Pressurization of the structure
A) Volume.
The volume of gas required to be introduced into the mega structure is:
V gas = V ellipsoid = 262,720.92164 au 3 = 8.79571 10 29 m 3
V Sun = 1.412210 27 → V gas 623 V Sun 8.12210 8 V Earth
B) Type of gas to be introduced into the De-sideribus.
The gases taken into consideration are hydrogen and helium, as both are very common in the Universe (see further on for evaluations on the availability of the gas). However, there are positives and negatives to choosing either gas.
The choice of hydrogen would decrease the waiting times of the hypothetical spectators due to a higher transmission speed of the sound waves inside it (see SECTION 4 A and SECTION 5 A) and it would be even more easily available than helium (just think that hydrogen alone constitutes approximately 71% of the mass of the entire Universe while helium constitutes “only” 25%). The only defect that could be identified in the choice of hydrogen lies in its flammability (the cloud of gas would certainly have no difficulty in generating a fire or a monstrous explosion being present, in the center of the Solar System, not only a spark, but a star whose surface burns at a temperature of 5778 K), however, as the atmosphere inside the ellipsoid would be totally composed of hydrogen and therefore there would be no oxidizing agent other than the fuel, the fire risk is negligible. A certainly safer alternative to hydrogen, as a noble gas, is helium. Also very common in the Universe (although it is less so than hydrogen), its only disadvantage is a speed of sound propagation lower than that of hydrogen.
Different gas mixtures could also be inserted, for example to make the air inside the structure breathable for humans (see SECTION 6).
C) Gas density.
The formula for the density of a gas is obtained from the real gas equation: pV=nRT (p = gas pressure in Pa; V = gas volume in m 3; n = amount of substance in moles = mM , where m = mass in grams and M = molar mass in grams per mole; R = perfect gas constant; T = absolute temperature in K) pV=nRTM → d=mV=pMRT the density of the gas depends on its temperature and its pressure. We impose the earth's atmospheric pressure as the pressure value, equal to 101325 Pa = 1 atm. The assumed temperature value, on the other hand, is equivalent to the average surface temperature of Saturn -186 °C = 87.15 K. The choice of the average surface temperature of Saturn as the temperature of the gas is due to the fact that the latter is located (with a certain approximation) at an average distance between the Sun and the boundary of the structure (actually its position is more towards the Sun than towards the boundary of the megastructure: however, let's take into consideration the average temperature of the surface of Saturn and not, for example, of Uranus given that there is a greater concentration of planets in the internal area of the Solar System than in the external area). Let's choose the terrestrial atmospheric pressure as the pressure value because if we consider a different value, the auditory apparatus of the spectators could be damaged, even seriously. If you wanted to choose a different temperature value, the speed of sound propagation in the gas would change, while if you chose a different pressure value, the density of the gas and all the calculations and evaluations that follow would change. Let's choose the terrestrial atmospheric pressure as the pressure value because if we consider a different value, the auditory apparatus of the spectators could be damaged, even seriously. If you wanted to choose a different temperature value, the speed of sound propagation in the gas would change, while if you chose a different pressure value, the density of the gas and all the calculations and evaluations that follow would change. Let's choose the terrestrial atmospheric pressure as the pressure value because if we consider a different value, the auditory apparatus of the spectators could be damaged, even seriously. If you wanted to choose a different temperature value, the speed of sound propagation in the gas would change, while if you chose a different pressure value, the density of the gas and all the calculations and evaluations that follow would change.
Now, let's calculate the density of the gas:
delium=mVellissoide=pMHeRT=1013254,0038,31487,15=559,789 g m3 =0,559789 kgm30,5597891,225=0,46 timesatmospheric, lev. sea
dH2=mVellissoid=pMH2RT=1013252,0168,31487,15=281,9 g m3 =0,2819 kgm30,28191,225=0,23 timesatmospheric, lev. sea
D) Mass of the gas.
From the density formula we can derive the necessary mass of gas:
Helium case:
melio=delioVellissoide=559.7898.795711029=4.92371032 g
= 492.370.000.000.000.000.000.000.000.000.000g
= 492.370.000.000 Yg (yoctagrams)
Hydrogen case:
mhydrogen=dihydrogenVellissoid=281.98.795711029=2.4791032 g
= 247.900.000.000.000.000.000.000.000.000.000g
= 247,900,000,000 Yg (yoctagrams)
E) Quantity of substance.
We apply the formula n=mM (where n is the amount of substance in moles, m the mass in grams and M the molar mass in grams per mol) to both gases to compare the amount of substance to be recovered in each of the two cases: nHe=4.923710324.003=1.231032 mol; nH2=2.47910322.016=1.231032 mol
F) Availability of gas.
The problem now arises of where to find such a quantity of gas.
We imagined two possible solutions. The first consists in taking the gas we need (hydrogen or helium) directly from space: we would literally have to dry up one (or more) nebulae to obtain a mass of gas sufficient to pressurize the structure.
But exactly, what is a nebula and how much gas can it hold?
Nebulae are clusters of interstellar gas and dust within which, due to the effect of gravity, the accumulation of matter often gives rise to new stars. They can have different characteristics and very different origins and are generally classified into three categories: diffuse nebulae, planetary nebulae and supernova remnants.
Let's briefly look at the characteristics of each of them:
diffuse nebulae are characterized by a cloud of gas whose density can vary, from very low to very high (as in the case of dark nebulae, so called because they are so dense as to prevent electromagnetic waves from passing through them: when observed from the Earth they appear like dark spots (the Horsehead Nebula is an example).
Planetary nebulae are formed when low-mass stars (similar to our Sun) in the final stage of their life expand and lose part of their gas, until only a small part remains: the star has turned into a so-called white dwarf .
Supernova remnants originate from the explosion of a very massive star: when the star can no longer support the weight of its own gas, it begins to compress and then explode and create a large cloud of gas.
In the light of these observations, the nebulae we are considering are the diffuse ones , as they contain the greatest amount of gas despite their density being on average lower than planetary nebulae or supernova remnants. On average, diffuse nebulae contain a mass of gas between 100 and 10,000 times that of the Sun.
mHe, solar masses=mHe, ellipsoiddemSun=4.923710322.01030=246.19 solar masses
mH2, solar masses=mH2, ellipsoiddemSun=2,47910322,01030=123,95 solar masses
In conclusion, both in the case of helium and in the case of hydrogen, it would be sufficient to drain "only" a medium-sized diffuse nebula (less than 250 solar masses of gas) to fill the structure with gas and finally make the marvelous notes of Holst to our passionate viewers. However, it is not enough to gut the nebula, it is also necessary to transport the gas from the nebula to the Solar System. Considering that the volume of gas we would need, converted into liquid for logistical reasons, would be worth
VHe, l=3.938961033 L for helium
VH2, l=3.493034951033 L for hydrogen,
we should fill, considering the average volume of a tanker, equal to approx
40,000 litres, tankers, He=3.94103340000=9.851028 tankers of liquid helium or
tankers, H2=3.49103340000=8.7251020 tankers of liquid hydrogen.
One of the closest diffuse nebulae (and most admired for its extraordinary beauty by astronomers and amateur astronomers) is that of Orion,
located in the homonymous constellation: it is 1270 light years from the Earth (which means that, if we asked our truck drivers to press on the accelerator until they reach the speed of light, it would take 1270 years to reach the nebula and as many to return.
It would therefore be necessary to organize in time to plan the pressurization works of the structure)
An alternative (attention: valid only in the case of hydrogen) could be to choose to use zero kilometer gas, producing electrolysis directly here on Earth.
The (global) formula of the electrolysis reaction is as follows:
2H2O2H2+O2
So with two moles of water you can produce two moles of hydrogen gas and one mole of oxygen gas.
Proportionally, it takes 1.231032 mol of water to produce 1.231032 mol of hydrogen. The estimated mass of water present on Earth is 1,400,000,000,000,000,000,000 kg, which corresponds to nH2O, tot=mH2O, totMH2O=1.41021(1.0082+16)=7.771019 mol. So in order to have enough water to undergo electrolysis in order to produce the gas to pressurize the structure we would need all the water present on nTerre=nH2nH2O, tot=1.2310327.771019=1.581012 Terre