Is my planet realistic? It doesn't need to be able to support life as it's just another planet in my solar system, but is a planet with such a high density and gravity really possible? I calculated the density and gravity with the following equation:

$$\text{Gravity} = \frac{\text{Mass}}{\text{Radius}^2}$$

$$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$

And these are the values for my planet:

Mass - 0.4 Earth masses

Radius - 0.3 Earth radius

Gravity - 4.44 Earth gravity

Density - 3.54 Earth density

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    $\begingroup$ Your planet is made of gold. (The average density of Earth is about 5.5. The density of gold is 19.3, just about 3.5 times the average density of Earth). $\endgroup$ – AlexP Apr 27 '20 at 11:43
  • $\begingroup$ nice, that might actually be useful $\endgroup$ – LonelyCryptid Apr 27 '20 at 11:53
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    $\begingroup$ @AlexP tungsten - 19.25g/cm3. Very refractory, should withstand the star going a red giant without evaporating (red giant temperature: 5000K. Tungsten boiling temperature: 5555C = 5828K) $\endgroup$ – Adrian Colomitchi Apr 27 '20 at 12:15
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    $\begingroup$ @AlexP with a whole planet on supply, gold will be as cheap as dirt. Literally :) $\endgroup$ – Adrian Colomitchi Apr 27 '20 at 12:34
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    $\begingroup$ @AdrianColmitchi Wolfram is another name for tungsten $\endgroup$ – Slarty Apr 27 '20 at 15:56

I think you have made some errors in your calculations and your planet is not realistic.

Let's say the Earth has radius 1 and mass 1, then its volume is $4/3\pi R^3$ and its density $1\over 4/3\pi \cdot 1^3$$=0.24$.

Your planet with radius 0.3 and mass 0.4 would have a density of 3.54, but this would be about 15 times the density of Earth.

The average density of Earth in metric units is 5.51 $g/cm^3$, therefore your planet would have an average density of 81.6 $g/cm^3$, about 4 times the density of osmium, the densest known element.

  • $\begingroup$ You say that osmium is the densest element, but are there any compounds more dense than it, possibly due to a more tightly-packed crystal structure or something? $\endgroup$ – nick012000 Apr 28 '20 at 14:35
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    $\begingroup$ @nick012000, atomic nuclei are way denser than osmium, but when in atoms they use a whole lotta of empty space which lowers the density a lot. As far as I know there is no compound denser than osmium outside of neutron stars. $\endgroup$ – L.Dutch - Reinstate Monica Apr 28 '20 at 14:44
  • $\begingroup$ Yeah, but I mean the overall configuration of the crystal as a whole. It's possible for different configurations of atoms to have different densities; a simple cubic structure has a packing efficiency of 52%, for instance, while a face-centered cube crystal structure has a packing efficiency of 74%. $\endgroup$ – nick012000 Apr 28 '20 at 15:04
  • $\begingroup$ @nick012000 while this is true, this is already included in the density for osmium. And even if there is a denser crystal structure the difference won't be a factor of 4. $\endgroup$ – Jens Schauder Apr 29 '20 at 5:56

Density and radius are reliant on what a planet is made out of

AlexP's idea of planet made out of tungsten from the comments may be less "sexy", than gold but it is more along the right idea. There is no circumstance where only gold would accrete into a planet, but a planet that has spent a long time really close to a star can evaporate away all the lighter elements. The highest density you can get with a planet would be from one that averages about 4600-5000°C. This will boil away everything else leaving just a molten mass of Tungsten, Osmium, Rhenium, and Tantalum. If something were to then happen that pulls or pushes the planet farther away from the star, you would be left with a solid heavy metal world with a density of somewhere between 16.65-22.59 g/cm³ depending on the ratios of these 4 remaining elements. Since you won't get a purely Osmium world this way, your actual density cap is probably going to be somewhere around 20 g/cm³. (Technically a purely Rhenium planet could be 21 g/cm³ but its boiling point is so close to the less dense Tungsten that boiling off Tungsten without also losing your Rhenium is unfeasible).

Since Earth has a density of 5.51 g/cm³, this means your max density will be about 3.63 times that of Earth.

All together this means that planet at 0.3 earth radius would have 0.027 Earth volumes and a maximum mass of about 0.1 Earths and 1.11G.

If your goal is instead 4.44G you need a radius just a bit over 1.2 Earths.

A third (possible?) solution would be if this planet contained several times as many neutrons as normal matter. Since neutrons contribute mass, but no charge, you can just bind them to normal matter to increase its mass and density. Doing so would give you the dimensions you are looking for (with L. Dutch's corrections). That said, such a planet would become extremely radioactive. I'm not sure how to calculate at what point such a planet would simply become a giant nuclear bomb; so, I'm not 100% sure that this is actually viable, but it would probably be the most believable explanation of such proportions. Perhaps this scenario could be explained by the planet forming in the debris of an exploded neutron star.

  • $\begingroup$ -1 because the difference is definitely not negligible, in fact it's quite significant: the surface gravity is inversely proportional to the square of the radius. $\endgroup$ – Cassiterite Apr 27 '20 at 13:54
  • $\begingroup$ @Cassiterite ran the calculations and you are right. Removed that part from my answer $\endgroup$ – Nosajimiki Apr 27 '20 at 14:20
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    $\begingroup$ As a penance for your wrong assertion, I think it's only fair to add some calculations on what the radius should be to actually hit the 4.44g with the refractory combination of metals you proposed :) (it'll improve the quality of the answer) $\endgroup$ – Adrian Colomitchi Apr 27 '20 at 14:29
  • $\begingroup$ @Nosajimiki-ReinstateMonica Cool, I removed my downvote :) $\endgroup$ – Cassiterite Apr 27 '20 at 18:06
  • $\begingroup$ You might want to qualify it that "there are no natural circumstances"; because it is possible with unnatural ones. $\endgroup$ – Xavon_Wrentaile Apr 27 '20 at 20:57

I'm curious how you arrived at 3.54 as the density.

But here's the simple way to illustrate the problem with the number: volume is proportional to the cube of the radius. A planet twice the radius has eight times the volume.

So Density is proportional to $$Mass/Radius^3$$.

Which is pretty easy to plug in: $$0.4 / (0.3 * 0.3 * 0.3) = 14.8 $$

  • $\begingroup$ 3.54 is plainly the density of a sphere with radius 0.3 and mass 0.4. $\endgroup$ – L.Dutch - Reinstate Monica Apr 29 '20 at 6:04

If you want to check your fictional planet against actual planets, you can browse Caltech's exoplanet archive, where they have tables organized by mass, radius, and all sorts of other interesting astrophysical characteristics.

If you want a "realistic" planet, just pick one from this list and change the name :)

  • $\begingroup$ OP is not asking "how can I find a realistic planet?", but if their planet is realistic $\endgroup$ – L.Dutch - Reinstate Monica Apr 28 '20 at 8:44
  • $\begingroup$ OP can assess whether or not their planet is realistic by comparing its density to the range of densities of known planets. In spite of comments here, exoplanets have been discovered with densities as high as 77.7 +/- 55 g/cm^3. While definitely on the high end of the spectrum, OPs planet is not impossible. $\endgroup$ – awwsmm Apr 28 '20 at 8:56
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    $\begingroup$ @awwsmm, do you have the source for that? This wikipedia page says that it is one of the densest planets ever found, and its density is only 17.5 g/cm^3. $\endgroup$ – justhalf Apr 28 '20 at 11:31
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    $\begingroup$ The +/-55 means that the measurement was very poor to begin with. At a 2-sigma confidence (based on measurements alone) it seems to mean there is about a 2.4% chance it is actually no more dense than the planets I've described, but given the sample size of the 4000+ exoplanets ever recorded, it is highly expected that some planets have been mismeasured by large enough of a margin of error to yield this kind of anomaly, even if none are actually greater than the density of Osmium. $\endgroup$ – Nosajimiki Apr 28 '20 at 13:29
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    $\begingroup$ When it comes to interpreting measurements, it is important to remember to be sceptical of any measurement that defies the known principles of physics or chemistry. Otherwise, one might also argue that Kepler-100d with a density of −5.72± 6.00g/cm^3 has about a 90% chance of being a negative mass entity. It would be a truly astonishing find if it was, but I wouldn't put any money on it. $\endgroup$ – Nosajimiki Apr 28 '20 at 13:34

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