<blockquote>
<p>What is the largest single-object mass that would allow two objects of equal mass to have a stable orbit, one each, in Earth's L4 and L5 Lagrange points?</p>
</blockquote>
<p>This is an <em>interesting question</em>, but the answer won't be so interesting.</p>
<p>The five Lagrange points are mathematical concepts, only valid when the two primary objects (in this case Sun and Earth) are the only masses considered, and they are in <em>circular</em> orbits around their center of mass. The problems here include:</p>
<ol>
<li>Earth's orbit isn't circular</li>
<li>There's that big 'ole Moon right next to it that has a wiggly tugging effect</li>
<li>There's Jupiter and the other gas giants, and Venus that all add perturbing gravitational effects</li>
<li>A question about &quot;largest mass&quot; can't be asked about a proper Lagrange point to begin with. Those spots are &quot;reserved&quot; for massless, mathematical test objects.</li>
</ol>
<h3>All that being said...</h3>
<p>Even though massive objects put near the real world Sun-Earth L4/L5-like regions would need some propulsive station-keeping ability to remain there for years or decades, it <em><strong>might be</strong></em> that having equal masses each can somehow add some stability to the now four-body problem, thereby making the required station-keeping maneuvers less expensive in terms of propellants, or allow them to at least &quot;hang out nearby&quot; those regions longer before drifting out into heliocentric orbits (as they will eventually all do.</p>

CC BY-SA 4.0
2023-05-02T04:01:41.040Z
While you have a point, [Wikipedia claims](https://en.wikipedia.org/wiki/Lagrange_point) "The Sun–Earth L4 and L5 points contain interplanetary dust and at least two asteroids, 2010 TK7 and 2020 XL5." So there's at least a minimum mass. I'm curious about the maximum.
JBH
CC BY-SA 4.0
2023-05-02T05:46:57.077Z
@JBH the bulleted item in your quote is incorrect as written; Wikipedia's great but not an authoritative source. Points can't "contain" asteroids, and those asteroids, while *associated* with Lagrange points, don't spend much time *anywhere near* them! Refer to [2010 TK7; Physical and orbital characteristics](https://en.wikipedia.org/wiki/2010_TK7#Physical_and_orbital_characteristics) and [(614689) 2020 XL5; Orbit and classification](https://en.wikipedia.org/wiki/(614689)_2020_XL5) Wikipedia is written and edited by a community of volunteers who use widely varying levels of care.
uhoh
CC BY-SA 4.0
2023-05-02T05:50:24.053Z
@JBH for more on asteroids that are *associated with* (not contained by) Sun-Earth Lagrange points, see [my answer to *What was the probability that Osiris Rex would find Earth Trojans?*](https://space.stackexchange.com/a/25493/12102) and [my answer to *Stabilization of Lagrange point asteroids*](https://space.stackexchange.com/a/34530/12102) and for more about tadpole orbits see [my answer to *Determining the area of Lagrange Points*](https://astronomy.stackexchange.com/a/35619/7982)
uhoh
CC BY-SA 4.0
2023-05-02T03:45:25.610Z
2023-05-02T03:45:25.610Z
uhoh
<p>What is the largest single-object mass that would allow two objects of equal mass to have a stable orbit, one each, in Earth's L4 and L5 Lagrange points?</p>

<orbit><earth><orbital-mechanics><celestial-mechanics><lagrange-point>
largest balanced mass objects in Earth's L4 & L5 Lagrange points?
JBH
# largest balanced mass objects in Earth's L4 & L5 Lagrange points?

(Asked by: username_0 on 2023-05-02)

What is the largest single-object mass that would allow two objects of equal mass to have a stable orbit, one each, in Earth's L4 and L5 Lagrange points?

**Tags:** orbit, earth, orbital-mechanics, celestial-mechanics, lagrange-point

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## 1 answers

### Answer by username_1 on 2023-05-02. Score: 2

> What is the largest single-object mass that would allow two objects of equal mass to have a stable orbit, one each, in Earth's L4 and L5 Lagrange points?

This is an *interesting question*, but the answer won't be so interesting.

The five Lagrange points are mathematical concepts, only valid when the two primary objects (in this case Sun and Earth) are the only masses considered, and they are in *circular* orbits around their center of mass. The problems here include:

1. Earth's orbit isn't circular
2. There's that big 'ole Moon right next to it that has a wiggly tugging effect
3. There's Jupiter and the other gas giants, and Venus that all add perturbing gravitational effects
4. A question about "largest mass" can't be asked about a proper Lagrange point to begin with. Those spots are "reserved" for massless, mathematical test objects.

### All that being said...

Even though massive objects put near the real world Sun-Earth L4/L5-like regions would need some propulsive station-keeping ability to remain there for years or decades, it ***might be*** that having equal masses each can somehow add some stability to the now four-body problem, thereby making the required station-keeping maneuvers less expensive in terms of propellants, or allow them to at least "hang out nearby" those regions longer before drifting out into heliocentric orbits (as they will eventually all do.

> **Comments:**
> **username_0**: While you have a point, [Wikipedia claims](https://en.wikipedia.org/wiki/Lagrange_point) "The Sun–Earth L4 and L5 points contain interplanetary dust and at least two asteroids, 2010 TK7 and 2020 XL5." So there's at least a minimum mass. I'm curious about the maximum.  
> **username_1**: @JBH the bulleted item in your quote is incorrect as written; Wikipedia's great but not an authoritative source. Points can't "contain" asteroids, and those asteroids, while *associated* with Lagrange points, don't spend much time *anywhere near* them! Refer to [2010 TK7; Physical and orbital characteristics](https://en.wikipedia.org/wiki/2010_TK7#Physical_and_orbital_characteristics) and [(614689) 2020 XL5; Orbit and classification](https://en.wikipedia.org/wiki/(614689)_2020_XL5) Wikipedia is written and edited by a community of volunteers who use widely varying levels of care.  
> **username_1**: @JBH for more on asteroids that are *associated with* (not contained by) Sun-Earth Lagrange points, see [my answer to *What was the probability that Osiris Rex would find Earth Trojans?*](https://space.stackexchange.com/a/25493/12102) and [my answer to *Stabilization of Lagrange point asteroids*](https://space.stackexchange.com/a/34530/12102) and for more about tadpole orbits see [my answer to *Determining the area of Lagrange Points*](https://astronomy.stackexchange.com/a/35619/7982)  

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