How do you measure the mass of the universe?

[Extended materials, optional reading, free of charge.] 】

The following excerpts of two methods on how to determine the mass of the universe are not precise and for reference only.

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Calculation 1:

If the total mass of our universe is constant, obeying the law of conservation of mass, and not allowing photons with relativistic mass to escape our universe, the more the universe expands, the density of matter gradually thins, and the temperature gradually decreases, and we reach the critical point where photons escape.

Let the masses of the universe and the photon be M and m, respectively, the distance of the photon from the center of the universe is r (which is also the maximum radius allowed by the universe), and the velocity of the photon is C. Since the centripetal force required for photon motion is provided by the gravitational force between the two, it can be obtained: F=GmM/r2, F=mc2/r, M=ρV=4ρr3π/3, known G =6.67×10-11N·m2/kg2, C=2.99792458×108 m/s, the theoretically calculated critical density is ρ=5×10-27kg/m3, π=3.141592653,

The total mass of the universe M=c3 (3/4ρπG3)0.5=3.415788×1053kg,

The maximum radius allowed by the universe r = 264.5 billion light years,

We live in a universe of about 200 billion galaxies, small galaxies have billions of stars, large galaxies have about 400 billion stars, each galaxy has an average of about 200 billion stars, and the total number of stars is about 3-4 trillion. i.e. (3-4) × 1022 capsules. The value is 3×1022

The Sun in our solar system is a medium-sized star with a mass of 1.98892 times 10 to the 33rd power. According to the above, we can get that we live in it

The mass of visible matter in the universe: M1 = 5.96676 times 10 grams to the 55th power = 0.596676×1053kg.

The mass of other matter (possibly the mass of dark matter): M2 = M-M1 = 3.415788×1053kg-0.596676×1053kg = 2.819112×1053kg and the matter we can see only accounts for about 17.46% of the total matter in the universe.

The mass of other matter (possibly the mass of dark matter) accounts for 82.54% of the total mass of the universe:

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Calculation 2:

Measuring quality requires a lot of prior knowledge, and it's a lot of work to talk about it...

The first thing to do is to get the mass of the sun:

With a relatively simple calculation of Newton's laws, the approximate mass of the sun can be obtained

But other stars are different from the sun

The mass of the star can be calculated by observing the orbit, velocity, and period of the celestial body in some binary star systems and star systems with planets

But not every star can be counted like that

After observing the mass of a certain number of stars, we can get a law, which describes the relationship between mass and luminosity, and what links them together is the spectrum of the star - for example, the greater the mass of the star in the main sequence, the higher the temperature, and the type of spectrum also has corresponding characteristics - in this way, the spectrum of a star can be analyzed, the measured brightness combined with the distance calculated to deduce the absolute brightness, and then inverted according to the above law, the mass of a star can be calculated

So you get the mass of all the stars?

No, because almost all the stars we can see are in the Milky Way, and most of the stars in the Milky Way are invisible to us (the part on the other side that is blocked by the Milky Way itself), so we need to determine the structure of the Milky Way. One is to map the distribution of stars in the visible part based on observations, and the other is to extrapolate the Milky Way by observing the morphology of galaxies outside the galaxy. So we got the approximate shape of the Milky Way, which is a spiral galaxy

This gives the quality of the visible part

We can see about 40% of the Milky Way, which is large enough to use its features to infer the characteristics of the entire Milky Way, so we know that 70% of the Milky Way is made up of stars like the Sun (or even weaker), and the remaining 30% are mostly massive stars, neutron stars, black holes, and a considerable number of brown dwarfs, (and countless planets, rubble, nebulae, etc., but their masses are negligible), so we get the mass of visible matter

So you get the mass of the Milky Way?

No. By observing the orbit rate of stars at different distances, it can be seen that visible matter alone is not enough to maintain the orbit of most stars around the galactic center, and dark matter accounts for a considerable proportion. By observing the velocity at which some of the dwarf galaxies in the Milky Way cluster fall towards the Milky Way, it is impossible for them to achieve such acceleration with visible matter alone. Some of the stars that have been thrown out of the Milky Way can also provide data. Based on many observations and calculations, dark matter accounts for more than 70% of the mass of the Milky Way. Counting their masses gives you the total mass of the Milky Way

Then you can take the characteristics of the Milky Way to calculate the mass of extragalactic galaxies

In the same way as extrapolating the mass of stars according to the law, with the data of the Milky Way, you can observe the total luminosity, spectral composition, size, and orbiting speed of nearby dwarf galaxies to calculate the approximate mass of an extragalactic galaxy

Do you want to count every galaxy?

Of course not, there are hundreds of billions of galaxies in the universe. However, after considerable observations, it can be concluded that the distribution of galaxies is basically isotropic, and if you look east, you can see 100 galaxies, and if you look west, you can see 100 galaxies, and the proportion of different types is about the same. Therefore, the quality of the uncounted area can be extrapolated based on the situation of the known area. This gives the total mass of all the visible substances

What about dark matter?

This brings us to the question of the accelerating expansion of the universe. Assuming that the energy that expands space is called dark energy, and the visible mass of matter is known, then the approximate mass of dark matter can be obtained by calculating the speed of expansion, etc. (I don't know which one to calculate). The results measured today are 73% for dark energy, 23% for dark matter, and less than 4% for ordinary matter

The end result?

10^53kg, which is an estimate