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Recently we had a question on gravitational SOI (Sphere of Influence) of planets but the image in answer has a plot showing that the SOI of Jupiter is less than that of Neptune. However, Jupiter's mass is 317 times Earth's mass, but Neptune has a mass of 17.15 times Earth's mass. Therefore, it would seem Jupiter's SOI would be larger than that of Neptune

source:Wikipedia

Is there a mistake in the graph, or is it in my justifiration ?

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    $\begingroup$ Note: The graph is of the Hill sphere, not the sphere of influence. These are distinct (but related) concepts. $\endgroup$
    – David Hammen
    Jun 23, 2014 at 18:41
  • $\begingroup$ Simply because Neptune's ~6x further from the Sun than Jupiter. $\endgroup$
    – smci
    Nov 21, 2014 at 22:52

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Let's look at what, exactly, SOI is: the Sphere Of Influence, the boundary inside of which the object has more force on other objects than the Sun does.

So, the weaker the force is from the Sun, the larger your sphere of influence is. Since gravity decreases as an inverse square ratio, the Sun's gravity is much weaker at Neptune (Perihelion 4,452,940,833 km) than it is at Jupiter (Perihelion 740,573,600 km). To clarify, that's 4.4 billion versus 740 million. A big difference, and one that makes an impact in the SOI.

ts;du*: (from geoffc's comment):

SOI is not about just the mass of the object, rather it is the comparison of the Sun's influence vs the mass of the object. Which clearly really makes a bit difference.

terribly stated; didn't understand

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  • $\begingroup$ So the key point is, SOI is not about just the mass of the object, rather it is the comparison of the Sun's influence vs the mass of the object. Which clearly really makes a bit difference. $\endgroup$
    – geoffc
    Dec 4, 2013 at 15:38
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    $\begingroup$ Exactly (and said much more clearly, thanks!) $\endgroup$
    – Undo
    Dec 4, 2013 at 15:39
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    $\begingroup$ Correction: Gravity in this context decreases as an inverse cube relationship rather than an inverse square relationship. The context of both the Hill sphere and the sphere of influence is a planet-centered frame. From this perspective, the Sun's gravitational influence on some object is the Newtonian gravitational acceleration of the object toward the Sun less the Newtonian gravitational acceleration of the planet toward the Sun. This is a tidal force, which varies roughly as $1/r^3$ as opposed to the $1/r^2$ Newtonian gravitational acceleration. $\endgroup$
    – David Hammen
    Jun 23, 2014 at 18:48

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