Civilization Springs, 5/5

I repeat: we are looking for the most likely alignment. Yes, at almost every turn of the argument the question is appropriate: “Is it possible the other way around?” And the answer will usually be: “Yes, it is possible. But the first option is considered the most common today. ”

Let's start with biochemistry. If we accept at all that the basis of the mind there is life, and the basis of life is chemistry, then this chemistry works much better in a liquid solvent. Molecules are close to each other. Free shuffle. And if the solvent is “good,” it also stabilizes the “right” molecules. Therefore, we need liquid. What are the candidates?

Let's look at the chemical composition of the universe:


^{(According to [ 990 ])}

In order of prevalence, which chemical compound of these elements is made first? Right. Water. H ₂ O. It is made of the first and third most common element. The following is methane CH ₄ , twice as rare. Then ammonia is NH ₃ , but in nature it is already 6 times less than water. Yes, of course, this is “an average for the hospital,” individual planets may differ in chemical composition. But, except for the loss of hydrogen, rather nontrivial assumptions are required to substantiate the planet, where, say, there will be more nitrogen than oxygen. The universe, in general, is fairly uniform in composition. And the water in it - the most common chemical compound. It is rather surprising that sometimes there are still places where there is almost no water ...

In addition to the prevalence, water has a number of advantages over the top ten alternative candidates. These are: high chemical stability; strong hydrogen bonds; existing, but moderate polarity, leading to the ability to dissolve a huge amount of substances without destruction and to support acid-base reactions; high heat capacity and heat of evaporation, increasing the temperature stability of water bodies; transparency; and, finally, the fact that water ice is lighter than liquid, due to which water bodies freeze to the bottom in winter less often.

Therefore, the most likely solvent "for them" is water.

The word "solvent" means a liquid state. This means that the average temperature on the surface of the planet should not be below at least 250 Kelvin. And where does the upper limit of 400 K come from? It is determined by the stability of carbon compounds. Why carbon? From the same considerations as with water. Yes, not only carbon is able to form complex polymers, "interleaved" by other elements. Boron, phosphorus, silicon-oxygen bundle, and even a number of metals can do this:



However, carbon hits them by the frequency of occurrence hundreds and thousands of times, leaving the “boron life” unless it is a completely exotic niche.

Since we are here, we will understand one more thing. What is the most common volatile compound that does not include hydrogen? The plate suggests: this is carbon dioxide CO ₂ . Of course, its specific content in one atmosphere or another (like gas) or bark (in the form of carbonates) cannot be called just like that. But it is extremely difficult to imagine a planet with a non-hydrogen atmosphere and normal temperature, where carbon dioxide (bound or free) would not exist at all. At least 0.01% should be found.

And this is important. For the prevalence of carbon dioxide in nature imposes an upper limit on the density of the atmosphere. Starting from a certain thickness, the atmosphere, where there is at least a bit of CO ₂ , will start not only to overheat due to the greenhouse effect. It will start to expel bound CO ₂ from the bark and, thus, warm up with overclocking. Something like Venus. It is hard to say at what pressure exactly this happens, and everything depends on a lot of parameters. But we are most likely talking about hundreds of atmospheres.

So, the atmosphere of the planet is not thick, like that of a giant. But not too thin. Because, if the pressure is substantially less than 0.1 atmospheres, the temperature range of the existence of water in a liquid form sharply narrows.

In the case of an atmosphere of moderate thickness, the temperature regime is largely determined by solar illumination. This means that the planet orbits around a star at a distance where natural sunlight illuminates the temperature at about the same 250-400 Kelvin. In the so-called "habitable zone" ^{[ 948 ]} .

But water, methane, ammonia and other "ices" poorly condense in vacuum at temperatures of 250 K and above. Consequently, in the region of the formation of the planet there will be few of them, and they will not become the predominant components of its composition. This means that “their” planet is formed from more high-boiling substances: metals and “stones”, i.e. oxides (and possibly carbides) of the ten most common elements listed above. From here we approximately know the density of its substance.

Further, a habitable planet with chemical evolution must maintain active tectonics for billions of years. Because otherwise the climate of the planet with water and CO ₂ in the atmosphere falls into an “ice ball” and / or Mars-like state. The Moon and Mars in the Solar System have been (almost) dead long tectonically. But the Earth and Venus - no. Hence, the lower limit of the diameter of the planet passes somewhere between Mars and Venus. By the eye of thousands so 8 kilometers. Yes, an excess amount of radionuclides can provide warming up and activity and a much smaller body. But this is a slightly less likely solution. Because the amount of radiogenic heat is proportional to the first degree of mass of the planet, and the accretionary and heat of differentiation is square. That is, “on average in nature” it is easier to ensure the activity of the subsoil with a greater mass than a greater concentration of radionuclides. And yes, of course, the planet, which is a satellite of some giant, may well be warmed up by tidal effects (like Io), but we haven’t really found the exolun yet, so this variant is unlikely to be typical.

The upper limit of the size is determined by the transition to gigantism. Above some mass, retention (or even capture) of hydrogen and helium begins, and at the output we get Neptune or even Jupiter. Estimates of the mass at which this happens vary, I saw numbers from 2 to ~ 10 terrestrial masses, but the exact upper limit, as we shall see, is not that important. So just take the upper radius of our 2, i.e. 13 thousand kilometers.

Well, the last. Knowing the approximate chemical composition ("stones" with metals) and size, you can estimate the density of the planet, taking into account the compression. There will be about 4000-9000 kg / m ³ .

^{Article written for the site https://habr.com . When copying please refer to the source. The author of the article is Evgeny Bobukh . B: 1KhPVPHw4XrxtuocDiBbh7KVSJ6nDTHtMq; E: 0x3d174b521004B08023E49C216e4fa2f67868210F; L: LZ3bFQHUxBAtpgxcNSfwv61LiwZVx3EGoo}

Recall the expression for the first cosmic velocity: V ₁ ² = GM _p / R. Expanding the mass of the planet M _p , we get V ₁ ² = (4 π / 3) GρR ² .

Next, what is u ? In a chemical rocket, it is no larger than √2 q , where q is the heat of combustion of the most high-energy chemical fuel. This implies:

V ₁ ² / u ² > (4 π / 3) GρR ² / q [10]

Now, remember that it happens on the planet. And the planet is such a thing, which cannot be shaped like a suitcase or a snowman, unlike the asteroid Ultima Thule ^{[ 950 ]} . For even if it somehow takes on this form in a catastrophic way, the material of the planet will immediately “float” under the pressure of its own weight and return to a spherical state. This property, in fact, is the key part of the definition of the planet ^{[ 960 ]} : "<...> the body <...> is massive enough to have a spherical shape under the influence of its own gravity <...>".

For example, the pressure in the center of the earth is ^{[ 970 ]} 3.5 * 10 ¹¹ pascal. This is much higher than the ultimate strength ^{[ 355 ] of the} most persistent minerals - for whatever reason, all of them in the depths of the planet behave more like viscous liquids than like solid substances.

Let us introduce into circulation the dimensionless "planetary coefficient" P , equal to the ratio of pressure in the center of the planet to the ultimate strength of the materials composing the planet:

P = p / σ [15]

For Earth, P is about 1700, for Mars - 250, and even for the Moon - about 45. In general, for large, tectonically active planets (regardless of composition) P > ≈ 1000-3000.

It remains a mere trifle: write a formula for pressure in the center of the planet. In the first approximation, it is estimated as p ≈ ρgR / 2 , where ρ is the density of the planet, and R is its radius. Substituting here g = GM / R ² and M = (4 π / 3) ρR ³ we get:

p ≈ (2 π / 3) Gρ ² R ² .

Wow! And this is very similar to the formula [10]. Almost the same factors. What if to combine? It turns out:

V ₁ ² / u ² > 2 p / ( ρq ) [20]

But p is tied to the "planetary coefficient". Namely, p = σP. Substitute and this:

V ₁ ² / u ² > 2 Пσ / ( ρq )

Rewrite a bit:

V ₁ ² / u ² > 2 П * ( σ / ρ ) / q

( σ / ρ ) is the Spring Limit of the energy content of matter. Being realized, however, if we substitute here the most durable materials like graphene. Real rocks are softer and less energy content will be. Let K times. That is, for real planets ( σ / ρ ) is the Spring Limit divided by K. What is q ? The same energy content of the best chemical fuel! Equal ... Spring Limit! The two Spring Limits are shortened, and it remains:

V ₁ ² / u ² > 2 P / K

K for typical stone materials is 100-1000. P at the major planets - from thousands and tens of thousands. Therefore, on most tectonically active planets with an atmosphere, the first cosmic velocity is significantly higher than the maximum speed of the outflow of a chemical engine.