How Big is the Universe?

How Big is the Universe?

For the understanding of the structure of the Universe – the outer world, or the Sky – the same role as Aristotelis system for the structure of matter was played by the Ptolemaic geocentric system of SPHERES.

According to it, the Universe reminds the well-known Russian doll – matrioshka. It is a set of moving spheres, placed one inside the other and the Earth is resting in the center of the  construction (like the egg yolk). The size of the Universe is comparable to the Earth alone.

Each sphere was considered to be solid, transparent and carrying just one attached to it planet – Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn and the sphere carrying all the rest of immovable stars.

 All spheres are circling around the Earth with less (for the Sun, the Moon and Stars) or more (for other planets) complicated cyclic regularity.

The system also included the last outer sphere – the sphere of the PRIME MOOVER – which was understood as the source of any motion noticeable at the sky.

IMPORTANT: the size of the Universe in this system is comparable to the Earth alone (!)

In the first half of 16-th century Polish astronomer, priest, doctor, fortification engineer, mathematician and amateur astronomer Nikolai Copernicus (in Polish Mikolaj Kopernik, 1473-1543) proposed the system, which mathematically looked much simpler: in his system the Sun was placed in the center and the Earth became just one of the planets with only Moon circling around it.

This system was really a problem for the Catholic Church, as it RELEGATED the Earth down to the level of one of many Planets.

Kopernik himself, being the catholic priest, understood it very well. That is why he was not in a hurry to publish his research. His book De revolutionibus orbium coelestium was published in Nuernberg (Germany) just several days before his death. It has a FOREWORD, where the author (or, probably, one of his disciples Retic) specially noted that the book contains just the description of a new mathematical approach to calculate the orbits of planets, which is much simpler than the old one, and that is all. NO REVOLUTION!

But the Chirch understood everything right and in 1616 forbid to all the Catholics to study or to teach the new system.

At the end of 16-th century the Danish astronomer Tycho Brahe (1546–1601) proposed a compromise system – with the immovable Earth at the very center, which served the center for the spheres of Moon, Sun and Stars, but the rest 5 spheres with planets are circling around the Sun. This system did not contradict to Catholic dogmas but from the mathematical point of view it preserves all the advantages of Copernicus system.

The revolution continued with the discoveries of Italian physicist, mathematician and – very important – a very good glass maker – Galileo Galilei (1564–1642).

He built very good optical tools – telescopes – which he was successfully selling to rulers, military and seamen. And he was probably the first, who used this tool to look at the sky! And immediately made plenty of discoveries.

1.    He saw mountains and planes at the surface of the Moon – they looked just like on Earth!

2.    He definitely saw that the dark parts of the Moon are simply in a shade (here You may see at the picture of shaded Moon, drawn by Halileo himself). And the light, coming from the Moon, actually is the reflection of the Sun light.

3.    Finally he saw 4 more Moons, circling around Jupiter. That was a crash for the “system of spheres”! How many more spheres we will need when we investigate the sky more thoroughly?

In 1624 a good friend of Galileo Matheo Barbierini was elected the new Pope (he took the name of Urban the 8-th), and the 60 years old Galileo made a childish mistake. Being sure that the new Pope will keep a stack hand on him, he published in 1632 in Italian language a book in defense of the banned Copernicus system: “The Dialogue about two Major Systems – Ptolemaic and Copernican”.

The result was better than could be. In 1633 he was convicted by the inquisition court not as “heretic” but as “strongly suspected in herecy” and was not burnt on fire (like Giordano Bruno several years before that), but just kept under home arrest for the rest of his years.

One year after Galileo has died (January 1642, in Arcetri, near Florence, Italy) in Lincolnshire (England) on the 4-th of January, 1643 a child was born, named Isaac, who’s destiny was to perform an ultimate revolution in physics, astronomy and mathematics.

We know this great person now as Sir Isaac Newton (1643-1727). In 1665-1666, being still a student of Trinity College in Cambridge, the 22-23-years old Isaac, inspired by lectures and ideas of his teacher of mathematics Isaac Barrow, as well as by works of Galileo, Descartes, Fermat, Huygens, Wallis and other mathematicians, has worked out the new method of mathematical computations- the differential and integral Calculus, Which in UK and USA

universities programs is usually denominated as simply “Calculus”. The strongest analytical research tool the humanity ever invented! Neither before nor after Newton. Probably this we may assume as the greatest achievement of Isaac Newton, but not the only one!

In September 1682 the exciting appearance of Galley comet in European sky raised an interest to Celestial mechanics. Edmond Galley, who calculated the period and predicted appearance of this commit proposed Newton to use his super-tool Calculus to calculate the orbits of all planets, based on available very detailed tables of observations and previously done calculations from Copernicus, Johan Kepler and others.

Newton published his results for celestial mechanics together with his general theory of motion, which we now call the Classical (Newton) Mechanics in his outstanding work “Mathematical Principles of Natural Philosophy” in 1686. Since this publication all the previous “Systems of Spheres” lost any sense.

According to Newton’s Classical Mechanics the motion of any body, having mass m. speed v and pulse p = mv is defined by the equation (2-nd Newton’s Law):

mdv/dt = dp/dt = F

where F is the integral force affecting this body from other physical bodies.

dv/dt = (v(t+dt) – v(t))/dt – is the mathematical derivative of the vector function v(t), which by itself consists of three coordinate components, each of them being also a derivative from corresponding coordinate.

vx(t) = dx/dt, vy(t) = dx/dt, vz(t) = dx/dt

Thus, knowing the coordinates and velocities of a body at some initial moment t = 0, using the equation of the 2-nd Newton’s Law and the Calculus one can precisely calculate what coordinates and velocities had or will have the body at any other moment t < 0 or t > 0, given it is known, how the acting force F depends on time and coordinates!

For Celestial mechanics Newton assumed that the force, acting between the Sun and each planet depends only on their masses and the distance between them, exactly as:

 

F(r)= Gm1m2/r2

and is directed exactly along the line, connecting their centers. Here G is the Gravitation constant, which has to be defined experimentally. Today we know that its value is

G    = 6.67•10–11 N•m2/kg2

Based on this assumption, one can precisely calculated the orbits of all planets in Solar system and find their shape (they are ellipses) and time characteristics (the period of rotation for each planets depends on its average distance r from the Sun proportional to r3/2. Everything exactly in compliance with observations and observation tables, collected by Johan Kepler and all other astronomers.

Only one question remained unclear: how the gravitation force affects the body through absolutely empty space? How it works? This question remained open until the General Relativity Theory, created by another genius Albert Einstein (1879–1955) in 1915, which we will discuss later.

Calculations based on the Newton Laws and observations of astronomers allowed to define the parameters of the Solar system and the planets in it. In short, they are listed in a table below:

       Planet    Distance from the      Year (rotation     Diameter, related   Relative mass

              Sun period around the      to the diameter of      (related to the

              (in astronomic    Sun)      Earth =  Earth mass =

              units.     In terrestrial years      12,74•103 km     6•1024 kg)

              1 a.u. = 1,5•108 km)               

0.    SUN      0     -      220 3.3•105

1.    Mercury 0.3 – 0.47     0.24       0.38       0,055

2.    Venus    0.718–0.728 0.615     0.95       0,815

3.    EARTH 1     1     1     1

4.    Mars      1.38-1.52     1.88       0.532     0.107

5.    Jupiter   5-5.2     11.86     11   318

6.    Saturn   9-10      29.46     9.14       95

7.    Uranus  18.4-20 84   3.98       14

8.    Neptune 30   164,8     3.86       17

After Newton and basing on his theory astronomers had discovered and calculated parameters of at least two new big planets (Neptune and Uranus), very many smaller planets, asteroids, comets and moons, circling around bigger planets. The complete updated list and all the interesting parameters anyone can nowadays found in reference books or on the Internet.

Just only note some peculiar facts: The mass of the Sun exceeds the Mass of the Earth approximately million times! And the total mass of all the planets in Solar system makes just 0.14% percent of the mass of the whole system. The rest 99.86% belongs to the Sun. Isn’t it reminding You about atoms and their nuclei?

On the picture to the left one may estimate the relative sizes of different planets. On the other picture the Venus planet (having approximately the same size as the Earth) is plotted over the Solar disk.

The radius of all Solar system (from the Sun to the most remote smaller planets and comets)

exceeds 5 billion kilometers (~ 35 times the distance from the Earth to the Sun). The message is:

the Solar system proved to be much bigger, than it was previously (before Newton) thought to be!

And the distances beyond the borders of the Solar system are even much-much bigger!

The distances in far space is not convenient to measure in kilometers or even in astronomical units, as it is convenient to do within the Solar system (1 a.u. = 1,5•108 km equals the average distance between the Sun and the Earth). 

Like moles are more convenient to calculate molecules, the LIGHT YEARs are more convenient to calculate distances in the Universe. 1 LIGHT YEAR is the distance, that the light passes in one year. 1 light year = 9.46•1015 m ( ~103 the diameter of the Solar system).

Even the nearest to the Sun stars are located at the distances of many light years! (The nearest one – the Proxima of Centaurus – 4.2 light years)

And the most far away known objects in the Universe are divided from us by the distances of ~ 109 – 1010 light years! The Universe is really big!

The question is: why it is so big? Or even we may put it in another way: why it HAS TO BE so big?

Let us for a while return back to molecular physics and thermodynamics. The systems of molecules, due to chaotic character of their motion, tend to go into a state with maximum possible (under this or that conditions) disorder. In physics there is a special value, that measures the degree of disorder in a system. This value has a name Entropy. 

The higher is disorder – the higher is the entropy of the system. And there is a the 2-nd Great Law of Thermodynamics, which states that any macroscopic system being taken out from the equilibrium state (means the state with maximal entropy and degree of disorder) and then left to itself (means the system is isolated from any external interference) will always change its state towards equilibrium. 

It means that the ENTROPY of the isolated system can either grow (towards equilibrium state) or remain constant (in equilibrium state, which has maximal possible value of entropy). ENTROPY is the measure of disorder of matter. The higher is the entropy – the less is the order.

If to apply the Second Great Law to the Universe taken as a whole, we may note, that

1.    The Universe is by definition the isolated system, as there is nothing beyond it, no external forces or influences are possible. According to the 2-nd Law the entropy (means

– disorder) in isolated systems MUST grow or remain constant. .

2.    Life (proteins, DNA, biological cells, living creatures and human beings) are definitely more ordered systems than any gas or liquid. It has incomparable less entropy, than the same set of atoms being dispersed (as it happens after it dies)

3.    Moreover – the Earth itself, being a complicated self-developing system, is much more ordered than a gas of atoms, from which it origins. The same we may say about the Sun and other stars. How it may happen, if the 2-nd Law of Therm. is true?

4.    The only chance: the entropy of a big system MUST only grow, but it is possible that in some small part of it the entropy may locally decrease.

5.    For existing of ordered self-organized systems (islands of order) it is necessary that they shall be surrounded by much bigger volume of disordered matter (ocean of disorder), where the excess entropy can be spread.

It means: Universe has to be BIG!

The old System of Spheres was not big enough and was thought to be very harmonious. The ORDER and HARMONY were ruling the system. Such a system cannot evolve from initial chaos by the laws of physics. It can be only created – and created directly into the final shape.

To have a chance to evolve from initial chaos and to have enough space to disperse excess quantity of entropy the Universe MUST be BIG! And MUST be from the very beginning NON-Equilibrium!