# Could a planet theoretically have a stable orbit between Venus and Earth OR Earth and Mars

Take a planet, identical to Earth in size, mass, gravity, rotation, etc.(but without the moon). Could this planet theoretically maintain a stable orbit for many hundreds of millions of years orbiting between Earth and Venus OR Earth and Mars? If so, how much would the inner rocky planets be affected?

• en.wikipedia.org/wiki/Near-Earth_object Aug 26, 2022 at 15:26
• I assume from your related question worldbuilding.stackexchange.com/q/234860 that this planet is just being "dropped" into place with the correct velocity. Aug 26, 2022 at 16:39
• We don't normally answer impossible hypothetical questions here. But I guess we can treat your question as a thought-experiment on the stability of the Solar System... Aug 26, 2022 at 16:43
• I'll add the only theoretically stable n-body solutions are the Lagrangian points, and even those only work with 3 bodies. Aug 26, 2022 at 18:38
• @Greg Miller The solar system has one star, eight planets, dozensofmons around theplanets, and that's the big objects. The orbits of all objects in the solar system are many times more complicated than a 3 body problem. And yet it is obvious that dozens of bodies in the solar system had had stable orbits for billions of years. So there are many observationally stable n-body solutions in our solar system. Aug 27, 2022 at 2:44

This is a cool question. The short answer is: probably not.

The long answer requires us to consider a few things:

## 1. Are the current planets stable?

To discuss this we first need to understand something about dynamical chaos. Let's imagine a situation where you're trying to predict whether a skilled soccer player will make a goal. Furthermore, let's say you're a particular enterprising soccer fan and consequently you know the direction they will kick and the power of kick with some accuracy. In addition, you measured the goal beforehand and know what its boundaries are. If you know all these initial conditions precisely you could simply run a simulation to predict the position of the ball over time and determine - for certain - whether the player makes the goal or not.

Now let's complicate the situation: instead of knowing the initial conditions perfectly, say there is some error. If you conduct your simulation in this case you'll find there are some cases where the ball ends up in the goal, and some cases where it does not. Even if we know exactly how to do the physics, Even if our simulation is perfect, the position of the ball at any given time in the future will be uncertain simply because the initial conditions are.

The solar system as a whole exhibits something called chaos, which, at the risk of oversimplifying, is fundamentally just a version of this same effect we found with the soccer player. The difference is that in the case of chaotic systems the error in a subsequent state grows quickly (typically exponentially) in time. Hence, dynamical studies of the solar system typically involve comparing large sets of simulations statistically - while we can't be confident in any individual simulation - the overall ensemble is interpretable!

Below is a plot from a paper by Laskar, J. & Gastineau, M. unfortunately behind paywall. They integrated identical copies of the solar system for 5 billion years with the only difference being that they shifted initial position of the planet Mercury by just a few meters between simulations. The plots show the resulting maximum eccentricity of the Mercury over time (first panel is using just Newtonian mechanics, and the second panel is using General Relativity). In either case, there are many cases where the eccentricity of mercury can grow extremely large, and most of these cases result in either ejection from the solar system or collision with another planet.

This implies that the current planets - just the 4 we have - aren't super stable as is. This isn't to say that the solar system will definitely shake itself apart - but it does show that the unstable trajectories are possible given what we know about the current state of the solar system.

If we wish to consider the addition of another planet, what's critical is its mass. If the new body has a small mass, it won't really destabilize the orbits of the more massive bodies, and it has a better chance of surviving. There are regions like this in the solar system - for example the "Earth-Mars Belt" (you can read the paper here: since it's public), a region between ~1.09 and ~1.17 AU where small bodies might be able to survive for billions of years.

Finally, we get to your case - what if the added body is the size of the earth? In this case, the body not only needs to survive, but it also has to do so in a system that is being destabilized by its own (earth sized!) gravitational field. Given that the solar system without such a body is barely stable, the addition of such a large body would almost destabilize the entire inner solar system - probably impacting another planet or being ejected. While the only way to find out for sure would be to run a ton of very time-consuming simulations, I'd be very skeptical that such a situation is possible.

There are some situations where planets can be found in what are called "Mean-Motion Resonances" with each other, and this tends to permit stability even in very closely packed systems. The poster child for this type of behavior is the Trappist-1 system, which exhibits several small planets all in resonance with each other. While such a configuration cannot be realized by simply adding a planet to our solar system - it is conceivable that there could exist systems in general with planets more tightly packed than what we have.

I'm not going to do any actual math for this, but I did have a python simulation of the solar system that's somewhat gravitationally accurate laying around, so I just inserted another Earth-like planet in between Earth and Venus and Earth and Mars.

It does not seem like the orbits would be stable, but it also doesn't seem to affect the orbits of the other inner planets too much (in the short term, I didn't run it for too long). Keep in mind that this is a very rough simulation that doesn't even include satellites.

(The numbers above each planet represent the distance to the sun in km at each point of the orbit).

Between Earth and Venus:

Between Earth and Mars:

Even with such a simple raw simulation you can see that this orbit is not concentric to the others and it's bound to be unstable over millions of years.

And here are the simulations as .gif:

https://gifyu.com/image/Sw9qC

https://gifyu.com/image/Sw9q0

• Why did you make them Venus/Mars crossing orbits. Such orbits are unlikely to be stable (unless you can achieve some kind of resonance like for Pluto/Neptune) You'd get a more stable orbit if they didn't cross the orbits of other planets. Aug 30, 2022 at 17:16
• @JamesK I didn't do anything to the orbits. I just created the planets at a certain distance from the Sun, all on the same axis. I made them move according to Newton's law of gravity and that's what happened. You can see from the gifs that they all start on the same line, then it gets pulled. Aug 30, 2022 at 19:28
• But you gave them an initial velocity, why did you give them so much velocity that they cross the orbit? Why not give them the right velocity to have a circular orbit? The orbits you have created are unstable in the long term. At some point, your planet will have a close encounter with Mars, and then bad things will happen. Aug 30, 2022 at 19:58
• The only way to avoid that is to change the initial conditions. And then run your simulation for a few million simulated years, to see if the planets don't get into some kind of disruptive resonance. Aug 30, 2022 at 20:03