<p>From my perspective, the Hill sphere is a characteristic parameter devised for ease of computation.  Unlike the Roche Lobe, the Hill sphere lacks a well-defined physical concept. Hence, it's not surprising to observe an inconsistency of approximately 10% when comparing values derived from distinct starting points.
In this study, I observed that attempting to calculate the size of the Hill sphere based on a rigorous physical interpretation yields differences with the commonly used expression that are significantly larger than 10%. (See <em>Stable satellites around extrasolar giant planets</em> <a href="https://articles.adsabs.harvard.edu/pdf/2006MNRAS.373.1227D" rel="nofollow noreferrer">doi:10.1111/j.1365-2966.2006.11104.x</a>)</p>
<p><code>According to Wikipedia, the Hill sphere is bounded along the primary-satellite axis by the L1 and L2 points.</code></p>
<p>The Wikipedia page lacks a reference for this statement, and I couldn't find support elsewhere. Given that this statement diverges from my understanding of the Hill sphere's concept, I cast doubt on its reliability.</p>

CC BY-SA 4.0
2023-12-24T16:12:34.767Z
2023-12-28T11:54:57.623Z
2023-12-28T11:54:57.623Z
HD189733b
<p>The Roche limit is defined as the minimal orbital distance within which a gravity-bound satellite will remain together rather than being disrupted by tidal forces. If I understand correctly, this is equivalent to saying that outside the Roche limit, a body on the satellite's surface is more strongly attracted to the satellite's center of mass than to the primary, or else saying that the Roche limit is the distance within which the satellite's L1 and L2 points are within the satellite itself.</p>
<p>The Hill sphere is defined as the sphere around a satellite within which the satellite exerts the primary gravitational influence over a free body, as opposed to the primary. According to Wikipedia, the Hill sphere is bounded along the primary-satellite axis by the L1 and L2 points.</p>
<p>Would it be correct to say that the Roche limit is the limit within which a satellite is not entirely within its own Hill sphere? Using the formulas on Wikipedia, when I plug in those numbers I find the satellite radius to be related to the Hill sphere by the constant <span class="math-container">$(\frac{2}{3})^{\frac{1}{3}}$</span>, about 0.87. But the formula for the Hill sphere is only an approximation, and I don't know how it's likely to apply in this edge case.</p>
<p>EDIT: To resolve ambiguity, I will state that I already read all of the questions proposed as &quot;already answered&quot;, and none of them answer my question.</p>
<p>For a given primary-satellite pair, the Roche limit is a sphere <em>around the primary</em>, whereas the Hill sphere is a sphere <em>around the satellite</em>. I do not need clarification of this point. Likewise, since the two spheres are described from different centers, the question of comparing the two's size is not particularly useful.</p>
<p>The Hill sphere is apparently also referred to as the Roche sphere, which introduces confusion. As used in this question, I am referring to the Roche limit, specifically, which is the sphere around the primary within which a satellite of a given density cannot remain intact. Meanwhile, the Roche lobe is apparently a similar concept to the Hill sphere, but used in the context of binary star systems. It is not relevant to the question I am asking.</p>
<p>My question relates specifically to the evolution of the Hill sphere <em>of the satellite</em> as the satellite's orbit changes in radius, and how that evolution relates to the Roche limit around the primary. None of the linked questions address this point at all.</p>

CC BY-SA 4.0
2022-02-09T16:46:16.433Z
Have you seen here? https://en.wikipedia.org/wiki/Roche_limit#Roche_limit,_Hill_sphere_and_radius_of_the_planet
Daddy Kropotkin
<roche-limit><hill-sphere>
Relationship between Roche limit and Hill sphere?
Tom Hunt
# Relationship between Roche limit and Hill sphere?

(Asked by: username_0 on 2022-01-28)

The Roche limit is defined as the minimal orbital distance within which a gravity-bound satellite will remain together rather than being disrupted by tidal forces. If I understand correctly, this is equivalent to saying that outside the Roche limit, a body on the satellite's surface is more strongly attracted to the satellite's center of mass than to the primary, or else saying that the Roche limit is the distance within which the satellite's L1 and L2 points are within the satellite itself.

The Hill sphere is defined as the sphere around a satellite within which the satellite exerts the primary gravitational influence over a free body, as opposed to the primary. According to Wikipedia, the Hill sphere is bounded along the primary-satellite axis by the L1 and L2 points.

Would it be correct to say that the Roche limit is the limit within which a satellite is not entirely within its own Hill sphere? Using the formulas on Wikipedia, when I plug in those numbers I find the satellite radius to be related to the Hill sphere by the constant $(\frac{2}{3})^{\frac{1}{3}}$, about 0.87. But the formula for the Hill sphere is only an approximation, and I don't know how it's likely to apply in this edge case.

EDIT: To resolve ambiguity, I will state that I already read all of the questions proposed as "already answered", and none of them answer my question.

For a given primary-satellite pair, the Roche limit is a sphere *around the primary*, whereas the Hill sphere is a sphere *around the satellite*. I do not need clarification of this point. Likewise, since the two spheres are described from different centers, the question of comparing the two's size is not particularly useful.

The Hill sphere is apparently also referred to as the Roche sphere, which introduces confusion. As used in this question, I am referring to the Roche limit, specifically, which is the sphere around the primary within which a satellite of a given density cannot remain intact. Meanwhile, the Roche lobe is apparently a similar concept to the Hill sphere, but used in the context of binary star systems. It is not relevant to the question I am asking.

My question relates specifically to the evolution of the Hill sphere *of the satellite* as the satellite's orbit changes in radius, and how that evolution relates to the Roche limit around the primary. None of the linked questions address this point at all.

**Tags:** roche-limit, hill-sphere
> **Comments:**
> **username_1**: Have you seen here? https://en.wikipedia.org/wiki/Roche_limit#Roche_limit,_Hill_sphere_and_radius_of_the_planet  

---

## 1 answers

### Answer by username_2 on 2023-12-24. Score: 2

From my perspective, the Hill sphere is a characteristic parameter devised for ease of computation. Unlike the Roche Lobe, the Hill sphere lacks a well-defined physical concept. Hence, it's not surprising to observe an inconsistency of approximately 10% when comparing values derived from distinct starting points.
In this study, I observed that attempting to calculate the size of the Hill sphere based on a rigorous physical interpretation yields differences with the commonly used expression that are significantly larger than 10%. (See *Stable satellites around extrasolar giant planets* [doi:10.1111/j.1365-2966.2006.11104.x](https://articles.adsabs.harvard.edu/pdf/2006MNRAS.373.1227D))

`According to Wikipedia, the Hill sphere is bounded along the primary-satellite axis by the L1 and L2 points.`

The Wikipedia page lacks a reference for this statement, and I couldn't find support elsewhere. Given that this statement diverges from my understanding of the Hill sphere's concept, I cast doubt on its reliability.


---

