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So according to this calculation here including:

  • A Gas Giant of 12 Jupiter Masses
  • A Sun like Star of 1047.57 Jupiter Masses
  • and a semi major axis of the Planet of 1 AU

enter image description here

The Gas Giant should have a hill sphere of 0.15627750286244 Astronomical Units. But that seems very large. And if i place a body in 0.1 AU Distance of the Planet, it will quickly leave its orbit.

What am i missing here?

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I don't know where you got that formula, but how it is filled in is simply wrong. It's fine if you don't use masses in kg but relative masses in formulas, but at least you should make sure they are relative to the same reference, and what you get out of the formula has nothing close to SI units attached to it.

You are putting together 12 Jupiter Masses and 1 Sol Mass, which is like adding 1 kg and 1 pound to calculate how much your purse weight once you put them in it.

That aside, the formula seems to be wrong on its own. According to Wikipedia the radius of Hill sphere is given by

$R_H \approx $a(1-e)$\sqrt[3]\frac {m_2}{3(m_1+m_2)}$

while you seem to be using

$R_H \approx $a(1-e)$\sqrt[3]\frac {m_2}{3(m_1)}$

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  • $\begingroup$ Ah i thought the units are computed automatically? Sorry. $\endgroup$
    – Zadai.Fehbiab
    Commented Apr 24 at 18:50
  • $\begingroup$ Now i converted everything to Jupiter masses and i have the same result. $\endgroup$
    – Zadai.Fehbiab
    Commented Apr 24 at 18:50
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    $\begingroup$ @Zadai.Fehbiab - if you've changed what your computation was, please update your question to match. $\endgroup$
    – jdunlop
    Commented Apr 24 at 20:20
  • $\begingroup$ Okay so i updated it. As far as I'm aware 12 Jupiter Masses is still considered a planet, 13 J.M enters the Brown dwarf territory? $\endgroup$
    – Zadai.Fehbiab
    Commented Apr 25 at 7:01
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The Gas Giant should have a hill sphere of 0.15627750286244 Astronomical Units. But that seems very large.

Your planet is 12 Jupiter masses in size... it is very large! It probably counts as a small brown dwarf... GU Piscium has a similar mass, for example. Your "planet" masses about as much as the whole of the solar system excluding the Sun.

Anyway, I get the same Hill radius that you did, so your calculation is probably correct.

And if i place a body in 0.1 AU Distance of the Planet, it will quickly leave its orbit.

The wikipedia article on the subject says "Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term; it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius".

Try placing the body at .5 AU instead.

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  • $\begingroup$ Good advice. I was thinking that a distance of 0.666 of the Hill Sphere was too far from the planet. $\endgroup$
    – M. A. Golding
    Commented Apr 25 at 3:04

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