I recall vaguely that planet vegeta was supposed to have 20X earth gravity and king kai's planet 10X.
I know this is a fictional universe, and that Toriyama doesn't have much of a mind for scientific coherence or even remembering his own canon, so taking this too seriously is fraught with problems to begin with, but I became curious about how this relates to density of rocky planets and their cores and how much mass it takes to produce gravitation like this.
I don't think we've been provided with a radius or volume for the planet, which makes figuring this all out a bit difficult, but if the planet has a similar structure to other rocky planets it would have a metallic core with a solid core and possibly liquid outer core, mantle of some thickness, and an outer crust/lithosphere layer.
that outer surface rock is going to have a density that averages around 3 g/cm3, and the mantle density of earth ranges between 5.8 to 4.5 g/cm3. It would probably take a significant shift in elemental makeup or a serious increase in pressure to alter the densities for these layers, even if the planet had significantly more gravity or was larger (and thus the layers had more volume).
Its important to remember, gravity relates to the distance from the center of mass, so these outer layers, being of roughly equivalent density to earths wouldn't contribute enough mass to offset the distance they're adding, so the planet probably has a similarly thin shell of outer rock layers. Thus... all the extra mass must come from the core layers.
But what kind of material could possibly offer that much density? At earth's surface, iron has a density ~7.874 g/cm3 at room temperature and 6.98 g/cm3 at melting point. Since both the solid and liquid core layers are significantly more dense than this (approximately 13 g/cm3 and 11 g/cm3 respectively), it stands to reason that other elements or elemental mixes would also experience a significant increase in density if collected within the core of a planet in large quantities.
Even if we push the envelope and look to Osmium, the densest metal, it is only 22.6 g/cm3. If we were to take earth and straight out replace the existing scenario for a core dominated by solid and liquid osmium (ignoring for a moment the changes to the thermodynamics and likely lack of a protective magnetic field that this would create), and presume that it similarly approximately doubles in density due to the extreme pressure, you'd have a core of ~45 g/cm3 and outer liquid layer probably ~38-40 g/cm3 {bear with me, these numbers are fudged. I'm not sure this is even possible, or how a mostly osmium alloy would actually behave at these temperatures and pressures, it may well have another state that allows for higher density than what we see with iron, but as I'm not as well versed in the physical chemistry properties of elements like osmium, or its behavior under these conditions, I've not got much to go on}. With the same sized core, you'd only end up with the mass increasing by approximately a factor of 1.8, and thus the G's likewise being approximately 1.8 (as the volume/radius is still the same).
So clearly an increase in volume of the core layers or the use of something SIGNIFICANTLY denser than osmium would be necessary to make any major impact. Are we talking white dwarf matter? I'm at a loss with regard to pursuing that line of inquiry, so on to the volumes!
Sticking with these densities, if the inner solid core has a radius ~5 times larger and the outer liquid core ~ 2 times larger, with a mantle ~1.5 times larger and crust of equivalent depth, applying a multiplier for water for the ocean based on the ratio of the surface areas (even though its actually a thin volume, this is probably a good enough approximation), you get a mass almost 2 orders of magnitude higher while only being a factor of 2 larger in the radius. this still only puts us at 7.5 G. We need something denser or a planet that is absolutely VAST. We're probably already beyond the limits of what silicate based planets are capable of.
Its a shame we can't easily map this onto actual physics, but such is the nature of fiction in general, especially when its a Toriyama numbers related ass-pull.
We can also use a cop out claiming fictional dragon ball physics make things like gravity work differently, but its still disappointing that you can't make sense of it.
I'm not sure what the theoretical limit is for the density of matter at the core of a rocky planet (or even just in general, lest it form a black hole), or at what strength of gravity you'd be likely to form a star or a gas giant. 20X earth Gs might already be beyond this limit.
Any suggestions for this, or criticisms of my math? Did I calculate anything horrendously incorrectly or am I missing some material or option that might get us closer?
Edit:
here is a link to google sheet showing the math:
I know this is a fictional universe, and that Toriyama doesn't have much of a mind for scientific coherence or even remembering his own canon, so taking this too seriously is fraught with problems to begin with, but I became curious about how this relates to density of rocky planets and their cores and how much mass it takes to produce gravitation like this.
I don't think we've been provided with a radius or volume for the planet, which makes figuring this all out a bit difficult, but if the planet has a similar structure to other rocky planets it would have a metallic core with a solid core and possibly liquid outer core, mantle of some thickness, and an outer crust/lithosphere layer.
that outer surface rock is going to have a density that averages around 3 g/cm3, and the mantle density of earth ranges between 5.8 to 4.5 g/cm3. It would probably take a significant shift in elemental makeup or a serious increase in pressure to alter the densities for these layers, even if the planet had significantly more gravity or was larger (and thus the layers had more volume).
Its important to remember, gravity relates to the distance from the center of mass, so these outer layers, being of roughly equivalent density to earths wouldn't contribute enough mass to offset the distance they're adding, so the planet probably has a similarly thin shell of outer rock layers. Thus... all the extra mass must come from the core layers.
But what kind of material could possibly offer that much density? At earth's surface, iron has a density ~7.874 g/cm3 at room temperature and 6.98 g/cm3 at melting point. Since both the solid and liquid core layers are significantly more dense than this (approximately 13 g/cm3 and 11 g/cm3 respectively), it stands to reason that other elements or elemental mixes would also experience a significant increase in density if collected within the core of a planet in large quantities.
Even if we push the envelope and look to Osmium, the densest metal, it is only 22.6 g/cm3. If we were to take earth and straight out replace the existing scenario for a core dominated by solid and liquid osmium (ignoring for a moment the changes to the thermodynamics and likely lack of a protective magnetic field that this would create), and presume that it similarly approximately doubles in density due to the extreme pressure, you'd have a core of ~45 g/cm3 and outer liquid layer probably ~38-40 g/cm3 {bear with me, these numbers are fudged. I'm not sure this is even possible, or how a mostly osmium alloy would actually behave at these temperatures and pressures, it may well have another state that allows for higher density than what we see with iron, but as I'm not as well versed in the physical chemistry properties of elements like osmium, or its behavior under these conditions, I've not got much to go on}. With the same sized core, you'd only end up with the mass increasing by approximately a factor of 1.8, and thus the G's likewise being approximately 1.8 (as the volume/radius is still the same).
So clearly an increase in volume of the core layers or the use of something SIGNIFICANTLY denser than osmium would be necessary to make any major impact. Are we talking white dwarf matter? I'm at a loss with regard to pursuing that line of inquiry, so on to the volumes!
Sticking with these densities, if the inner solid core has a radius ~5 times larger and the outer liquid core ~ 2 times larger, with a mantle ~1.5 times larger and crust of equivalent depth, applying a multiplier for water for the ocean based on the ratio of the surface areas (even though its actually a thin volume, this is probably a good enough approximation), you get a mass almost 2 orders of magnitude higher while only being a factor of 2 larger in the radius. this still only puts us at 7.5 G. We need something denser or a planet that is absolutely VAST. We're probably already beyond the limits of what silicate based planets are capable of.
Its a shame we can't easily map this onto actual physics, but such is the nature of fiction in general, especially when its a Toriyama numbers related ass-pull.
We can also use a cop out claiming fictional dragon ball physics make things like gravity work differently, but its still disappointing that you can't make sense of it.
I'm not sure what the theoretical limit is for the density of matter at the core of a rocky planet (or even just in general, lest it form a black hole), or at what strength of gravity you'd be likely to form a star or a gas giant. 20X earth Gs might already be beyond this limit.
Any suggestions for this, or criticisms of my math? Did I calculate anything horrendously incorrectly or am I missing some material or option that might get us closer?
Edit:
here is a link to google sheet showing the math:
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