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From a Flat to a Spherical Earth
• From very early in human civilization, humans have tried to explain
the universe.
• An early Babylonian idea was that Earth was a flat stationary plate,
and the sky above was like a moving dome, or a roof enclosing earth
as a half-circle.
• Later, the ancient Greeks figured out that Earth could not be flat.
As travelers, the Greeks were navigating using the stars for
orientation. One orientation point was the North Star. They noticed
that starting out from Athens, the North star would hover just above
the horizon, but the farther they traveled north, the further it would
raise above the horizon. This could only be explained if the Earth was
round and not flat.
• They also experimented with sticks of equal length placed on
different locations on earth, for example, one in Athens and one in
Alexandria. They would place them standing in right angles to the
Earth, and measure the shadows they were throwing at one
particular date and time. They now noticed that when one stick at
one date and time threw no shadow in Alexandria, the stick in
Athens at the same date and time would have a shadow. If the earth
were flat, they should throw the same shadow; only if it was curved,
the shadows would be different.
Below: a man, living on the flat earth, under a dome
of sun, moon, and stars, try to break out of the
dome and take a look at the other side. If he goes
any further he falls down.
That the earth was flat was obvious from sense
experience: earth is experienced as flat and we
don’t fall off. That the sky was moving was also
obvious from experience, since all the objects in the
sky seem to be moving around us in a half-circle
from morning to dusk: the sun, the moon, the stars.
The Ptolemaic conception of the universe.
To different renditions, First, a Medieval: Earth is not only
in the center of the universe, it is also huge compared to
the sun and the other planets orbiting it. Second, a more
formal model illustrating the centered earth and the eight
• The Greeks had the idea that the most perfect movement had to be
• The circle was the most perfect geometrical form, so if sun, moon,
and star revolved around earth, they would do so in perfect circles.
• Ptolemy elaborated on Aristotle’s ideas, and came up with a model
of the universe, that would last for nearly two thousand years.
• In the middle we have Earth, and revolving around earth, we have
eight different spheres, that each of them control the movement of
different bodies in the sky. The sphere closest to earth would thus
account for the movement of the moon; the fourth sphere would be
the sphere of the sun; the eighth sphere, farthest away, would be the
sphere of the fixed stars.
• The universe was like an onion. In the middle, the earth, from there
you can go out layer by layer, until the eighth sphere. What was
outside the onion, nobody knew or asked about. One assumed that
this was the sphere of God and his heaven.
Problems with the
Perfect Circles
• There was problems with Ptolemy’s model. Not all bodies on
the sky seemed to move in perfect circles.
• Some bodies seemed to wander around in strange patterns,
one therefore gave these bodies the name, planetos, the Greek
for wanderer.
• One tried to account for these strange movements by adding
epi-circles to the original circles; one added a circle to the
original circle, such that the second circle had a center moving
with the original circle. ‘Strange movements’ could now be
explained by epi-circles; and if not by one epi-circle, then by
adding an extra epi-circle, creating an epi-epicircle, etc.
• Ptolemy’s model survived. And when Christianity became the
official religion in Europe, the theologians adopted the model
too, because of its simplicity and perfection.
• The circle was still regarded as perfect; and could God have
created the universe other than perfect? That the eighth
sphere was a natural boundary of the universe also fit into
Christian thinking. One had created enough space for heaven
and hell. The church liked the model, and regarded every attack
on it as heretic.
Below we still have Ptolemy’s model. Earth is in
the center, and various planets and stars are
orbiting around it in perfect circles. But we see a
modification of the model, because one has
added to the perfect circles so-called epi-circles.
Observation had shown the early physicist that
the sky was filled with so-called ‘wandering stars’
(Planetos), that were wandering forth and back
on the sky. How to solve the problem, without
destroying the idea of perfect circles? By creating
The Copernican Revolution
• The problem with the Ptolemaic model was the
peculiar epi-circular movements. One problem was – as
Copernicus understood – that every movement could be
explained by means of epi-circles, depending on how big
one made the circle and how many of them one invented
to do the job. Therefore, epi-circles were applied
dogmatically, and did not correspond to observable facts.
Secondly, because of all these epi-cicles, and epi-epicircles, etc., the Ptolemaic model had become extremely
• In physics you always seek the simplest explanation.
And Copernicus realized that placing the sun in the
center of the universe, and the planets orbiting this
center, would both be simpler, and would explain
observable fact, that before could not be explained.
• In this new ‘helio-centric’ universe, earth was no longer
stationary, and it was no longer the center of the
• Later Kepler took up the model, and refined it. but it
was not before Galileo, the idea was supported with
observable facts.
• At this point, the new model began to concern the
church, and they deemed the idea heretic, and forced
Galileo to retract his observations.
The two models below look the same, but
everything has changed from one to the other.
The first is the Ptolemaic; it is GEO-CENTRIC:
the Earth in the center, the Sun orbiting
around. The second is the Copernican; it is
HELIO-CENTRIC: Sun in the center, and Earth is
orbiting around
Newton and Gravity
• Although the trinity, Copernicus, Kepler, and Galileo had suggested an
entirely new picture of the universe, much remained unresolved. One for
example did not know why the planets were forced into these orbits around
the sun, and believed it had to be a kind of magnetic forces attracting them.
• It was not before Newton, one understood the law of gravity. According to
Newton’s law, two bodies will attract each other with a force that is
proportional to their mass, and inverse proportional to their distance. If we
have the bodies, Earth and an apple, the two bodies attract each other, but
because the Earth is enormous compared to an able, we only experience a
pull in one direction, the able falls downwards. Newton extrapolated, the
moon also ‘falls downwards,’ but because of the centrifugal force pulling it in
the other direction, it would be held in a stable orbit around earth.
• Since the gravitational force is a weak force, we don’t perceive two bodies
of similar mass attracting each other on earth. Two apples on a plate attract
each other, but not visibly.
• However, if we talk about massive objects, like moon, planets, sun, then
the attraction is significant. The pull of the gravitational force keep them in
place. Otherwise, they would just be moving in straight lines through space.
In one body’s orbit around another body, there is a balance between the
gravitational pull in one direction, and the centrifugal force in the other.
Thanks to this balance, planets orbit around stars, and moons around
• Newton’s law for Gravitational
attraction: “each body in the
universe is attracted toward
every other body by a force that
is stronger the more massive the
bodies and the closer they are to
each other.” Hawking, p. 5
• Below: two bodies with the
masses M and m. The force of
the gravitational attraction one
finds by multiplying M and m,
and the gravitational constant, G,
and thereupon divide the result
by the square of the distance
between the bodies.
Distances in the Universe: Planets, Stars, and Galaxies
• During the history of Cosmology our image of the universe has continuously been expanding. The universe not only
expends in actuality, it expands in our imagination. Historically, it was first nothing but a flat earth with a dome on top; then
it became a solar system; then a galaxy; then astronomers started to speculate on the existence of other galaxies; today we
know that our visible universe consists of 1-200 billion galaxies. We also know that this is only our observable universe and
that it must be bigger. Cutting edge cosmology speculates that there may exist an infinite number of alternative universes;
that we consequently live in a “multiverse.”
• When we measure distances in the universe, we no longer measure in kilometers, but in light-years. The distance traveled
by light in one year is a light-year. It takes the light of the sun eight minutes to travel to earth, so the sun is eight light
minutes away from us. It takes light from the star closest to our own (Alpha Centauri) about four years to travel to us, so, it
is four light-years away from us.
• If we adopt a scale where the Sun is an orange and Earth is a pinhead, the distance between the orange and pinhead is around
15 meters.
Our Address in the Universe
• In our galaxy, the Milky Way, there are billions of stars like our sun (approximately 100 billions). We assume that there
are billions of planets orbiting these stars, but we can’t detect them easily, because they are small and they don’t emit light.
• Since there are billions of galaxies in the universe, and these billions of galaxies are composed of billions of stars, around
which trillions of planets must be orbiting, astronomers seriously believe – given the huge number –that life must exist on
some of these other planets.
• Our location in the Milky Way is somewhat in the outskirts of the galaxy. It is fortunate that we are not too close to the
center, because it consists of a super-massive black hole, that ribs everything apart coming too close.
Speed of Light
• Einstein discovered that light has a speed, and it is invariable. It takes time for light
to travel. A thousand kilometers takes around 0.0033356 second, and a million
kilometers 3.3356 seconds. In other words, light travels at a speed of approximately
300,000 kilometers per second.
• Since light has an invariable speed, and we know its value, we can measure
distances by measuring the time it takes for light to travel from one event to another
(therefore, we no longer measure distances in a metrical system). In Hawking’s
illustration to the right, one sends a pulse of radio-waves (traveling with the same
speed as light) out to an object, and measure the time it takes for it to be reflected
back. Time is measured on the vertical y-axis; while distance is measured on the
horizontal x-axis. To know the distance to the object, we take the time for the pulse
to be reflected back to us, divide it by two (since it took a round-trip), and multiply
time with the speed of light. Consequently, we have the distance to the object.
• We have said that the distance from the sun to Earth is about 8 Light-minutes. This
means that the sunlight we see now is eight minutes old, or, it was emitted eight
minutes ago. It also implies that we can know nothing about the sunlight that is
being emitted in our present now. And since nothing travels faster than light, there is
no way we can know the present
• On Hawking’s illustration to the left, we have the Sun and the Earth lined up at
time 0 on the x-axis. Time 0 represents the absolute present. At time 0, we imagine
that the sun implodes and disappears; however, Earth is still unaffected, because it is
outside the light cone of the sun; it is in what Hawking calls the Elsewhere. As the
clock ticks, we move up along the vertical time axis, and after 8 minutes, we enter
the light cone of the sun, and experience what happened 8 minutes ago, that the
sun has vanished.
The Light Cone
• When we enter the sun’s light-cone, we experience the implosion, although it is
eight minutes old. It is in the so-called absolute past — that is, from our point of
view. There are light cones for as well absolute future and absolute past. They
are relative to what we decide is the present observation point. The light cone in
the figure illustrates the relations between absolute past, present, and absolute
The Future and
Past Light Cone
• When we observe
clusters, we only see
what is past. The father
away the object is, the
longer it takes for its light
to reach us, and the
further we look back into
the Past Light Cone.
• What happens in our
present, we cannot know;
we cannot know what
space is on the so-called
Hyper-Surface of the
• Relative to the Future
Light Cone of an object,
we are in the Elsewhere;
only as time passes, we
move into the light
emitted from the object.
On a Cosmological Scale we can never Know the Present
• When applying these insights to the universe as a whole, we understand that we
always only see the absolute past. The present of a distant galaxy is from our point of
view in the absolute future, and we have absolutely no access to the absolute future. In
relation to the absolute future we are in the Elsewhere. We are consequently limited to
observe the absolute past. We see only galaxies from which light has been traveling for
millions and billions of years. So, the deeper we look in the universe, the younger a
universe we see.
• There is certainly a universe of galaxies co-present to our galaxy (the so-called “HyperSurface of the Present” on figure above), but we cannot observe it, because light has not
arrived yet.
• It is also not possible to overcome that barrier and somehow take a peak at what our
co-present universe looks like, because light is a constant and it is not possible to travel
faster than light.
• When a body approximates the speed of light, it also increases in mass. This is a
consequence of Einstein’s equation: E = mc2. There is a correlation between energy and
mass; it takes still more energy to accelerate an object that will have still larger mass as
it approaches the speed of light. Near the speed of light the mass would be infinite, and
one would need infinite energy to move it.
• We can compare it to a car. If you want it to go faster, you also need to equip the car
with a larger more powerful engine, but with this you increase the mass of the car. The
faster you want the car to go, the bigger the engine has to be, but the heavier becomes
the car. Near the speed of light, you would need such a huge engine that the mass of
In order to understand the next discovery about our universe, we
must understand the doppler effect.
The doppler effect is well-known in our experience of sound.
When for example a car comes toward us, the sound of the car
increases in pitch (the sound waves are compressed), and when it
moves away, the sound decreases in pitch (the sound waves are
stretched out). As with the police-car in the example. When the
sound moves toward us (when sound-waves are compressed), the
waves are blue-shifted. When the sound moves away from us, the
waves are red-shifted.
The same is the case with light. When observing light emitted by a
star, one breaks it up into a spectrum spanning from the deep red
to the deep blue. Depending of the chemical composition of the
star, the spectrum reveal patterns of absorptions lines (i.e., patterns
of dark lines in the spectrum that indicates the presence of various
elements, such as Helium, Hydrogen, Carbon, etc.) From the
laboratory we know these patterns well enough, and from looking
at them the astronomer can quickly determine the star’s chemical
However, as in sound, there is a difference in the light spectrum
according to whether the object moves away from us, or toward
us. If it is moving toward us, the pattern of absorption lines is
‘shifted’ toward blue. If it is moving away from us, the pattern is
‘shifted’ toward red.
In 1929, the astronomer Edwin Hubble applied the notion of
the Doppler effect to his observations of galaxies. He
expected to see a random distribution of blue-shifted and
red-shifted galaxies, but observed instead that distant
galaxies are moving rapidly away from us; they were all redshifted.
Furthermore, not only were galaxies moving away, but there
was a correlation between their distance from us and their
velocity. In other words, the father away they are from us, the
faster they move away.
In the model to the right, the x-axis represents the distance
from the observer; the y-axis represents the velocity (speed)
of the galaxy. Galaxies close to us, moves away from us with
slower speeds. Distant galaxies moves away with higher
speeds. The father away a galaxy is, the faster does it also
move away. The relation is a constant (diagonal line; Hubble’s
Constant: H0 = 72)
The Universe is Expanding
from a Singularity
This observation could only imply that the universe is expanding, and more
rapidly so, the deeper we go into the universe.
The universe expands, like if you blow up a balloon, or set a raisin bread to
rise. In the form of the raisins, you have certain points representing stars or
galaxies. We choose one of the raisins to be our observation point, and in the
vicinity of that point, we follow the expansion of other raisins. When the
dough starts to raise, the raisins start to expand away from our observations
point, and the further away they are, the more they expand. On the model,
the point nearest us expands from 5 cm to 10 cm; the point farthest away
from us expands from 10 cm to 20 cm.
Understanding this logic, it did not much thinking to figure out that if galaxies
are expanding, they must at some point have been closer together than they
are now. If they are expanding today, they must have been closer together
yesterday, and still closer the day before yesterday, and so on until we find a
beginning of the expansion.
Hubble was able to calculate the rate by which they expand, that is, the
velocity of expanding galaxies. This made it possible to estimate the time it
has taken the universe to expand this far, and estimate the distant beginning
of the universe; a point called a singularity, or better known as the big bang.
The universe was no longer eternal and unchanging. It had a beginning, and it
was, and is still, constantly changing. The universe had a birth, a creation
from where it came into being.
A Model of the Universe Expanding from an
“Inflationary Hot Big Bang” Event
A model of the expanding
universe. It starts in a super-hot Big
Bang ‘explosion’ in the first fraction
of a second (T = 10-43). At this point,
there are no particle formation and
no physical forces; consequently no
physical laws.
• At T = 10-32 seconds, this big
bang singularity starts to inflate
(with a doubling time of 1
picosecond). The model illustrates
how the different forces starts to
form, first strong, then weak, the
gravitational, and how the first
particles start to form.
• Not before at around one second
after the ‘explosion,’ light elements
start to form like He, D, Li. The
exploding universe continues to
produce clouds of mass, until the
gravitational effect takes over, and
mass starts to collapse into stars
and galaxies. After around 13.7
billions years, the universe reaches
is current state.
• To the left, we have a model that depicts us in the middle, as observing the universe. The universe is
consequently all around us, and the deeper we look into the universe with advanced telescopes like Hubble,
the earlier an universe we see. With the current telescopes with can see until the blue line, the so-called
Hubble Ultra Deep Field, which approximately corresponds to the formation of the first galaxies. Further out
we have the radiation era, the Cosmic Microwave Background, and the outer periphery would represent the
Big Bang, 13.7 billion years ago. In this perspective the Big Bang is all around us. We notice that the universe
expands from the inner core, i.e., from the center of the circle, pressing the periphery outwards
• To the right, we have a model that depicts the Big Bang in the middle, therefore a ‘realistic’ model where
the universe starts in the Big Bang, then expands up till the outer periphery, which represents the present
state of the universe.
The Cosmic Microwave Background
The white noise one picks up in radios and television sets is coming from the Cosmic Microwave Background,
the universe as it had formed 400.000 thousand years after the big bang. The Microwave Background is a
plasma of high-density matter. Stars and galaxies have as yet not formed. The minute differences temperatures
(in the order of 1/10,000) can be picked up, and be depicted as in the colored map as below. These difference
will eventually end up as the differences in galaxy concentrations in our universe. The Microwave Background is
like the embryo of the universe. The existence of the Microwave Background is proof of the Big Bang theory and
the expansion of the universe.