<p>It isn't an exact <em>concept</em>. In theory, every body in the Universe influences the trajectory of every other body. The &quot;sphere of influence&quot; just gives you a rough idea of when that influence will be strong on an orbital time scale.</p>

CC BY-SA 4.0
2024-11-29T17:48:54.077Z
Thank you for the answer! I had figured that, but wanted to make sure there wasn't a more accurate approximation to be found than the one given by the standard equation.
Eocasea_martini
CC BY-SA 4.0
2024-11-29T12:10:11.040Z
2024-11-29T12:10:11.040Z
John Doty
<p>As far as I have found, the following equation is the one the vast majority of sources give as an approximate way to find the radius of the sphere of influence (SOI):
<span class="math-container">$$
r_{SOI} = r \left( \frac{m}{M} \right)^{\frac{2}{5}}
$$</span></p>
<p>where r is the distance between two bodies (with one body orbiting the other), m being the mass of the much less massive mass, and M being the mass of the much more massive mass.</p>
<p><strong>Question</strong>: Is there a more exact method to describe the sphere of influence?</p>

CC BY-SA 4.0
2024-11-29T17:22:38.883Z
An n-body simulation would be the most accurate.  Next best would be the area the body's gravitational pull is greater than any other body.  But, it really depends on the requirements of the specific application as the what is "good enough".
Greg Miller
<astrophysics>
Is there a more precise method of describing/calculating the sphere of influence? If so, what is it?
Eocasea_martini
# Is there a more precise method of describing/calculating the sphere of influence? If so, what is it?

(Asked by: username_0 on 2024-11-28)

As far as I have found, the following equation is the one the vast majority of sources give as an approximate way to find the radius of the sphere of influence (SOI):
$$
r\_{SOI} = r \left( \frac{m}{M} \right)^{\frac{2}{5}}
$$

where r is the distance between two bodies (with one body orbiting the other), m being the mass of the much less massive mass, and M being the mass of the much more massive mass.

**Question**: Is there a more exact method to describe the sphere of influence?

**Tags:** astrophysics
> **Comments:**
> **username_1**: An n-body simulation would be the most accurate.  Next best would be the area the body's gravitational pull is greater than any other body.  But, it really depends on the requirements of the specific application as the what is "good enough".  

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## 1 answers

### Answer by username_2 on 2024-11-29. Score: 4 | Accepted answer

It isn't an exact *concept*. In theory, every body in the Universe influences the trajectory of every other body. The "sphere of influence" just gives you a rough idea of when that influence will be strong on an orbital time scale.

> **Comments:**
> **username_0**: Thank you for the answer! I had figured that, but wanted to make sure there wasn't a more accurate approximation to be found than the one given by the standard equation.  

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