Hypothetical planet jump: Will it perturb star systems?

In a more speculative corner of SE somebody was dreaming up a story of planets traveling between star systems through wormholes.

I was wondering how much the appearing/disappearing of a planet the size of Earth would perturb the orbits of the other bodies in a solar system like ours. After all, the bodies in the system all interact, and the current situation appears to me as the delicate result of an evolution during which bodies collided, were ejected or were nudged into specific (dynamic) "places" which are stable, for example because they resonate with or are far enough away from others.

How much havoc would the sudden appearance of an Earth-sized planet in the habitable zone wreak on this balance? Both long-term and short-term (on astronomical scales; short-term may be 100 years) disturbances are interesting. Would it directly perturb the orbits of nearby planets (in our case Earth and Mars) enough to be prohibiting? For example, even relatively minor changes of the orbit can have an impact on climate.

Could it lead to catastrophic events much later, for example because some Trojan bodies are pushed out of their Lagrange neighborhood and start marauding the Solar System, increasing the chance of catastrophic impact events on Earth or an inhabited Mars?

• It does depend on exactly where it appears and how fast it is moving. The standard gravitational parameter of the Earth is $3.986 \times 10^{14} \text{m}^3 / \text{s}^2$ and of the Sun is $1.327 \times 10^{20}$, so at 1 AU one earth has a few parts per million gravitational effect on a heliocentric orbit. Over time it might interact more strongly and change the climate a small amount. However if the 2nd Earth appeared on a collision course with our Earth then of course the outcome would be more interesting.
– uhoh
Jul 9, 2020 at 8:30

There is essentially no room in our habitable zone for another Earth-sized planet. The exact timescale for instability would depend on the details of where you put it, but the system couldn't survive long term.

Most investigations of the long-standing question of solar system stability (without any additional planets) find that the system is stable in the long term with about 99% probability, e.g. this page by Scott Tremaine and this discussion on Wikipedia, but that there is some chance of instability even with the current set of planets, and no room for another.

It appears that many extrasolar planetary systems are "full" as well, although selection effects make it hard to know whether there are planets we aren't seeing in systems that aren't yet known to have multiple planets.

The "fullness" of these solar systems suggests that it may be that even more planets form initially, but then some are ejected until the system reaches a stable configuration.

Interestingly, in our own inner solar system, the place where there is the most dynamical space for another planet is inside the orbit of Mercury, say with a semimajor axis of 0.1 AU or so. That might seem counterintuitive, since the spacings between Earth (1 AU), Venus (0.7 AU), Mercury (0.4 AU), and a planet at 0.1 AU would all be about 0.3 AU, the same in absolute terms. But what matters most for stability is the ratio of the semimajor axes, so Mercury to an inner planet would be a factor of 4, whereas Earth/Venus is only 1/0.7 = 1.4.

Such a planet isn't in the habitable zone, and it likely wouldn't be stable on very long timescales with our current configuration of other planets, but we do know that many (perhaps even most) extrasolar planetary systems have planets at those very small orbital radii - see the image below, made from data from the NASA Exoplanet Archive. There are strong selection effects there (close-in planets are the easiest to detect with both the transit and radial velocity methods), but the high frequency does tell us that such planets are relatively common and can have stable orbits.

• Very informative, thanks. I should perhaps add to my question that planets in this SF universe are common means of transportation, so that they won't stay "very long" (whatever that means; certainly not "very long" on astronomical scales). So long-term (astronomical long-term) is an interesting question, but the severity of short-term perturbations would also be interesting, e.g. the asteroid question, or some additional Earth axis precession. Jul 9, 2020 at 16:00
• As an aside, I didn't even know that we have already discovered thousands of Exoplanets. Pretty exciting. Jul 9, 2020 at 16:04
• Yes, “short” and “long” can have a lot of different meanings here. Certainly there are plenty of places you could put an Earth-mass planet in the habitable zone where the inner solar system would change dramatically in just decades. But how long you could make it last with a careful choice of placement? I don’t think there is a definitive answer to that short of actually modeling the system. There’s also not broad agreement on just how big we should take the habitable zone to be. Jul 9, 2020 at 17:33