Talk:Sphere of influence (astrodynamics)

Hill sphere

There ought to be some explanation of how this concept relates to the Hill sphere. —Tamfang (talk) 22:24, 24 April 2009 (UTC)

Agree. I will also place this on the Hill sphere discussion page to see if we can garner comment. At a glance, it appears that the "Hill sphere" and the "SOI (astrodynamics)" are one and the same thing. So this might make them candidates for a merge?

 —  Paine (Ellsworth's Climax)  16:54, 19 June 2010 (UTC)

They are different concepts. The Sphere Of Influence as discussed on this page is a synonym for the Laplace Sphere (of influence). Note the power of 2/5 derived on this page as opposed to the power of 1/3 used in the Hill Sphere. The two concepts are derived from different points of view. The Hill Sphere results from looking at things from the perspective of a rotating frame with the SOI results at looking at things from the perspective of a non-rotating frame. 2601:2C4:C400:5730:3DE7:8347:70A3:8FCD (talk) 14:39, 19 November 2023 (UTC)

The Hill sphere for Earth, as given in that article, has radius of 1.5 million km, which is about 932,000 miles. That article also states that it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. This article on the SoI gives a radius value of 925,000 km, which is about 575,000 miles, or about 62% of the radius of the Hill sphere. So:

• Hill radius = 1,500,000 km or 932,000 miles
• SoI radius = 925,000 km or 575,000 miles

Now comes the truly interesting part. Editors please note the derivation from this SoI article:

The general equation describing the radius of the sphere $r_{SOI}$ of a planet:

$r_{SOI}=a_{p}({\frac {m_{p}}{m_{s}}})^{2/5}$

where

$a_{p}$ is the semimajor axis of the planet's orbit relative to the largest body in the system, usually the Sun

$m_{p}$ and $m_{s}$ are the masses of the planet and Sun, respectively.

And now, please note the derivation from the Hill sphere article:

$R_{H}=a\left({\frac {M_{\mathrm {planet} }}{M_{\star }}}\right)^{1/3}$

I'm no math wizard, yet it seems to me that these formulas tell us that the SoI radius is greater than the Hill radius for any given mass relationship. Am I missing something? Isn't the SoI supposed to be smaller than the Hill sphere?
 —  Paine (Ellsworth's Climax)  05:04, 5 July 2010 (UTC)

PS. I placed this same information at Talk:Hill sphere#SOI (astrodynamics)  —  Paine (Ellsworth's Climax) 

Guys the SOI and the Hill Sphere are identical and the radius derived on the current Hill Sphere entry is for the distance of the Lagrange points L1 & L2 not the Hill Sphere. —Qraal (talk) 11:48, 2 September 2010 (UTC)

The classical SOI and Hill Sphere are not the same thing. The SOI is intended to indicate which body has the "primary gravitational influence". The Hill Sphere is the region at which gravitational capture is ensured. While you have to be "close enough" to the primary body for this to happen, it is based on a stability argument and not just the balance of gravitational forces. If anything, the Hill Sphere page is somewhat misleading or at least too light on details to make this point clear.

The point of the Hill Sphere is to indicate where objects within the Hill Sphere can orbit an massive body indefinitely. The point of the SOI is to help decided how to set up patched conics, normally used for a flyby. Two different applications. Uluhtc (talk) 17:59, 22 April 2015 (UTC)

Milky Way solar SoI?

I am wondering what size is the solar SoI sphere and Hill sphere to the Milky Way? Reddwarf2956 (talk) 22:22, 28 April 2012 (UTC)

Slight issue with "Moon" in table

The Moon, which is placed in the table with its own value of SOI radius, is a special case here since exitting the Moon's SOI would put a body into the SOI of the Earth, and not the Sun. For all of the other entries in the table, leaving their SOI means entering the SOI of the Sun instead. I'm not sure of the best way to format the insertion of a note on this uniqueness, but text saying "Since the Moon's orbit lies entirely within the SOI of the Earth, leaving the SOI of the Moon does not place a body in the SOI of the Sun, like the other planets on this list, but that of the Earth instead" would be appropriate. siafu (talk) 23:27, 1 March 2015 (UTC)

I do not see the reason to have the moon if other moons are not included. John W. Nicholson (talk) 01:21, 2 March 2015 (UTC)

Why not? It is calculated completely analogously, just with the major mass being Earth, not the Sun. Other moons could be added instead, if you like. --JorisvS (talk) 11:07, 2 March 2015 (UTC)

It is clear in the literature what SOI means for the Moon. And the exception is noted in the text that is is "usually the Sun". It is also true for moons of other planets that they have an SOI associated with their parent planet. But I think it is worth pointing out the Moon as a specific example where big "M" is not the Sun since it is specifically included in the table. Uluhtc (talk) 23:24, 16 April 2015 (UTC)

Why is there an unreferenced link to the Laplace Sphere in the article?

The sphere of influence discussed in this article is the Laplace Sphere; note the power of 2/5 as opposed to 1/3 for the Hill Sphere (of influence). What should be done is to create a Laplace Sphere page that redirects to this page.