<p>This is a cool question. The short answer is: probably not.</p>
<p>The long answer requires us to consider a few things:</p>
<h2>1. Are the current planets stable?</h2>
<p>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.</p>
<p>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.</p>
<p>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!</p>
<p><a href="https://i.sstatic.net/7d3Rp.png" rel="noreferrer"><img src="https://i.sstatic.net/7d3Rp.png" alt="enter image description here" /></a></p>
<p>Below is a plot from a paper by <a href="https://ui.adsabs.harvard.edu/abs/2009Natur.459..817L/abstract" rel="noreferrer">Laskar, J. &amp; Gastineau, M.</a> 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.</p>
<p>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.</p>
<h2>2. Alright, but what about adding another one?</h2>
<p>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 &quot;Earth-Mars Belt&quot; (you can read the paper <a href="https://arxiv.org/abs/2010.01225" rel="noreferrer">here</a>: 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.</p>
<p>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.</p>
<h2>3. What about resonances?</h2>
<p>There are some situations where planets can be found in what are called &quot;Mean-Motion Resonances&quot; 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.</p>

CC BY-SA 4.0
2022-08-30T23:43:30.513Z
2022-08-30T23:43:30.513Z
user2944352
<p>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.</p>
<p>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.</p>
<p>(The numbers above each planet represent the distance to the sun in km at each point of the orbit).</p>
<p>Between Earth and Venus:</p>
<p><a href="https://i.sstatic.net/FmVj2.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FmVj2.jpg" alt="enter image description here" /></a></p>
<p>Between Earth and Mars:</p>
<p><a href="https://i.sstatic.net/YJDKL.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/YJDKL.jpg" alt="enter image description here" /></a></p>
<p>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.</p>
<p>And here are the simulations as .gif:</p>
<p><a href="https://gifyu.com/image/Sw9qC" rel="nofollow noreferrer">https://gifyu.com/image/Sw9qC</a></p>
<p><a href="https://gifyu.com/image/Sw9q0" rel="nofollow noreferrer">https://gifyu.com/image/Sw9q0</a></p>

CC BY-SA 4.0
2022-08-30T17:16:38.390Z
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.
James K
CC BY-SA 4.0
2022-08-30T19:28:46.567Z
@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.
Marco Leonardi
CC BY-SA 4.0
2022-08-30T19:58:00.017Z
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.
James K
CC BY-SA 4.0
2022-08-30T20:03:24.807Z
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.
James K
CC BY-SA 4.0
2022-08-30T16:41:23.323Z
2022-08-30T16:41:23.323Z
Marco Leonardi
<p>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?</p>

CC BY-SA 4.0
2022-08-26T15:26:04.097Z
https://en.wikipedia.org/wiki/Near-Earth_object
Nilay Ghosh
CC BY-SA 4.0
2022-08-26T16:39:01.740Z
I assume from your related question https://worldbuilding.stackexchange.com/q/234860 that this planet is just being "dropped" into place with the correct velocity.
PM 2Ring
CC BY-SA 4.0
2022-08-26T16:43:29.507Z
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...
PM 2Ring
CC BY-SA 4.0
2022-08-26T18:38:28.427Z
I'll add the only theoretically stable n-body solutions are the Lagrangian points, and even those only work with 3 bodies.
Greg Miller
CC BY-SA 4.0
2022-08-27T02:44:45.333Z
@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.
M. A. Golding
CC BY-SA 4.0
2022-08-27T02:52:18.353Z
KaffeeByte asked a similar question in the worldbuilding  stack exchange.  https://worldbuilding.stackexchange.com/questions/234860/where-could-we-add-a-new-planet-to-the-inner-solar-system/234868#234868  So someone who answers here should also answer there, and vice versa.
M. A. Golding
<orbit><planet><solar-system><orbital-mechanics>
Could a planet theoretically have a stable orbit between Venus and Earth OR Earth and Mars
KaffeeByte
# Could a planet theoretically have a stable orbit between Venus and Earth OR Earth and Mars

(Asked by: username_0 on 2022-08-26)

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?

**Tags:** orbit, planet, solar-system, orbital-mechanics

> **Comments:**
> **username_1**: https://en.wikipedia.org/wiki/Near-Earth_object  
> **username_2**: I assume from your related question https://worldbuilding.stackexchange.com/q/234860 that this planet is just being "dropped" into place with the correct velocity.  
> **username_2**: 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...  
> **username_3**: I'll add the only theoretically stable n-body solutions are the Lagrangian points, and even those only work with 3 bodies.  
> **username_4**: @username_3   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.  
> **username_4**: username_0 asked a similar question in the worldbuilding  stack exchange.  https://worldbuilding.stackexchange.com/questions/234860/where-could-we-add-a-new-planet-to-the-inner-solar-system/234868#234868  So someone who answers here should also answer there, and vice versa.  

---

## 2 answers

### Answer by username_5 on 2022-08-30. Score: 8

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!

[![enter image description here](https://i.sstatic.net/7d3Rp.png)](https://i.sstatic.net/7d3Rp.png)

Below is a plot from a paper by [Laskar, J. & Gastineau, M.](https://ui.adsabs.harvard.edu/abs/2009Natur.459..817L/abstract) 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.

## 2. Alright, but what about adding another one?

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](https://arxiv.org/abs/2010.01225): 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.

## 3. What about resonances?

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.


---

### Answer by username_6 on 2022-08-30. Score: 1

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:

[![enter image description here](https://i.sstatic.net/FmVj2.jpg)](https://i.sstatic.net/FmVj2.jpg)

Between Earth and Mars:

[![enter image description here](https://i.sstatic.net/YJDKL.jpg)](https://i.sstatic.net/YJDKL.jpg)

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>

> **Comments:**
> **username_7**: 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.  
> **username_6**: @username_7 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.  
> **username_7**: 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.  
> **username_7**: 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.  

---

