<p>I am planning out ideas for a science-fiction world, and I want to make sure that what I include is reasonable and mathematically sound (outside of things like FTL as that is neccessary for the story to work I know it doesn't make sense).</p>
<p>Would it be possible for a planet to be massive enough for a sattelite to be of approximate Earth size. I am thinking between 0.7 and 1.3 g, with a similar density. So a density of approximately 5.51 g/cm3.</p>
<p>So, from what I found, it would mean a radius between 4456.5 km and 8276.33 km, and a mass bwteen 2.0427816158×10^24 kg and 1.3084393744×10^25 kg. (I used a formula that would find the required mass for a sphere of a certain radius, and then tested for the gravity of said planet, to find the desired range)</p>
<p>I ask because from what I read, planets of a high enough mass tend to not be able to properly hold large moons. Which raises the question of if a planet could potentially be less than this critical mass, and still be massive enough to hold a sattelite within the described range. At least at the lower 0.7 to 1 g end of the scale.</p>
<p>And if so, what would be the required mass of the planet it is orbiting? I hope I provided enough information for this to be able to be calculated. Is there a general formula for the largest moon a planet of a certain mass could reasonably hold in a stable orbit? I also do not care if the orbited planet is telluric or a gas giant, either is acceptable.</p>
<p>Your help is much appreciated.</p>
<p><strong>Note:</strong> To clarify, I do not care about how unlikely it would be for such a moon to form, as I know it is unlikely for some large gas giants and such to capture moons, with most forming from the planetary disc. I can try to find an excuse for how it formed or was captured. I simply require answers on if a body of this size can act as a sattelite, and how massive the planet it orbits has to be for this to work. I just wanted to get this clarification out of the way so that nobody feels the need to bring it up.</p>

CC BY-SA 4.0
2023-09-18T21:38:53.703Z
"what I read, planets of a high enough mass tend to not be able to properly hold large moons."  That seems unlikely to me. Please let me know where you read this.  Also, are you aware of the [worldbuilding.se] site, where this kind of question might already have been answered
James K
CC BY-SA 4.0
2023-09-18T22:35:53.710Z
I can't find anything on that Stack Exchange that answers my question, with them largely brushing that part of the question aside. Ultimately just assuming a random mass and saying what would happen at said arbitary mass, instead of giving a way to find the minimum necessary mass to hold such a moon in a stable orbit.
DanceroftheStars
CC BY-SA 4.0
2023-09-19T01:11:37.140Z
Another problem is that big planets tend to have strong magnetic fields, which can create extremely dangerous radiation zones. So your large moon probably needs to be as far as possible from its primary, while still remaining within its Hill sphere.
PM 2Ring
CC BY-SA 4.0
2023-09-19T01:52:52.173Z
I find the idea that large planets can't hold onto large moons interesting.  I've not heard this idea before and I'd like to read about it.  Otherwise I think a planet can hold onto any size moon, Binary planets of two bodies of equal mass are stable.  So the smallest planet to hold onto an earth sized moon is an Earth sized planet.  And there is no upper bound.....
James K
CC BY-SA 4.0
2023-09-19T14:19:55.893Z
Well, technically there is an upper bound, a planet can't have a moon of a signifigantly greater mass than itself, as that would turn the main planet into a moon itself. But I get what you mean. Thank you for the help, I should create another question to ask about the radiation field to find the range of safe orbits.  A Hill Sphere is easy enough to calculate, but not sure how to do the field.
DanceroftheStars
CC BY-SA 4.0
2023-09-19T18:01:26.883Z
Determining radiation field safety will be a function of the size and strength of the field, which are themselves complex calculations. You may be interested in the particulars of [Van Allen radiation belts](https://en.wikipedia.org/wiki/Van_Allen_radiation_belt). "Safety" may also be a function of the animals/plants encountering the radiation (perhaps some have innate resistance), or countermeasures in place, such as artificial magnetic fields on the moons themselves or subterranean dwellings.
Michael Bonnet
CC BY-SA 4.0
2023-09-20T01:37:16.503Z
I made a seperate post on the radiation aspect of the system. I would not want it to be forced into subterranean dwellings, and want it to be safe for humans. So those ideas won't work. The difficulty I find with finding radiation at a certain distance, is you can't just easily do an inverse square law, as it just doesn't work like that. It makes this weird wavy torus shape. Not a sphere.
DanceroftheStars
<exoplanet><natural-satellites><mathematics>
Question regarding potential moon sizes
DanceroftheStars
# Question regarding potential moon sizes

(Asked by: username_0 on 2023-09-18)

I am planning out ideas for a science-fiction world, and I want to make sure that what I include is reasonable and mathematically sound (outside of things like FTL as that is neccessary for the story to work I know it doesn't make sense).

Would it be possible for a planet to be massive enough for a sattelite to be of approximate Earth size. I am thinking between 0.7 and 1.3 g, with a similar density. So a density of approximately 5.51 g/cm3.

So, from what I found, it would mean a radius between 4456.5 km and 8276.33 km, and a mass bwteen 2.0427816158×10^24 kg and 1.3084393744×10^25 kg. (I used a formula that would find the required mass for a sphere of a certain radius, and then tested for the gravity of said planet, to find the desired range)

I ask because from what I read, planets of a high enough mass tend to not be able to properly hold large moons. Which raises the question of if a planet could potentially be less than this critical mass, and still be massive enough to hold a sattelite within the described range. At least at the lower 0.7 to 1 g end of the scale.

And if so, what would be the required mass of the planet it is orbiting? I hope I provided enough information for this to be able to be calculated. Is there a general formula for the largest moon a planet of a certain mass could reasonably hold in a stable orbit? I also do not care if the orbited planet is telluric or a gas giant, either is acceptable.

Your help is much appreciated.

**Note:** To clarify, I do not care about how unlikely it would be for such a moon to form, as I know it is unlikely for some large gas giants and such to capture moons, with most forming from the planetary disc. I can try to find an excuse for how it formed or was captured. I simply require answers on if a body of this size can act as a sattelite, and how massive the planet it orbits has to be for this to work. I just wanted to get this clarification out of the way so that nobody feels the need to bring it up.

**Tags:** exoplanet, natural-satellites, mathematics

> **Comments:**
> **username_1**: "what I read, planets of a high enough mass tend to not be able to properly hold large moons."  That seems unlikely to me. Please let me know where you read this.  Also, are you aware of the [worldbuilding.se] site, where this kind of question might already have been answered  
> **username_0**: I can't find anything on that Stack Exchange that answers my question, with them largely brushing that part of the question aside. Ultimately just assuming a random mass and saying what would happen at said arbitary mass, instead of giving a way to find the minimum necessary mass to hold such a moon in a stable orbit.  
> **username_2**: Another problem is that big planets tend to have strong magnetic fields, which can create extremely dangerous radiation zones. So your large moon probably needs to be as far as possible from its primary, while still remaining within its Hill sphere.  
> **username_1**: I find the idea that large planets can't hold onto large moons interesting.  I've not heard this idea before and I'd like to read about it.  Otherwise I think a planet can hold onto any size moon, Binary planets of two bodies of equal mass are stable.  So the smallest planet to hold onto an earth sized moon is an Earth sized planet.  And there is no upper bound.....  
> **username_0**: Well, technically there is an upper bound, a planet can't have a moon of a signifigantly greater mass than itself, as that would turn the main planet into a moon itself. But I get what you mean. Thank you for the help, I should create another question to ask about the radiation field to find the range of safe orbits.  A Hill Sphere is easy enough to calculate, but not sure how to do the field.  
> **username_3**: Determining radiation field safety will be a function of the size and strength of the field, which are themselves complex calculations. You may be interested in the particulars of [Van Allen radiation belts](https://en.wikipedia.org/wiki/Van_Allen_radiation_belt). "Safety" may also be a function of the animals/plants encountering the radiation (perhaps some have innate resistance), or countermeasures in place, such as artificial magnetic fields on the moons themselves or subterranean dwellings.  
> **username_0**: I made a seperate post on the radiation aspect of the system. I would not want it to be forced into subterranean dwellings, and want it to be safe for humans. So those ideas won't work. The difficulty I find with finding radiation at a certain distance, is you can't just easily do an inverse square law, as it just doesn't work like that. It makes this weird wavy torus shape. Not a sphere.  

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## 0 answers

