"
    }
}