<p>There is a symmetry in the rotating gravitational field, which means that capture of an asteroid to the L4 is just as likely as to the L5 Lagrange point.</p>

<p>In the case of Mars the split is 1:6, and a simple binomial model suggests a probability of 0.0625 (the probability of a 1:6 or 0:7 split given the hypothesis that they are distributed randomly is 0.0625) This doesn't give a reason to suppose there is anything unusual happening, and as noted in the comments, there is no favouring of L5 when other planets are considered.</p>

<p>As noted by UserLTK: "Earth has an L4 asteroid, none in L5. Uranus also has an L4, no L5 and Neptune has more L4 than L5 objects."</p>

<p>The conclusion is that <em>No, the greater number of L5 martian trojans is just a random effect</em>.</p>

CC BY-SA 3.0
2016-03-10T18:21:02.670Z
See the comment above. Earth has 1 L4 and no L5, Neptune also has more  L4 than L5
James K
CC BY-SA 3.0
2016-03-11T21:05:20.223Z
edited with the information from UserLTK's comment
James K
CC BY-SA 3.0
2016-03-09T22:10:58.840Z
2016-03-11T21:04:38.533Z
2016-03-11T21:04:38.533Z
James K
<p>Mars has much more trojans in L5. Does it reflect a common pattern?</p>

CC BY-SA 3.0
2015-07-10T23:40:45.017Z
I think, likely, the answer is no.   Earth has an L4 asteroid, none in L5.   Uranus also has an L4, no L5 and Neptune has more L4 than L5 objects.   https://en.wikipedia.org/wiki/List_of_objects_at_Lagrangian_points#Sun.E2.80.93Mars_Lagrangian_points and https://en.wikipedia.org/wiki/Earth_trojan  Jupiter is the king of trojans and it appears to have similar amounts in it's L4 (Greek camp) and it's L5 (Trojan camp).  https://en.wikipedia.org/wiki/List_of_Trojan_asteroids_%28Greek_camp%29 and https://en.wikipedia.org/wiki/List_of_Trojan_asteroids_%28Trojan_camp%29
userLTK
CC BY-SA 3.0
2015-07-11T20:42:03.687Z
@userLTK what is about theoretical proof based on Newtonian mechanics and/or GR? Is there at least a subtle difference in likelihood?
Anixx
CC BY-SA 3.0
2015-07-12T03:05:41.967Z
That's why I made a comment and not an answer.   I don't know of any proof, though I suspect mathematically L4 and L5 are the same, though Jupiter's orbital resonance could affect Mars' L4 and L5 I think.   That's possible, but that would be a coincidental and non permanent effect.
userLTK
<orbit><trojan-asteroids>
Are trojans in L5 more likely than in L4?
Anixx
# Are trojans in L5 more likely than in L4?

(Asked by: username_0 on 2015-07-10)

Mars has much more trojans in L5. Does it reflect a common pattern?

**Tags:** orbit, trojan-asteroids

> **Comments:**
> **username_1**: I think, likely, the answer is no.   Earth has an L4 asteroid, none in L5.   Uranus also has an L4, no L5 and Neptune has more L4 than L5 objects.   https://en.wikipedia.org/wiki/List_of_objects_at_Lagrangian_points#Sun.E2.80.93Mars_Lagrangian_points and https://en.wikipedia.org/wiki/Earth_trojan  Jupiter is the king of trojans and it appears to have similar amounts in it's L4 (Greek camp) and it's L5 (Trojan camp).  https://en.wikipedia.org/wiki/List_of_Trojan_asteroids_%28Greek_camp%29 and https://en.wikipedia.org/wiki/List_of_Trojan_asteroids_%28Trojan_camp%29  
> **username_0**: @username_1 what is about theoretical proof based on Newtonian mechanics and/or GR? Is there at least a subtle difference in likelihood?  
> **username_1**: That's why I made a comment and not an answer.   I don't know of any proof, though I suspect mathematically L4 and L5 are the same, though Jupiter's orbital resonance could affect Mars' L4 and L5 I think.   That's possible, but that would be a coincidental and non permanent effect.  

---

## 1 answers

### Answer by username_2 on 2016-03-09. Score: 4

There is a symmetry in the rotating gravitational field, which means that capture of an asteroid to the L4 is just as likely as to the L5 Lagrange point.

In the case of Mars the split is 1:6, and a simple binomial model suggests a probability of 0.0625 (the probability of a 1:6 or 0:7 split given the hypothesis that they are distributed randomly is 0.0625) This doesn't give a reason to suppose there is anything unusual happening, and as noted in the comments, there is no favouring of L5 when other planets are considered.

As noted by UserLTK: "Earth has an L4 asteroid, none in L5. Uranus also has an L4, no L5 and Neptune has more L4 than L5 objects."

The conclusion is that *No, the greater number of L5 martian trojans is just a random effect*.

> **Comments:**
> **username_2**: See the comment above. Earth has 1 L4 and no L5, Neptune also has more  L4 than L5  
> **username_2**: edited with the information from UserLTK's comment  

---

