<p>Here is an example of what is asked for, or something very similar:</p>
<blockquote>
<p>The Saturnian moons Janus and Epimetheus share their orbits, the difference in semi-major axes being less than either's mean diameter. This means the moon with the smaller semi-major axis will slowly catch up with the other. As it does this, the moons gravitationally tug at each other, increasing the semi-major axis of the moon that has caught up and decreasing that of the other. This reverses their relative positions proportionally to their masses and causes this process to begin anew with the moons' roles reversed. In other words, they effectively swap orbits, ultimately oscillating both about their mass-weighted mean orbit.</p>
</blockquote>
<p><a href="https://en.wikipedia.org/wiki/Co-orbital_configuration" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Co-orbital_configuration</a></p>
<p><a href="https://en.wikipedia.org/wiki/Janus_(moon)" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Janus_(moon)</a></p>
<p><a href="https://en.wikipedia.org/wiki/Epimetheus_(moon)" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Epimetheus_(moon)</a></p>

CC BY-SA 4.0
2021-11-17T03:37:07.497Z
Reference link: https://worldbuilding.stackexchange.com/a/162785 (cc @fasterthanlight)
Nilay Ghosh
CC BY-SA 4.0
2021-11-17T13:40:00.327Z
Yes, I've heard of this system before, but are there any solar-orbiting objects (non-moons) whose orbit passes within some SOI distance from another body (ie Jupiter)
WarpPrime
CC BY-SA 4.0
2021-11-16T21:35:49.457Z
2021-11-16T21:35:49.457Z
M. A. Golding
<p>Ok, I'm asking this question because the obvious counterexample is <strong>trojans.</strong> Trojans typically intersect the orbit of its relative body. Typically, these are stable in the long-term, especially when the planet is massive. However, these never come within a close enough distance to be affected by the gravitational pull of the planet (<span class="math-container">$\text{MOID}\leq \text{Hill sphere}$</span>). Are such orbits which intersect the orbit of a massive body within the distance of its Hill sphere ever stable? If so, when?</p>
<p><strong>Edit:</strong> <a href="https://astronomy.stackexchange.com/posts/comments/102325">As @ConnorGarcia said in a comment</a>, moons are another counterexample. To specify, I am talking about objects whose velocity is greater than the escape velocity in the Hill sphere (unbound objects).</p>

CC BY-SA 4.0
2021-11-16T16:48:28.277Z
Moons are another counterexample, or do you mean to exclude bodies with less than escape velocity in the Hill sphere?
Connor Garcia
CC BY-SA 4.0
2021-11-16T17:25:07.447Z
@ConnorGarcia I've edited that into the post.
WarpPrime
CC BY-SA 4.0
2021-11-17T13:05:17.303Z
Just to confirm: Do you  just want the orbits of the objects to get close to each other, or do you want the objects to actually spend time inside each others' Hill spheres?
notovny
CC BY-SA 4.0
2021-11-18T01:11:44.370Z
It's not really clear what you want to know. There are many examples of nearby orbits that remain stable and share the same space (=intersect). These are almost always orbital resonances of some kind, which prevent very close interactions/encounters. Away from resonances, intersecting orbits cannot be long-term stable, since eventually a close encounter must occur.
Walter
<orbit><hill-sphere>
Are intersecting orbits ever stable?
WarpPrime
# Are intersecting orbits ever stable?

(Asked by: username_0 on 2021-11-16)

Ok, I'm asking this question because the obvious counterexample is **trojans.** Trojans typically intersect the orbit of its relative body. Typically, these are stable in the long-term, especially when the planet is massive. However, these never come within a close enough distance to be affected by the gravitational pull of the planet ($\text{MOID}\leq \text{Hill sphere}$). Are such orbits which intersect the orbit of a massive body within the distance of its Hill sphere ever stable? If so, when?

**Edit:** [As @ConnorGarcia said in a comment](https://astronomy.stackexchange.com/posts/comments/102325), moons are another counterexample. To specify, I am talking about objects whose velocity is greater than the escape velocity in the Hill sphere (unbound objects).

**Tags:** orbit, hill-sphere
> **Comments:**
> **username_1**: Moons are another counterexample, or do you mean to exclude bodies with less than escape velocity in the Hill sphere?  
> **username_0**: @ConnorGarcia I've edited that into the post.  
> **username_2**: Just to confirm: Do you  just want the orbits of the objects to get close to each other, or do you want the objects to actually spend time inside each others' Hill spheres?  
> **username_3**: It's not really clear what you want to know. There are many examples of nearby orbits that remain stable and share the same space (=intersect). These are almost always orbital resonances of some kind, which prevent very close interactions/encounters. Away from resonances, intersecting orbits cannot be long-term stable, since eventually a close encounter must occur.  

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## 1 answers

### Answer by username_4 on 2021-11-16. Score: 2

Here is an example of what is asked for, or something very similar:

> The Saturnian moons Janus and Epimetheus share their orbits, the difference in semi-major axes being less than either's mean diameter. This means the moon with the smaller semi-major axis will slowly catch up with the other. As it does this, the moons gravitationally tug at each other, increasing the semi-major axis of the moon that has caught up and decreasing that of the other. This reverses their relative positions proportionally to their masses and causes this process to begin anew with the moons' roles reversed. In other words, they effectively swap orbits, ultimately oscillating both about their mass-weighted mean orbit.

<https://en.wikipedia.org/wiki/Co-orbital_configuration>

<https://en.wikipedia.org/wiki/Janus_(moon)>

<https://en.wikipedia.org/wiki/Epimetheus_(moon)>

> **Comments:**
> **username_5**: Reference link: https://worldbuilding.stackexchange.com/a/162785 (cc @fasterthanlight)  
> **username_0**: Yes, I've heard of this system before, but are there any solar-orbiting objects (non-moons) whose orbit passes within some SOI distance from another body (ie Jupiter)  

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