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.
A rogue supermassive gas giant throws earth on a highly eccentric orbit. The moon is decidedly unimpressed.
We may not always admit it, but breaking things is fun. But breaking things can also be hard, when those things are massive balls of roughly 6 * 10^24kg of iron and silicates making rounds around even more massive balls of 2 * 10^30gk of plasma. And some things just shouldn’t be destroyed if we want to live on…
Anyways, I wrote a little script suite to try and virtually destroy the Earth nonetheless. What it does is throw a little brown dwarf or large rogue planet (0.01 solar masses, e.g. more than 10 jupiters) at the inner solar system, at a relative velocity of 35 km/s. You’d think that this is the end of the world (and it may well be the end for us if the rogue planet throws a large asteroid at us on its way out — I didn’t really model a lot of asteroids for computation time reasons), but most of the time the result is decidedly boring: If the rogue planet has moons/satellites, it may lose those — but even that doesn’t happen all of the time. If it passes very close to one of the inner planets, it might throw them on very eccentric orbits. In no single iteration — and I’ve run a few during debugging and since, creating 9GB of simulated data by now — does any of our planets get ejected.
The worst that happens is what’s depicted above: On its way out, our rogue planet comes close to earth and throws it on a highly eccentric orbit, so much so that it crosses Venus’ orbit once a year. But even then, the moon keeps hugging the earth. It does get thrown on a slightly more eccentric orbit, but one that’s on average even closer to earth than it used to be. (Left: moon-earth distance over time. Right: polar view of moon’s orbit; the narrow band top right is it’s original, fairly circular orbit — more circular than in reality in fact; the broad band further in is its final eccentric orbit.
So I’m wondering: maybe it’s actually possible to eject the earth-moon system from the solar system without breaking it up? I guess I’ll have to run a few simulations with a more massive trespasser to find out…
Just for fun, the result of a different simulation: Here, the sun seems to be able to hold on to one of the rogue planet’s satellites — on a comet-like, mercury-crossing orbit (black ellipsis). All distances in metres from sun.