<p>They are pulled out of stable orbits by Jupiter.</p>
<p>The details are in <a href="https://ui.adsabs.harvard.edu/abs/2012jsrs.conf..225B/abstract" rel="nofollow noreferrer">https://ui.adsabs.harvard.edu/abs/2012jsrs.conf..225B/abstract</a></p>
<p>Full text <a href="https://syrte.obspm.fr/jsr/journees2011/pdf/baudisch.pdf" rel="nofollow noreferrer">https://syrte.obspm.fr/jsr/journees2011/pdf/baudisch.pdf</a></p>
<blockquote>
<p>The planet Jupiter is solely responsible for the hole of instability for short time integrations
(<span class="math-container">$T &lt; 10^{7}$</span>) compared to the age of the planetary system. On the long term scale this planet also destabilizes the whole region around the Saturnian libration points. If we find in the future Trojans of Saturn,
these Trojans could only be captured asteroids, in orbits in the 1:1 MMR for a short time</p>
</blockquote>

CC BY-SA 4.0
2020-11-09T18:56:24.200Z
How come Mars' trojans aren't equally as destabilized by Jupiter's gravity then? Mars comes closer, and is on average closer, to Jupiter than Saturn.
user177107
CC BY-SA 4.0
2020-11-09T19:39:50.583Z
Because they are not or else they are short term captures.  The paper shows that the only way this was discovered was by brute force numerical integration of the laws of motion. You can't deduce this from any general principle, only by simulation.
James K
CC BY-SA 4.0
2020-11-11T00:10:01.267Z
@JamesK there was a huge amount of mathematical work on the stability of three-body orbits and perturbation theory before numerical techniques were available. Just because people use numerical extensively now does not alone prove that there is no other way to do it. It just means that nobody wants to anymore.
uhoh
CC BY-SA 4.0
2020-11-09T18:00:51.617Z
2020-11-09T18:00:51.617Z
James K
<p>Every planet apart from Mercury and Saturn has trojans in its L4 and/or L5 points.</p>
<p>Mercury is easy enough to explain: It is small, has an eccentric orbit that precesses, and any trojans it has would be heavily perturbed by the Sun's gravity.</p>
<p>However Saturn doesn't have any of those complications. The answer given to this question is that Jupiter's gravity perturbs any trojans at Saturn's L4 and L5 points.</p>
<p>But if Mars, which is much less massive than Saturn and comes closer to Jupiter, can have multiple trojans then there's no reason why Saturn shouldn't.</p>

<saturn><trojan-asteroids>
Why is Saturn the only large planet without any trojans?
user177107
# Why is Saturn the only large planet without any trojans?

(Asked by: username_0 on 2020-11-09)

Every planet apart from Mercury and Saturn has trojans in its L4 and/or L5 points.

Mercury is easy enough to explain: It is small, has an eccentric orbit that precesses, and any trojans it has would be heavily perturbed by the Sun's gravity.

However Saturn doesn't have any of those complications. The answer given to this question is that Jupiter's gravity perturbs any trojans at Saturn's L4 and L5 points.

But if Mars, which is much less massive than Saturn and comes closer to Jupiter, can have multiple trojans then there's no reason why Saturn shouldn't.

**Tags:** saturn, trojan-asteroids

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## 1 answers

### Answer by username_1 on 2020-11-09. Score: 4

They are pulled out of stable orbits by Jupiter.

The details are in <https://ui.adsabs.harvard.edu/abs/2012jsrs.conf..225B/abstract>

Full text <https://syrte.obspm.fr/jsr/journees2011/pdf/baudisch.pdf>

> The planet Jupiter is solely responsible for the hole of instability for short time integrations
> ($T < 10^{7}$) compared to the age of the planetary system. On the long term scale this planet also destabilizes the whole region around the Saturnian libration points. If we find in the future Trojans of Saturn,
> these Trojans could only be captured asteroids, in orbits in the 1:1 MMR for a short time

> **Comments:**
> **username_0**: How come Mars' trojans aren't equally as destabilized by Jupiter's gravity then? Mars comes closer, and is on average closer, to Jupiter than Saturn.  
> **username_1**: Because they are not or else they are short term captures.  The paper shows that the only way this was discovered was by brute force numerical integration of the laws of motion. You can't deduce this from any general principle, only by simulation.  
> **username_2**: @JamesK there was a huge amount of mathematical work on the stability of three-body orbits and perturbation theory before numerical techniques were available. Just because people use numerical extensively now does not alone prove that there is no other way to do it. It just means that nobody wants to anymore.  

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