In Which The Earth Takes a Trip into the Kuiper Belt (and Beyond), While Hugging the Moon

Ejecting Earth

In my last post, I presented a simulation where a trespassing rogue gas planet kicks the earth into a more eccentric orbit – all without loosing the moon. Running the model again with a more massive intruder (1/30 solar masses) gave in one instance a scenario where the earth and moon were ejected from the system – still without loosing sight of each other.

This is of course more likely to happen with a more massive body: A less massive body has to come much closer in order to have a chance of significantly altering the Earth’s trajectory. But since gravitational acceleration decreases with the square of the distance, being much closer means that there’s potentially a significant difference between its pull on the moon and its pull on the earth. A more massive body can throw the system off track at a relatively larger distance, where its pull on earth and moon are effectively the same, so it will divert them in the same direction.

At the end of the simulations, 35000 steps of 8 hours each, or roughly 32 years, Earth and Moon are moving away from the inner solar system at roughly 13km/s, already having reached a distance of 78 au – beyond the Kuiper Belt, and way above the escape velocity at that distance from the sun.



The inner solar system, all time. Light blue is the trajectory of one of the brown dwarf’s satellites that gets captured in the solar system, on a highly eccentric orbit with its aphelion in the asteroid belt and its perihelion inside of Mercury’s orbit. The line for the moon all but covers earth’s line.


Before the encounter. Everyone goes their rounds in circular (almost too circular) orbits.


The year of the encounter


A larger view. We see that out of the brown dwarf’s three satellites, one is captured by the sun, one is flung away, and one holds on (although on an eccentric orbit). Neptune is also on its way to the inner solar system, would be interesting to see what it will do when it gets there.


Plot of the moon’s distances from earth. The interruption does cause it to move into a more eccentric orbit, but it stays put. The regular increases in decreases in eccentricity before the encounter are due to interferences from the sun – they’re gone when earth and moon no longer orbit the sun.


Initial parameters

In the following, the first figure is the celestial object’s mass (in kg), the tuples are initial position and direction/velocity of movement in cartesian coordinates, with the ecliptic as the x/y-plane.

Sun 1.989e+30 [ 0.  0.  0.] [ 0.  0.  0.]

asteroid0 4.95089749149e+17 [ -5.01755633e+08   4.13900315e+11  -6.13763085e+09] [-17906.06256478    -21.70683959    308.96457257]

asteroid1 1.69029085855e+19 [  3.81735451e+11   2.77179475e+11   5.30950062e+08] [ -9856.03735831  13573.87254501     25.83109118]

asteroid2 8.03257565564e+13 [ -7.87139511e+10  -4.99448700e+11  -3.41795573e+09] [ 16005.7032121   -2522.52561819    -40.93365982]

asteroid3 5.78057960759e+19 [ -1.72741157e+11  -3.39330214e+11  -1.42589424e+10] [ 16621.258058    -8461.30176685   -877.87874527]

asteroid4 2.16582378235e+16 [  2.20772858e+11  -5.41343780e+11  -1.08982259e+10] [ 13933.98694308   5682.61101281   -783.43590622]

asteroid5 2.31406635104e+18 [  1.30579921e+11   5.68705818e+11  -2.20147695e+10] [-14678.49118236   3370.31231832    826.57238042]

asteroid6 3.80011679217e+17 [ -3.68151646e+11   3.27640524e+11  -3.15091885e+09] [-10901.32027957 -12249.21434369   -688.50928195]

asteroid7 6.97315764312e+17 [ -4.28166352e+11   3.24692079e+11   1.44015286e+10] [ -9493.47476335 -12518.89629348   -435.20168064]

asteroid8 6.62865906755e+17 [  2.06547893e+11   3.09064045e+11  -1.25414664e+10] [-15706.1911349   10496.46744955   -497.64841904]

asteroid9 2.42279982172e+15 [  1.69666538e+11  -3.20331880e+11   3.62515771e+09] [ 16894.34556576   8948.23555397   -848.40541196]

MERCURY 3.3e+23 [ -4.53252251e+10   3.60282385e+10  -5.02935597e+09] [-29684.48696642 -37344.48613946   4113.71872941]

VENUS 4.87e+24 [ -6.93196489e+10   8.30784345e+10  -5.77781715e+09] [-26885.30684823 -22432.77742909   -906.56255853]

EARTH 5.97e+24 [ -1.30899317e+11   7.24260236e+10   0.00000000e+00] [-14421.4971132 -26064.7212481      0.       ]

MOON 7.3e+22 [ -1.30524601e+11   7.23420924e+10   2.86289701e+07] [-14199.11709328 -25071.89480119    -49.53431192]

MARS 6.42e+23 [ -3.19508625e+10  -2.25649180e+11   7.20560255e+09] [ 23895.08883     -3383.43218898   -241.3581778 ]

JUPITER 1.898e+27 [ -7.30279265e+11   2.70018804e+11   1.53942735e+10] [ -4528.02279263 -12246.2624954    -145.33152363]

SATURN 5.68e+26 [ -1.32668918e+12   5.42971507e+11  -4.46729609e+10] [-3643.26669469 -8901.90822451   293.88895004]

URANUS 8.68e+25 [  2.76928478e+12  -7.63097688e+11  -1.17371773e+10] [ 1805.77844812  6553.17771507   -90.76308178]

NEPTUNE 1.02e+26 [  7.03809930e+11   4.43965940e+12   2.37714689e+09] [-5364.62478456   850.44276055   170.6993041 ]

PLUTO 1.46e+22 [  5.90638813e+12  -1.18414378e+10   1.30560381e+12] [    9.30646451  4641.96936697   962.92363184]

Vagrant 6.63e+28 [ -1.30899317e+11   1.05444260e+13   0.00000000e+00] [   -99.90001676 -35000.             56.46669406]

sattelite0 1.45620602427e+24 [ -1.52225420e+11   1.05380961e+13  -5.22582082e+08] [  3894.53905259 -48457.70313461  -1302.17115787]

sattelite1 1.926310658e+24 [ -2.63442515e+11   1.06832960e+13   6.11449015e+08] [ -3566.63440722 -38308.79424261   -232.74348287]

sattelite2 1.31678894213e+21 [ -1.58944981e+11   1.06597125e+13   3.61262845e+09] [ -6032.51356199 -36443.22289817    180.71192886]


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