The Physics of the Universe - Difficult Topics Made Understandable

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A Few Random Facts

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Luke Mastin

A Few Random Facts

Index of Random Facts:

Here is a selection of interesting statistics and snippets of physics information I picked up along the way. Most are in some way related to the topics discussed here; some are a little off-topic, but nevertheless fascinating. I have grouped them together under general question headings.


A precocious child might write his or her full address as Main Street, Toronto, Canada, the Earth, the Solar System, Orion Arm, the Milky Way, the Local Group, the Virgo Supercluster, the Universe.

The Solar System consists of the Sun and those objects bound to it by gravity (the terrestrial planets, Mercury, Venus, Earth and Mars; the gas giants, Jupiter, Saturn, Neptune and Uranus; and various dwarf planets, proto-planets and asteroids). However measured, it is less than a light year across.

The Milky Way galaxy is a barred spiral galaxy with a diameter of about 100,000 light-years and containing about 200 billion stars. Our Solar System is located towards the edge of one of the Milky Way's outer spiral arms, known as the Orion Arm or Local Spur, about 25,000 to 28,000 light years from the galactic centre.

The Local Group is a small group or cluster of gravitationally-bound galaxies, which includes the Milky Way, the Andromeda galaxy and the much smaller Triangulum galaxy, along with smaller satellite and dwarf galaxies such as the Large Magellanic Cloud, the Sagittarius Dwarf Galaxy and Canis Major Dwarf Galaxy.

The Virgo Supercluster is an irregular group of clusters of galaxies, between 100 and 200 million light years in diameter, which incorporates our Local Group of galaxies and about 100 other clusters. The Local Group is located in a small filament on the outskirts of the supercluster. It is thought that superclusters may also be arranged in even larger structures called walls (such as the Sloan Great Wall, which is about 1.5 billion light years long), although these may not be true structures as their parts are not gravitationally bound together.

The universe is what we usually think of as the totality of known or supposed objects and phenomena throughout space. The observable part alone contains over ten billion trillion stars arranged in about 100 billion galaxies, and is estimated to be around 156 billion light years in diameter. By definition, we are at the centre of our observable universe, but it is totally unknown where we are in the universe as a whole.


A person on the equator is rotating around the Earth at about 1,660 kilometres per hour. A person at the north or south pole actually has a rotational speed of zero, and is effectively turning on the spot. Somewhere in between, a person’s rotational speed decreases as they move from the equator towards the pole: for example, a person in Toronto, at around 45°N, is travelling about 1,230 kilometres per hour.

Actually, rotational speed around the Earth is also dependent on altitude above sea level, and a person at the top of a mountain on the Equator is actually travelling faster than 1,660 kilometres per hour (as he has further to go with each revolution). Taking this to an extreme, an object in geostationary orbit around the Earth at an altitude of about 36,000 kilometres above the ground has to travel at about 11,000 kilometres per hour.

But that is not all. The Earth circles around the Sun at about 107,000 kilometres per hour. Our Solar System is rotating around the Milky Way galaxy at about 700,000 kilometres per hour. The galaxy is also travelling at huge speed away from every other galaxy as the universe continues to expand, although with vastly differing relative speeds depending on the distances of the galaxies from us. To give some indication, scientists have calculated that our galaxy is travelling at about 2.2 million kilometres per hour relative to the cosmic background radiation which pervades the universe.


The reasoning used by Rømer in 1675 to determine the speed of light - click for larger version
(Click for a larger version)
The reasoning used by Rømer in 1675 to determine the speed of light
(Source: U. of Califormia Lectures:
Light travels at exactly 299,792,458 metres per second in a vacuum (about 300,000 kilometres per second or just over 1 billion kilometres per hour). As a comparison, sound waves travel at a paltry 343.14 metres per second (about 1,235 kilometres per hour), almost a million times slower than light waves, and the fastest military airplane, the SR-71 Blackbird, can fly at about 980 metres per second (about 3,500 kilometres per hour).

At that speed light takes:

  • 0.0000033 seconds to travel 1 kilometre;
  • 1.3 seconds to reach us from the Moon;
  • 8.32 minutes to reach us from the Sun;
  • 4.37 years to reach us from Alpha Centauri, the nearest star system to the Solar System (Alpha Centauri is therefore said to be 4.37 light years away);
  • 26,000 years to reach us from the centre of our Milky Way galaxy;
  • 2,500,000 to reach us from the Andromeda Galaxy, our next nearest galaxy (and the most distant object visible to the naked eye, although only as a barely perceptible smudge);
  • 59 million years to reach us from the Virgo Cluster, the nearest large galaxy cluster;
  • and, theoretically, about 78 billion years to reach us from the edge of the observable universe (this is actually longer ago than the 13.7 billion year age of the universe, because the continued expansion of space has significantly increased the distance the light from these early objects has had to travel).

Earth’s atmosphere is divided up into several layers: the troposphere from about 6 - 20 kilometres up; the stratosphere from 20 - 50 kilometres; the mesosphere from 50 - 85 kilometres; the thermosphere from 85 - 690 kilometres; and the exosphere out to about 10,000 kilometres. “Space” is often considered to start at about 100 kilometres up, known as the Kármán line, where the Earth's atmosphere becomes too thin for aeronautical purposes. The International Space Station orbits the Earth about 350 kilometres up (in the thermosphere).

The Moon is about 360,000 kilometres away from the Earth (and it is receding from us at a rate of about 4 centimetres a year as its orbit gradually speeds up). The nearest planet to the Earth is either Venus, which varies between 42 million kilometres and 258 million kilometres away (its orbit is highly irregular), or Mars which varies between 56 million kilometres and 100 million kilometres away. The Sun is about 150 million kilometres away from the Earth (sometimes referred to as 1 astronomical unit, or 1 AU).

The next nearest star to us (other than the Sun) is Proxima Centauri, in the Alpha Centauri star system (still part of our Milky Way galaxy), which is about 40 trillion (40,000,000,000,000) miles away or, using the more convenient unit based on the distance light travels in a year (which is about 9.46 trillion kilometres), 4.24 light years. Sirius A and B, in the Sirius star system, are about 81 trillion (81,000,000,000,000) kilometres or 8.58 light years away.

The centre of the Milky Way galaxy is about 26,000 light years, or roughly 246 quadrillion (246,000,000,000,000,000) kilometres. Our next closest galaxy is the Andromeda Galaxy, which is about 2.5 million light years away, or roughly 24,000,000,000,000,000,000 kilometres. The best estimate of the size of the observable universe (given that it has been expanding for 13.7 billion years), is about 93 billion light years (880,000,000,000,000,000,000,000 kilometres) across.


Picture of a distant part of the universe by the Hubble Space Telescope - click for a larger version
(Click for larger version)
Picture of a distant part of the universe by the Hubble Space Telescope
(Source: Hubble Site:
About 3,000 stars are visible to the unaided eye on a clear moonless night. About 100,000 stars can be seen using a small telescope. There are an estimated one hundred billion (100,000,000,000) stars in our own Milky Way galaxy, although some estimates range up to four times that many, much depending on the number of brown dwarfs and other very dim stars.

A typical galaxy may contain anywhere between about ten million and one trillion stars. Therefore, using a very rough estimate of a hundred billion galaxies in the observable universe, and the number of stars in our own galaxy as a reasonable average, there may be around ten billion trillion (10,000,000,000,000,000,000,000 or 1022) stars in the observable universe, or quite possibly anywhere up to 1024.


The nuclear fusion process in the sun - click for a larger version
(Click for a larger version)
The nuclear fusion process in the sun
(Source: U. of Berkely:
The Sun, or any star for that matter, “shines” or “burns” due to a process of thermonuclear fusion, not due to a chemical reaction like the oxygen-driven fires on Earth.

Because the Sun is so massive, it has great gravity and so its core is under tremendous levels of pressure and heat. This pressure and heat is so high in the Sun’s core (about 15 million °C) that the protons of the hydrogen atoms which largely make up the Sun collide into each other with enough speed that they stick together or “fuse” to create helium nuclei. It effectively takes four hydrogen nuclei to fuse together to produce one nucleus of helium, although it is actually a more complicated three-part process (hydrogen to deuterium, deuterium to helium-3 and helium-3 to helium).

However, the net mass of the fused helium nuclei is actually slightly smaller than the sum of the masses of its constituent hydrogen atoms, and this tiny amount of lost mass is converted into an enormous amount of energy, according to the mass-energy equivalence relationship E = mc². To give an idea of the scale of this process, each second of every day our Sun converts about 700 million tons of hydrogen into about 695 million tons of helium. The missing 5 million tons is converted into energy equivalent to the detonation of about 100 billion one-megaton bombs, two hundred million times the explosive yield of every nuclear weapon ever detonated on Earth. And this happens every second.

The fusion process therefore releases huge amounts of energy, initially as gamma ray photons, that traverse the interior of the Sun through a combination of radiation and convection, and are then radiated into space as electromagnetic energy, including visible light. The process also emits particle radiation, known as the “stellar wind”, a steady stream of electrically charged particles, such as free protons, alpha particles and beta particles, as well as a steady stream of neutrinos. It is the internal pressure of this nuclear fusion process that prevents the Sun from collapsing further under its own gravity (known as a state of hydrostatic equilibrium).

Hydrogen is by far the most common element in the Sun (and in the universe as a whole) and helium is the second most common. A star will spend most of its life, called the “main sequence” phase, fusing hydrogen into helium, but, in larger hotter stars, the helium which accumulates in the core becomes more and more compressed and hot until the helium atoms begin fusing to form oxygen and carbon. These stars are therefore continually creating heavier elements from the less heavy: helium from hydrogen, oxygen from helium, and so on and so on. Even in the largest of stars, however, this process stops at the ultra-stable element iron, which will not easily fuse to form heavier elements, at which point the inward pressure of gravity takes over, crushing the core and resulting in a supernova explosion and the creation of a neutron star or black hole.


There are several different main types of stars, depending on their size, luminosity and lifespan:

    Evolution of high and low mass stars - click for larger version
    (Click for a larger version)
    Evolution of high and low mass stars
    (Source: RedOrbit:
    - Credit: Thomas Learning)
  • brown dwarfs - "failed stars", which form from clouds of interstellar gas, as other stars do, but never reach sufficient mass, density and internal heat to start the nuclear fusion process (i.e. less than 8% of the mass of our Sun). Although they may glow dimly when newly formed (and are therefore in fact red not brown), they start to cool soon after and so are very difficult to spot. They may actually be among the most common type of stars.
  • red dwarfs - small and relatively cool stars, bigger than brown dwarfs, but less than 40 - 50% of the mass of our Sun. Most of the stars in our galaxy (excluding possible unseen brown dwarfs) are red dwarfs. They are much dimmer than our Sun (even the largest red dwarf has only about 10% of the Sun's luminosity), burn much more slowly, and typically live much longer.
  • yellow dwarfs - main-sequence stars like our own Sun, Alpha Centauri A, Tau Ceti, etc, typically about 80 - 100% of the size of the Sun, and actually more white than yellow. They are also known as G V stars for their spectral type G and luminosity class V.
  • white stars - bright, main-sequence stars with masses from 1.4 to 2.1 times the mass of the Sun and surface temperatures between 7,600°C and 10,000°C, such as Sirius A and Vega.
  • red giants - luminous giant stars of low or intermediate mass (usually between 0.5 and 10 solar masses) in a late phase of stellar evolution, such as Aldeberan and Arcturus. When a main-sequence star has fused all its hydrogen into helium, it then starts to burn its helium to produce carbon and oxygen, and expands to many times its previous volume to become a red giant. After a relatively short time (in the region of two hundred million years), the red giant puffs out its outer layers in a gas cloud called a nebula and collapses in on itself to form a white dwarf. The largest red giants are known as red supergiants, and are the largest stars in the universe in terms of volume (well-known examples are Antares and Betelgeuse).
  • white dwarfs - small, dense, burnt-out husks of stars, no longer undergoing fusion reactions, and representing the final evolutionary state of most of the stars in our galaxy. When a red giant has used up its helium to produce carbon and oxygen, and has insufficient mass to generate the core temperatures required to fuse carbon, it sheds its outer layers to form a planetary nebula, and leaves behind an inert mass of carbon and oxygen. A white dwarf is typically only the size of the Earth, but 200,000 times more dense.
  • black dwarfs - hypothetical stellar remnants created when a white dwarf becomes cool and dark after about ten billion years of life. Black dwarfs are very hard to detect, and very few would exist yet anyway in a universe only 13.7 billion years old.
  • blue giants - bright, giant stars, between 10 and 100 times the size of the Sun, and between 10 and 1,000 times its luminosity. Because of their mass and hotness, they are relatively short-lived and quickly exhaust their hydrogen fuel, ending as red supergiants or neutron stars. The biggest and most luminous stars are referred to as blue supergiants and hypergiants. The best known blue supergiant is Rigel, the brightest star in the constellation of Orion, which has a mass about 20 times that of the Sun and a luminosity more than 60,000 times greater. The biggest and brightest ever found is 10 million times as bright as the Sun.
  • neutron stars - stellar remnants that can result from the gravitational collapse of massive stars during a supernova event. They are composed almost entirely of crushed neutrons, and are very hot and very dense. Although a typical neutron star has a mass of only between 1.35 and about 2.1 times that of our Sun, it is 60,000 times smaller than the Sun (usually in the region of just 20 - 30 kilometres across) and, because of this huge density, has a gravity of over 200 billion times that we experience on Earth. They rotate very fast (especially soon after the supernova explosion) and some emit regular pulses of radiation and are known as pulsars. Smaller collapsed stars will usually become white dwarfs, and larger ones (over about 5 solar masses) will collapse completely into a black hole singularity.
  • variable stars - stars that grow and shrink in size periodically and appear to pulsate. The changes in apparent brightness may be due to variations in the star's actual luminosity, or to variations in the amount of the star's light that is blocked from reaching Earth.
  • binary stars - two stars in close proximity which orbit around their common centre of mass. In fact, the majority of stars are part of binary, triplet or multiple star systems, and well-known examples are Sirius in the Canis Major constellation and Alpha Centauri.

Periodic Table of Elements - click for larger version
(Click for a larger version)
Periodic Table of Elements
(Source: Wikipedia:
The human body is made up of elements in the following approximate proportions (by weight): 65% oxygen, 18% carbon, 10% hydrogen, 3% nitrogen, 2% calcium, 1% phosphorus, and 1% other elements such as potassium, sodium, iron, zinc, etc. By the number of atoms, however, the proportions are: 63% hydrogen, 24% oxygen and 12% carbon, with only tiny traces of the others.

The earth’s crust is made up (by weight) of: 46% oxygen, 27% silicon, 8% aluminium, 5% iron, 4% calcium, 2% sodium, 2% potassium and 2% magnesium, plus traces of the other 84 naturally occurring elements. The air we breathe contains roughly (by volume): 78% nitrogen, 21% oxygen, 1% argon, 0.038% carbon dioxide, and trace amounts of other gases.

The Sun is composed of: 75% hydrogen, 24% helium and 1% oxygen, with tiny traces of carbon, neon and iron. In fact, hydrogen and helium are estimated to make up roughly 74% and 24% respectively of all the matter in the universe as a whole, along with tiny amounts of oxygen (1.07%), carbon (0.46%), neon (0.13%), iron (0.109), nitrogen (0.1%), silicon (0.065%), magnesium (0.058%) and sulphur (0.044%).


Each cubic metre of air on Earth contains about 10 trillion trillion molecules. This falls to around 4 trillion trillion at the top of Mount Everest. A hundred kilometres up, sometimes considered to be the border of space, there are around a million trillion molecules per cubic metre. At the International Space Station, roughly 350 kilometres away, there are only around 10 trillion.

100,000 kilometres from the Earth (over a third of the way to the Moon, where there is absolutely no influence from the Earth’s atmosphere), there are around seven million particles per cubic metre. At the edge of the Solar System, the density is down to about a thousand atoms per cubic metre. In intergalactic space, there are only about ten atoms per cubic metre of space.


If the history of the universe were compressed into a single year, with the Big Bang occurring at 12:00am on January 1st:

  • the very first stars and galaxies formed at about 7:00am on January 8th;
  • our Sun was born at about 8:00am on September 1st and the Earth at about 2:00am on September 11th;
  • the earliest life on Earth occurred at 1:00pm on September 30th, although the first multi-cellular life did not appear until 11:00pm on December 14th;
  • dinosaurs appeared on Earth at 3:00am on December 27th and died out just 3 days later at 10:00am on December 30th;
  • the first humans arrived as late as 11:39pm on December 31st;
  • the philosophers of ancient Greece flourished about 5 seconds before midnight on December 31st and everything since Columbus “discovered” America happened within the last second of the year.

On the same scale:

  • our Sun will become a red giant star, burning up the Earth in the process, next May 2nd at around 4:00pm, and around the same time, our nearest galactic neighbour, Andromeda, will start to crash into our own galaxy;
  • by 1:00pm on May 7th the Sun will have become a cold, dead white dwarf star.

Absolute zero, the temperature at which thermal energy is theoretically zero and which is therefore generally considered the coldest possible temperature, is -273.15°C Celsius (or 0°K on the absolute Kelvin scale). The cosmic microwave background radiation which uniformly permeates all of space has a temperature of 2.725°K, or around -270°C.

Within the Solar System, the average temperature on Pluto is around -235°C, on Neptune around -220°C, on Uranus -210°C, on Saturn -184°C and on Jupiter -153°C. The temperature on Mars varies between about -87°C and -5°C, with an average of around -46°C. The lowest natural temperature on Earth (recorded at Vostok, Antarctica in 1983) is -89°C; the highest surface temperature on Earth (recorded at Al 'Aziziyah, Libya in 1922) is 58°C; the mean overall temperature on Earth is 14°C.

Water at standard pressure on Earth freezes at 0°C, and boils at 100°C. Lead melts at around 328°C, iron at 1,535°C, titanium at 1,668°C, and carbon in the range of 3,550°C to 3,675°C depending on the type. The temperature of an incandescent light bulb is round 2,200°C. A lightning bolt can reach 28,000°C. The temperature in a working fusion reactor is around 100 million °C. The highest man-made temperature, about 2 billion °C, was generated by the so-called Z-Machine at the Sandia National Laboratories in Albuquerque, New Mexico.

Continuing through the Solar System, the mean daytime temperature on the Moon is 107°C, while the mean nighttime temperature is -153°C. The temperature on Venus is a relatively uniform 462°C. The surface temperature on Mercury varies between 466°C on the sunward side and -184°C on the other side. The surface of the Sun has a temperature of about 5,700°C, and the core of the Sun about 15 million °C (although the temperature in the Sun’s corona can rise to over 2 million °C).

Red dwarf and red giant stars typically have surface temperatures in the range of 2,500°C to 3,500°C. Blue supergiant and hypergiant stars have surface temperatures ranging anywhere from 3,500°C to 35,000°C. The explosion of a supernova can generate temperatures in excess of 100 billion °C. The Planck Temperature is the temperature of the universe at 1 Planck Time after the Big Bang, and is considered the de facto maximum possible temperature. It has been calculated to be approximately 1.4 × 1032°C (140,000,000,000,000,000,000,000,000,000,000°C).


The electromagnetic spectrum - click for a larger version
(Click for a larger version)
The electromagnetic spectrum
(Source: Wikipedia:
The electromagnetic spectrum is the range of possible electromagnetic radiation frequencies. They are usually described in terms of either their wavelengths (the distance between waves) or their frequency (the number of waves per second). From high to low wavelengths (low to high frequencies), the spectrum covers:

  • radio waves - wavelengths ranging from about 1,000 metres down to about 1 metre, roughly on the scale of buildings and people, with radio and television frequencies ranging from AM radio at about 1,000 to 100 metres, and FM radio at about 10 to 1 metres;
  • microwaves - wavelengths of between 1 metre and 1 millimetre (or 0.001 of a metre), roughly on the scale of people and insects;
  • infrared - wavelengths from about 1 millimetre down the edge of visible light at about 750 nanometres (or 0.00000075 of a metre), roughly the size of the point of a needle;
  • visible light - wavelengths of about 750 nanometres (0.00000075 of a metre) down to about 400 nanometres (0.0000004 of a metre), roughly the size of cells, following the familiar colour spectrum of red, orange, yellow, green, blue, indigo, violet;
  • ultraviolet - wavelengths of 400 nanometres (0.0000004 of a metre) down to 10 nanometres (0.00000001 of a metre), roughly the size of molecules;
  • x-rays - wavelengths of 10 nanometres (0.00000001 of a metre) down to 0.01 nanometres or 10 picometres (0.00000000001 of a metre), roughly the size of atoms;
  • gamma rays - wavelengths below 10 picometres (0.00000000001 of a metre), roughly the size of atomic nuclei.

While it might seem obvious what a planet is, the definition has become more complex since 2006 when the International Astronomical Union voted to reduce the status of Pluto (discovered in 1930 and considered a planet ever since then) to dwarf planet, so that it is officially no longer the ninth planet in the Solar System.

Under the new definition, a planet has to be large enough that its gravity forces it into the shape of a sphere (smaller, oddly-shaped asteroids therefore do not qualify); it has to be orbiting a star, and not a satellite of another planet (several moons in the Solar System are bigger than Pluto); it has to be not massive enough to cause thermonuclear fusion (in which case it would classify as a star); and it must have cleared its neighbouring region of planetesimals and other objects by its gravitational pull.

It was the last of these requirements that Pluto failed. Pluto is effectively part of the Kuiper Belt Objects, a wide belt of space towards the edge of the Solar System (between about 4.5 billion kilometres and 8 billion kilometres from the Sun) which contains millions of small, icy, rocky objects, of which more than 70,000 have been identified over 100 kilometres in diameter. Haumea and Makemake are two other dwarf planets in this region, and the dwarf planet Eris (which is actually larger than Pluto) is even further out, roughly three times Pluto’s distance from the Sun. Ceres, the largest object in the asteroid belt between Mars and Jupiter, is also technically a dwarf planet (which essentially means a small, more or less spherical planetoid, whose gravity is not sufficient to have cleared its local area of debris).

The distinction between dwarf planets, asteroids, meteoroids and comets is perhaps less clearly defined. Simplistically, asteroids are relatively small inactive bodies composed of rock or metals; dwarf planets are the largest asteroids; meteoroids are smaller particles of asteroids (called meteors or "shooting stars" when they burn up in the atmospere, and meteorites if they manage to penetrate to the Earth's surface); comets are mainly composed of dirt and ices rather than solid rock or metal, and tend to have dust and gas tails when close to the Sun.


Paradoxically, it is the Sun's gravity that keeps the planets in orbit around it, just as the Earth's gravity keeps the Moon and satellites in orbit around it. The reason they do not just fall into the Sun is that they are travelling fast enough to continually "miss" it.

An analogy helps to explain this: if you throw a rock out from the top of a high tower, it will travel a certain distance before curving down and hitting the Earth. Once thrown, the rock has inertia and would continue in a straight line of motion if there were not some force (gravity) pulling it down. The faster you throw the rock out, the further it travels, until eventually, if you could throw it fast enough (and assuming no air resistance), it would travel all the way around the Earth (and hit you in the back!). The rock is therefore now in orbit: it is still always falling towards the Earth, but the round surface of the Earth is falling away just as fast. Throw the rock a little faster and it would still travel around the Earth but at a higher orbit. If you could throw the rock at what is called the "escape velocity", it would break away from the gravity of the Earth completely and never fall back.

The reason the planets are travelling at just that speed which allows them to orbit the Sun (and not spiral into it or whirl away into space) is not a coincidence or evidence of divine intervention, but goes back to when the Solar System was just a spinning cloud of gas and dust. Everything that was spinning slowly was incorporated into the Sun itself under the force of gravity; everything that was spinning too fast escaped into outer space; everything else remained in orbit around the Sun and gradually coalesced into the planets, retaining its speed of spin and therefore its orbit (encountering little resistance in the near-vacuum of space).

Because the Sun and planets all formed from the same spinning nebular cloud, this is also why they all rotate in the same direction. As the nebula continued to contract under the influence of gravity it rotated faster and faster due to the conservation of angular momentum. Centrifugal effects caused the spinning cloud to flatten into a flattish disk with a dense bulge at its centre (which would coalesce into the Sun). This is why the planets orbit the Sun in a more or less flat plane, known as the ecliptic.

In a simple system, the orbit of a planet around a star would be a perfect circle, but the gravitational influence of other large bodies in the system (in our case, Jupiter and the other gas giants) perturbs the circular orbits into elliptical ones.

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