Introduction to the Heliocentric
Hypothesis/System
The heliocentric system is defined
as the system in which the planets orbit around the Sun. The Sun is
considered to be in the center of our system and the center of each planet's
orbit. I will keep the heliocentric system like this for simplicity's
sake (in reality, the Sun and the planets orbit around a common center of mass.
The Sun is basically at the center of the Solar System since the Sun makes up
about 99.9% of the Solar System. However, the Sun is not directly in the center
of each planets' orbit. Because the Earth is very small compared to the Sun,
the barycenter - center of mass they orbit
around - places the Sun very close to the center. However, with planets that
have a larger mass such as Jupiter and Saturn, the barycenter is not as close
to the Sun. Therefore, while the large planet is orbiting the Sun, the Sun
is revolving around the barycenter, thus creating an illusion that the Sun is
moving back and forth, i.e Figure 2. This is visible with spectrometers and NOT
to the naked eye. If one was observing the Sun from Jupiter, they would not see
the slight wobble from the Sun traveling around its barycenter. The center of
mass that a certain planet and the Sun revolve around differ based on distance
and mass of the specific planet. From this point on I will refer to the Sun
as the center of the Solar System because we are observers from Earth. The Sun
is basically at the center for us).
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Figure
1. Exaggerated version of a planet and the Sun revolving around their
barycenter
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Figure
2. Side view (the back and forth illusion due to the revolution around the
barycenter. The planet orbits the barycenter faster because of its
smaller mass, while the Sun is orbiting around the barycenter at a slower
rate due mostly to its weight.
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The heliocentric system became
somewhat popular when an astronomer/mathematician by the name of Nicolaus
Copernicus proposed a geometric mathematical model to explain that the Earth
was revolving around the Sun, rather than the Sun revolving around the Earth.
The geocentric model was the accepted hypothesis during this time
(especially Aristotle's 'universe' which was accepted for many centuries). This
model showed the Earth in the center with the Sun and other planets revolving
around it. This was a very popular belief during the time of ancient
civilizations until up to Copernicus' time. Although the geocentric model
of the Solar System seems absurd to us today, this hypothesis was very logical
during the time when technology was not as advanced as it is today.
Observers on Earth during the era where the geocentric model was
thoroughly explained (approximately 611 BC - 140 AD), saw the Sun rise in the
east and set in the west. Each of the celestial objects observed seemed a lot
smaller than the Earth, and most importantly they always saw the Moon.
The stars were accepted to be much larger than Earth. Thus, the sphere
they were located on moved slowly around the Earth in a diurnal motion (rise
east, set west). These specific reasons alone, convinced people that the Sun
and planets were revolving around the Earth. The Earth never 'leaves' the Moon,
so if the Earth revolved around the Sun then the Earth would leave the Moon behind.
Another belief during that time was that because everything heavy on Earth
was impossible to move (such as a boulder), then the massive Earth was too huge
and sluggish to be able to revolve around anything. This belief held
strong and a well-known philosopher, Aristotle came along and proposed a
hypothesis supporting the geocentric model. His model was accepted for
centuries.
Background Information: Geocentric Model
Aristotle stated that the Earth was
spherical and at rest (note: most people at this time believed the Earth was spherical and not flat). To prove that the Earth was at rest, he noted
that if the Earth was truly in motion, the observers would see the stars in the
night sky move instead of being in their fixed positions (this excludes rising
and setting). An interesting observation that Aristotle stressed was that
because the Earth is spherical, lunar eclipses show shadow segments as a curved
line instead of a flat line. Also, when one travels north or south, the
stars position appear to change. Because of this, he stated that the
stars were also on a celestial sphere and this allowed them to retain their
positions. Aristotle expanded a hypothesis made by his predecessors
(Anaximander, Pythagoras, Plato, Eudoxus). Eudoxus came up with a model that
tried to explain the geocentric model. His model contained 27 spheres:
the stars had 1 (diurnal motion), the Moon had 3 (diurnal motion, monthly
movement with respect to the stars: eastward, and deviation from the ecliptic:
5 degree tilt of orbit), the Sun had 3 (diurnal motion, annual motion east with
respect to stars, and one to keep symmetry with the Moon), 4 orbits for each of
the 5 planets: Mercury, Mars, Venus, Jupiter and Saturn (diurnal motion,
prograde motion, and 2 for retrograde motion). Aristotle elaborated and
modified Eudoxus' model by adding 28 more spheres to have a total of 55 spheres
for his model. Aristotle also added that the 4 elements seen in chemistry
(earth, water, air, and fire) had their own natural motion toward their natural
place in the universe: Earth downward, fire upward, water and air falling in
between. He also mentioned that the Earth was not orbiting the Sun
because then they would observe a heliocentric parallax. This means that if the Earth was
revolving around the Sun, they would have seen the positions of the stars
change with the seasons. In other words, there would be an observable parallax
of the stars. One cannot see stellar parallax with the naked-eye, so Aristotle
concluded that the Earth must be at rest. However, the stars are so far away,
that one needs a good telescope to measure stellar parallax. The first measured parallax was in 1838.
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Figure
3. Heliocentric parallax (not seen with naked eye). The movement of a nearby
star relative to the background of much more distant stars
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Aristotle's hypothesis was
supported with logic that made sense during his time. For about a century, his
hypothesis was widely accepted by scholars and the public. One man skeptical of
Aristotle's hypothesis, came along hoping to change everyone's mind.
Aristarchus of Samos and the
Heliocentric Hypothesis
Aristarchus was a Greek astronomer/mathematician noted as being the first to propose a model that placed the Sun at the center of the 'universe' and the planets revolving around it. Aristarchus also believed that the stars in the 'universe' were like the Sun; they were just further away. Because of this, there is no observable parallax (to the naked eye). Since the telescope did not exist at the time, this idea was rejected. Note that the first telescope that gained much attention was Galileo's. It is said that he was not the first to invent the telescope, but his telescope gained popularity due to what he observed. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter (named the Galilean Moons in his honor), and the observation and analysis of sunspots. It is said that Aristarchus explained the heliocentric system through geometric models (before Copernicus). He described a spherical Moon illuminated by the Sun which was closer to the Earth than the Sun. However, his hypothesis may have been rejected due to Aristotle's logical (at the time), popular theory. Did Aristarchus propose and support this hypothesis before Copernicus? Did Copernicus get credit for Aristarchus' work? I plan to answer these questions, but there is something I must note: it is said that Aristarchus' original text was lost/destroyed in Alexandria. Fortunately, some of his work has been retrieved and academics such as Archimedes, an ancient Greek mathematician/physicist/engineer/astronomer referenced Aristarchus' hypotheses.
Aristarchus' Surviving Work
Interestingly enough, Aristarchus' only known surviving work (included in Book VI of the Collection preserved by students of Pappus of Alexandria) is based on a geocentric viewpoint named On The Sizes And Distances Of The Sun And Moon. Why this is the case is unknown, however it might be a possibility that this is his only work regarding the geocentric model, and his later work on the heliocentric model could have been destroyed due its rejection. Because his other work was destroyed, and I don't have access to them, I cannot speculate any further. On Sizes contains geometric mathematical models of the Earth and luminaries. These mathematical models were used to derive sizes and distances of the Earth, Sun and the Moon. The text begins with 6 assumptions referred to as 'hypotheses.' There are two groups of hypotheses included in On Sizes. The first group consists of three hypotheses:
- That the Moon receives its light from the Sun.
- That the Earth has the ratio of a point and a center to
the sphere of the Moon.
- That, when the Moon appears to us halved, the great
circle dividing the dark and the bright portions of the Moon points
toward (neÚein e„j) our eye.
These hypotheses are considered to
be geometric. This means that they explain the celestial world with
mathematics. They do not explain the 'natural' world (the world the people live
in). The next set of hypotheses are considered to be computational. This means
that they were used as assumptions of the physical or 'natural' world.
Numerical variables were used to try to solve these assumptions:
4.
That, when the Moon appears to us halved, its distance from the Sun is less
than a
quadrant by a thirtieth of a
quadrant [87◦].
5. That the
breadth of the shadow is two Moons.
6. That the Moon
subtends a fifteenth part of a zodiacal sign [2◦].
Hypothesis #5 means that the width
of the Earth’s shadow falling on the Moon’s orbit appears to us as twice the
angular span of the Moon.
To explain these hypotheses, Aristarchus came up
with 3 propositions. 18 propositions follow after containing the demonstrations.
Aristarchus proposed that the
distance of the Sun from the Earth is greater than eighteen times, but less
than twenty times. The distance of the Moon according to the hypothesis (concerning the dividing in half); is that the diameter of the Sun has the same
relationship to the diameter of the Moon; and that the diameter of the Sun has
a relationship to the diameter of the Earth greater than that of 19 to 3, but
less than that of 43 to 6. He tried to prove
these ideas with mathematical models. These models would later be
called the Lunar Dichotomy (Figure 4 and 5) method and the Eclipse
Diagram.
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Figure
4. Lunar Dichotomy:
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Figure 5. Aristarchus' Diagram of
Lunar Dichotomy. Top picture: from left to right - Sun, Earth, Moon. Bottom
Picture: from top to bottom - Moon, Earth, Sun
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Aristarchus claimed that at half Moon
(1st or 3rd quarter Moon), the angle between the Sun and the Moon was 87
degrees. Using geometry (lengths and angles), Aristarchus proposed that the Sun
was 18 times further away (from the Earth) than the Moon. Although he is
correct about the fact that the Moon is closer to the Earth compared to the Sun's
proximity to Earth, his reference/datum of 87 degrees was inaccurate, skewing
his results. The Sun is now shown to be about 400 times away from the Earth
compared to the Moon and also about 400 times the size of the Moon.
Because these two values can 'cancel out,' the Sun usually looks the same
size or a bit larger than the Moon. Knowing this, one can understand why
people during Aristotle's time (and other ancient civilizations) thought that
the Earth was huge and the Sun and the Moon were small objects that orbit the Earth.
There are a number of mathematical formulas (trigonometry and geometry) that Aristarchus used to calculate and prove his hypotheses. I will
include all references if anyone is interested in looking at his work.
Aristarchus & The Heliocentric
Model/System
Aristarchus' other work supposedly on the heliocentric model, have been lost or destroyed. However, multiple scholars have accredited him for hypothesizing a heliocentric model. Archimedes, who cited Aristarchus with the most detail is known for building off and modifying Aristarchus and other scholars' work. One of Archimedes' surviving work, The Sand Reckoner mentions Aristarchus' hypothesis on the heliocentric model. Archimedes states that Aristarchus proposed a universe much greater than what was thought during their time (c. 287 BC – c. 212 BC). According to Archimedes (this has been translated):
"His hypotheses are that the fixed stars and the Sun
remain unmoved, that the Earth revolves about the Sun in the circumference of a
circle, the Sun lying in the middle of the orbit, and that the sphere of the
fixed stars, situated about the same centre as the Sun, is so great that the
circle in which he supposes the Earth to revolve bears such a proportion to the
distance of the fixed stars as the centre of the sphere bears to its surface.
Now it is easy to see that this is impossible; for, since the centre of the
sphere has no magnitude, we cannot conceive it to bear any ratio whatever to
the surface of the sphere. We must however take Aristarchus to mean this: since
we conceive the Earth to be, as it were, the centre of the universe, the ratio
which the Earth bears to what we describe as the 'universe' is the same as the
ratio which the sphere containing the circle in which he supposes the Earth to
revolve bears to the sphere of the fixed stars. For he adapts the proofs of his
results to a hypothesis of this kind, and in particular he appears to suppose
the magnitude of the sphere in which he represents the Earth as moving to be
equal to what we call the 'universe.''
Archimedes stated that in
Aristarchus' original text, the 2 degree for the angle subtended by the Sun and
Moon is actually too large. He clarifies that according to Aristarchus'
meticulous calculations and correct use of the evidence of eclipses, it was
actually stated to be 1/2 degree. This could have been an error during
translation. Archimedes has also cited Aristarchus multiple times in his work.
These excerpts are from The Sand Reckoner:
"I say then that, even if a sphere were made up of the
sand, as great as Aristarchus supposes the sphere of the fixed stars to be, I
shall still prove that, of the numbers named in the Principles*) some exceed in
multitude the number of the sand which is equal in magnitude to the sphere
referred to, provided that the following assumptions be made." (p.222)
"It is true that, of the earlier astronomers,
Eudoxus declared it to be about nine times as great, and Pheidias my father
twelve times, while Aristarchus tried to prove that the diameter of the Sun is
greater than 18 times but less than 20 times the diameter of the Moon. But I go
even further than Aristarchus, in order that the truth of my proposition may be
established beyond dispute, and I suppose the diameter of the Sun to be about
30 times that of the Moon and not greater." (p.223)
"I make this assumption because Aristarchus discovered
that the Sun appeared to be about 1/720 part of the circle of the zodiac, and I
myself tried, by a method which I will now describe, to find experimentally
(untranslated text) the angle subtended by the Sun and having its vertex at the
eye (untranslated text)." (p.223)
"From this we can prove further that a sphere of the
size attributed by Aristarchus to the sphere of the fixed stars would contain a
number of grains of sand less than 10,000,000 units of the eighth order of
numbers [or 10^56+7 = 10^63]." (p. 232)
Archimedes' Sand Reckoner work is similar to that of On Sizes. It begins with a number of
hypotheses, two of which are explicitly based on the preceding work of
Aristarchus. From these assumptions, Archimedes proceeds to develop a more
accurate measurement (measurements and sizes are a lot larger today) for the
size of a greatly expanded cosmos. He then filled this cosmos with sand to
exhibit a number. He used a method well known to Greek mathematicians: the
ratio of the volumes of two spheres is the third power of the ratio of their
diameters. Because he wanted a cosmos that was as large as possible, he
introduced a heliocentric hypothesis, which he attributed to Aristarchus.
According to Kings Academy abbreviated version of The Sand
Reckoner,
"He begins with a poppy seed
which, you will recall, was not less than one 40th of a finger-breadth. A
sphere of diameter 40 poppy seeds would therefore have a volume no greater than
64,000 poppy seeds. Since each poppy seed contains no more than 10,000 grains
of sand, a sphere of one finger-breadth contains at most 640,000,000 grains of
sand. The latter number consists of 6 units of the second order plus 40,000,000
units of the first order, a quantity that is not more than 10 units of the
second order in Archimedes’ numbering scheme. A sphere of one finger-breadth
contains no more than 10 units of the second order of sand grains."
Diameter of Sphere Number
of Grains of Sand
100 finger-breadths
< 1,000,000 x 10 = 10,000,000 units of the
second order
10,000 finger-breadths
< 1,000,000 x previous number < 100,000
units of the third order
The Greek measure of larger distances, the stadium, is less
than 10,000 finger-breadths, according to Archimedes. Thus,
one stadium
< 100,000 units of the third order
100 stadia
<1,000,000 x prev. number< 1,000 units of the fourth order
10,000 stadia
< 1,000,000 x
previous number < 10 units of the fifth order
1,000,000 stadia
< 10,000,000 units of
the fifth order
100,000,000 stadia
< 100,000 units of the sixth order
10,000,000,000 stadia
< 100,000 units of the sixth order
A sphere of the size
attributed by Aristarchus to the sphere of fixed stars would contain a quantity
of sand no greater than 10,000,000 units of the eighth order of numbers. (i.e.,
10^63). Archimedes made the working assumption that
the distance of the fixed stars was in the same relation to the radius of the Earth's
orbit as that orbit was in relation to the Earth itself. Under these
conditions, he could demonstrate that stellar parallax would have been beyond
then-current observers' ability to detect (with the naked eye since telescopes
were not invented at that time). Using Aristarchus' work, Archimedes concluded
that these findings would be incredible to anyone who did not study mathematics,
however, the ones who had given thought to the question of the distances and
sizes of the Earth, the Sun, the Moon and the whole universe, the proof would
carry conviction. His ideas were also rejected due to no observable parallax.
It is also said that Archimedes was killed by a Roman soldier.
There are multiple accounts of how and what he was doing before he died,
this is one example (translated from Latin):
"I should say that Archimedes’ diligence also bore
fruit if it had not both given him life and taken it away. At the capture of
Syracuse Marcellus had been aware that his victory had been held up much and
long by Archimedes’ machines. However, pleased with the man’s exceptional
skill, he gave out that his life was to be spared, putting almost as much glory
in saving Archimedes as in crushing Syracuse. But as Archimedes was drawing
diagrams with mind and eyes fixed on the ground, a soldier who had broken into
the house in quest of loot with sword drawn over his head asked him who he was.
Too much absorbed in tracking down his objective, Archimedes could not give his
name but said, protecting the dust with his hands, “I beg you, don’t disturb
this,” and was slaughtered as neglectful of the victor’s command; with his
blood he confused the lines of his art. So it fell out that he was first
granted his life and then stripped of it by reason of the same pursuit."
Archimedes was not the only one who
cited Aristarchus' work, other ancient authorities unanimously attribute the
heliocentric system to Aristarchus. Plutarch (c.
100 AD), a Greek historian, biographer and essayist gave a similar brief
account of Aristarchus' hypothesis, stating specifically that the Earth
revolves along the ecliptic and that it is at the same time rotating on its
axis. In the first two excerpts from Plutarch's work called On the
Apparent Face in the Orb of the Moon, Plutarch cites Aristarchus' work On
The Sizes And Distances Of The Sun And Moon, the third one cites
Aristarchus' idea that the Earth revolved around the ecliptic path and rotated
around its own axis:
"And consider, leaving out of the case the other fixed
stars and planets, what Aristarchus points out in his treatise ‘ Upon
Magnitudes and Distances,’ that the distance of the Sun is more than eighteen
times, but less than twenty times the distance of the Moon, by which she is
separated from us: and yet the computation that gives the greatest elevation to
the Moon says she is distant from us fifty-six times the space from the center
of the Earth [to the circumference]: this length is of forty thousand stadia,
according to those who make a moderate calculation of it. And, calculated from
this basis, the Sun’s distance from the Moon amounts to over four thousand and
thirty myriads of stadia. So far, then, is she separated from the Sun by reason
of her weight, and approximated to Earth, that if one must define substances by
localities, the constitution and beauty of Earth attracts the Moon, and she is
of influence in matters and over persons upon Earth, by reason of her
relationship and proximity. And we do not go wrong, I think, when we assign to
those bodies above denominated such immense depth and distance, and leave to
that which is below a certain circular course and broadway as much as lies
between Earth and the Moon: for neither the man who pretends the summit of
heaven to be the sole ‘above,’ and denominates all the rest as ‘below,’ is
reasonable in his definition; nor yet is he who circumscribes ‘below’ by the
limits of Earth, or rather by the Center, to be listened to: but even moveable.
. . . inasmuch as the universe allows of the interval required by reason of its
own extensiveness."
"But Aristarchus proves that the Moon’s diameter bears
a proportion [to that of Earth] which is less than sixty to nineteen, but
somewhat greater than one hundred and eight to forty. Consequently Earth
entirely takes away the Sun from sight, by reason of her magnitude; for the
obstruction she presents is extensive, and endures the space of a night,
whereas the Moon, even though she may occasionally hide the Sun, the
occultation has no time to last, and no extensiveness, but some light shows itself
round his circumference that does not allow the darkness to become deep and
unmixed. Aristotle (the ancient one, I mean) gives as one cause, besides some
others, of the Moon’s being seen eclipsed more frequently than the Sun, ‘that
the Sun is eclipsed by the obstruction of the Moon, whereas the Moon is . . .
.’ But Posidonius thus describes the phenomenon: ‘The eclipse is the
conjunction of the Sun and the shadow of the Moon, of which the eclipse . . . .
for to those people alone is the eclipse visible from whom the Moon’s shadow
shall occupy and block out the sight of the Sun.’ And when he agrees that the
shadow of the Moon is projected as far as us, I do not know what more he has
left himself to say, for of a star there can be no shadow, because that thing
which is unillumined is designated shadow—now light does naturally not produce
shadow, but destroy it.”
"Thereupon Lucius laughed and said: "Oh sir, just
don't bring suit against us for impiety as Cleanthes thought that the Greeks
ought to lay an action for impiety against Aristarchus the Samian on the ground
that he was disturbing the hEarth of the universe because he sought to save the
phenomena by assuming that the heaven is at rest while the Earth is revolving
along the ecliptic and at the same time is rotating about its own axis."
The heliocentric model (the
one Aristarchus thought to be true), was rejected due to a non-observable
parallax. As mentioned previously, Aristarchus hypothesized that the
stars were extremely far from Earth and that is why they did not observe a
heliocentric parallax. Plutarch mentions in the last excerpt above that
Aristarchus assumed that the heaven was at rest, while the Earth was revolving
and rotating.
Vitruvius - a Roman author,
architect, civil engineer and military engineer during the 1st century BC,
known for his multi-volume work entitled De architectura -
also cited Aristarchus in his work:
"Those unto whom nature has been so bountiful that they
are at once geometricians, astronomers, musicians, and skilled in many other
arts, go beyond what is required of the architect, and may be properly called
mathematicians, in the extended sense of that word. Men so gifted, discriminate
acutely, and are rarely met with. Such, however, was Aristarchus of Samos..."
(p.4)
"I shall now subjoin what Aristarchus, the
Samian mathematician, learnedly wrote on this subject, though of a different
nature. He asserted, that the Moon possesses no light of its own, but is
similar to a speculum, which receives its splendour from the Sun’s rays. Of the
planets, the Moon makes the smallest circuit, and is nearest to the Earth;
whence, on the first day of its monthly course, hiding itself under the Sun, it
is invisible; and when thus in conjunction with the Sun, it is called the new Moon.
The following day, which is called the second, removing a little from the Sun,
it receives a small portion of light on its disc. When it is three days distant
from him, it has increased, and become more illuminated; thus daily elongating
from him, on the seventh day, being half the heavens distant from the western Sun,
one half of it shines, namely, that half which is lighted by the Sun. 4. On the
fourteenth day, being diametrically opposite to the Sun, and the whole of the
heavens distant from him, it becomes full, and rises as the Sun sets; and its
distance being the whole extent of the heavens, it is exactly opposite to, and
its whole orb receives, the light of the Sun. On the seventeenth day, when the Sun
rises, it inclines towards the west; on the twenty-first day, when the Sun
rises, the Moon is about mid-heaven, and the side next the Sun is enlightened,
whilst the other is in shadow. Thus advancing every day, about the
twenty-eighth day it again returns under the rays of the Sun, and completes its
monthly rotation. I will now explain how the Sun, in his passage through a sign
every month, causes the days and hours to increase and diminish." (p.109-110)
"The semicircular form, hollowed out of a square block,
and cut under to correspond to the polar altitude, is said to have been
invented by Berosus the Chaldean; the Scaphe or Hemisphere, by Aristarchus of
Samos, as well as the disc on a plane surface;"
In this case, Vitruvius is stating
that Aristarchus created two new types of sun-dials, one with a full, concave,
hemispherical surface, and another with a fully circular equatorial dial with
a nodus. The hemispherical shaped sun-dial was named the hemispherium or
scaphe and the fully circular one was called the discus (a
disc on a plane surface).
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Figure
6. hemispherium or scaphe
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Figure
7. Similar to the discus
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These inventions of the sundials are
important to note because although the sundials do not prove heliocentrism, it
does show Aristarchus' desire to look at the Sun's apparent position in the
sky. All three of these ancient Greek authorities have cited Aristarchus' work.
Not only on his measures of the distances between the Sun, Moon, and Earth but
also of Aristarchus' work on the heliocentric model. During this era
however, Aristarchus' model and other scholars' work based on Aristarchus' model
were rejected due to no observable parallax and how popular the geocentric
model was during that time. About 1800 years later Copernicus proposed the
heliocentric model and due to his evidence, and the time that he was living, his
work about the heliocentric system was more popular with the public (one reason is
because he did a lot of underground work). However, his work was disregarded by the
Catholic Church because it did not fit Ptolemy's model. Because Ptolemy's
model was highly accepted within the Catholic Church, they did not believe that
Copernicus' model/work proved much about a heliocentric model. It is when
Kepler, Galileo, and Newton's work are combined, that ultimately prove that the Earth
really did revolve around the Sun and that the Sun was actually in the center
of the solar system. The Catholic Church put Copernicus' final published
manuscript of De revolutionibus orbium coelestium on the
forbidden list, but his work was popular among curious individuals of the
public. Copernicus did cite Aristarchus in a earlier version (unpublished) of De
Revolutionibus (which still survives), though he removed the reference
from his final published manuscript. Some questions are why did he do that? And
although he may have expanded on this model (with his own evidence), was the
model similar enough to Aristarchus' that he should have been cited? Other
scholars before Copernicus' time cited, or attributed the heliocentric model to
Aristarchus and scholars after Copernicus' time cited their predecessors (even
though they expanded/modified hypotheses/theories to fit observations).
Copernicus and the Heliocentric
Model/System
Nicolaus Copernicus (19 February 1473 – 24 May 1543) was a Renaissance mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe. His work that explained this was in a book he published called De revolutionibus orbium coelestium, translated to On the Revolutions of the Celestial Spheres. Copernicus first wrote the "Commentariolus" (40-page outline of an early version of his heliocentric theory of the universe) some time before 1514 and circulated copies to his friends and colleagues. In this short manuscript, he mentions his postulates/assumptions, the 'order' of the spheres, the apparent motion of the Sun, how 'Equal motion should be measured not by the equinoxes but by the fixed stars, information regarding the motion of the Moon, the 'superior' planets (Jupiter, Saturn, Mars during his era), Venus and Mercury. These excerpts are from "Commentariolus:"
- There is no one center of all the celestial circles or
spheres.
- The center of the Earth is not the center of the
universe, but only of gravity and of the Moon's orbit.
- All the planets revolve about the Sun as their
mid-point, and therefore the Sun is the center of the universe.
- The ratio of the Earth's distance from the Sun to the
height of the firmament is so much smaller than the
ratio of the Earth's radius to its distance from the Sun that the distance
from the Earth to the Sun is imperceptible in comparison to the height of
the firmament.
- Whatever motion appears in the firmament arises not
from any motion of the firmament, but from the Earth's motions. The Earth
together with its circumjacent elements (Note: Copernicus
is referring to the atmosphere and the waters that lie upon the surface of
the Earth) performs a complete rotation on its poles in a daily
motion, while the unmoved firmament and highest heaven abide unchanged.
- What appear to us as motions of the Sun arise not from
its motion but from the motion of the Earth and our sphere, with which we
revolve about the Sun like any other planet. The Earth has, then, more
than one motion.
- The apparent retrograde and direct motion of the
planets arises not from their motion but from the Earth's. The motion of
the Earth alone, therefore, suffices to explain so many apparent
inequalities in the heavens.
The Order of the Spheres
"The celestial spheres are arranged in the following
order. The highest is the immovable sphere of the fixed stars, which contains
and gives position to all things. Beneath it is Saturn, which Jupiter follows,
then Mars. Below Mars is the sphere on which we revolve; then Venus; last is
Mercury. The lunar sphere revolves about the center of the Earth and moves with
the Earth like an epicycle. In the same order also, one planet surpasses
another in speed of revolution, according as they trace greater or smaller
circles. Thus Saturn completes its revolution in thirty years, Jupiter in
twelve, Mars in two and one-half, and the Earth in one year; Venus in nine
months, Mercury in three."
I must note that although Copernicus
put the Sun in the center, and the planets revolving around the Sun, he still
used epicycles to explain for retrograde motion
of the planets.
 |
Figure
8. Copernicus' illustrations on a heliocentric model that included epicycles
|
It isn't until Johannes
Kepler comes along and publishes Astronomia nova
(1609), Epitome Astronomiae Copernicanae (1617-1621), and Harmonices
Mundi (1619) where he states that the orbits around the Sun are
elliptical and not perfectly circular. This gets rid of epicycles because it
explains for retrograde motion of the planets.
The Apparent Motions of the Sun
"The Earth has three motions. First, it revolves
annually in a great circle about the Sun in the order of the signs, always
describing equal arcs in equal times; the distance from the center of the
circle to the center of the Sun is 1/25 of the radius of the circle. The radius
is assumed to have a length imperceptible in comparison with the height of the
firmament; consequently the Sun appears to revolve with this motion, as if the Earth
lay in the center of the universe. However, this appearance is caused by the
motion not of the Sun but of the Earth, so that, for example, when the Earth is
in the sign of Capricornus, the Sun is seen diametrically opposite in Cancer,
and so on. On account of the previously mentioned distance of theSun from the
center of the circle, this apparent motion of the Sun is not uniform, the
maximum inequality being 2 1/6ø. The line drawn from the Sun through the center
of the circle is invariably directed toward a point of the firmament about 10ø
west of the more brilliant of the two bright stars in the head of Gemini,
therefore when the Earth is opposite this point, and the center of the circle
lies between them, the Sun is seen at is greatest distance from the Earth. In
this circle, then, the Earth revolves together with whatever else is included
within the lunar sphere.
The second motion, which is peculiar to the Earth, is the
daily rotation on the poles in the order of the signs, that is, from west to
east. On account of this rotation the entire universe appears to revolve with
enormous speed. Thus does the Earth rotate together with its circumjacent
waters and encircling atmosphere.
The third is the motion in declination. For the axis
of the daily rotation is not parallel to the axis of the great circle, but is
inclined to it at an angle that intercepts a portion of a circumference, in our
time about 23 1/2ø. Therefore, while the center of the Earth always remains in
the plane of the ecliptic, that is, in the circumference of the great circle,
the poles of the Earth rotate, both of them describing small circles about
centers equidistant from the axis of the great circle. The period of this
motion is not quite a year and is nearly equal to the annual revolution on the
great circle. But the axis of the great circle is invariably directed toward
the points of the firmament which are called the poles of the ecliptic. In like
manner the motion in declination, combined with the annual motion in their
joint effect upon the poles of the daily rotation, would keep these poles
constantly fixed at the same points of the heavens, if the periods of both
motions were exactly equal. Now with the long passage of time is has become
clear that this inclination of the Earth to the firmament changes. Hence it is
the common opinion that the firmament has several motions in conformity with a
law not yet sufficiently understood. But the motion of the Earth can explain
all these changes in a less surprising way. I am not concerned to state what
the path of the poles is. I am aware that, in lesser matters, a magnetized iron
needle always points in the same direction. It has nevertheless seemed a better
view to ascribe the changes to a sphere, whose motion governs the movements of
the poles. This sphere must doubtless be sublunar."
Copernicus cited Aristarchus in his
manuscript before he published a finalized version called De
revolutionibus orbium coelestium. He ended up deleting the citations for the final draft. This deleted material, which was not printed in the first four editions
of the Revolutions (1543, 1566, 1617, 1854), was
incorporated in those published after the recovery of
Copernicus' autograph (1873, 1949, 1972):
"The motion of the Sun and Moon can be demonstrated, I
admit, also with an Earth that is stationary. This is, however, lea suitable
for the remaining planets . Philolaus believed in the Earth's motion for these
and similar reasons. This is plausible because Aristarchus of Samos too held
the same view according to some people, who were not motivated by the
argumentation put forward by Aristotle and rejected by him [Heavens, II,
13-14). But only a keen mind and persevering study could understand then
subjects. They were therefore unfamiliar to most philosophers at that time, and
Plato does not conceal the fact that there were then only a few who mastered
the theory of the heavenly motions."
In this statement, Copernicus admits
that Aristarchus proposed the heliocentric model before him (i.e theory of the
heavenly motions), however, philosophers at the time rejected his theory
because of Aristotle's popularity. Although Philolaus was an important
figure to Copernicus, Philolaus was not as accurate as Aristarchus was when
explaining the 'heliocentric' model. Philolaus' ideas showed that the cosmos
and everything in it was made up of two basic types of things, limiters and
unlimiteds. Unlimiteds were defined as continua untouched by any structure or
quantity; they included the traditional material elements such as earth, air,
fire and water but also space and time. Limiters set limits in such unlimiteds
and included shapes and other structural principles. Limiters and unlimiteds are
not combined in a random way but are subject to a “fitting together” or
“harmonia.” Philolaus' primary example
of such a harmonia of limiters and unlimiteds is a musical scale, in which the
continuum of sound is limited according to whole number ratios, so that the
octave, fifth, and fourth are defined by the ratios 2 : 1, 3 : 2 and 4 : 3. Since the whole world is structured according to number, we only
gain knowledge of the world as we grasp these numbers. The cosmos comes
to be when the unlimited fire is fitted together with the center of the cosmic
sphere (a limiter) to become the central fire. Philolaus was the precursor of
Copernicus in moving the Earth from the center of the cosmos and making it a
planet, but in Philolaus' system it does not orbit the Sun but rather the
central fire. Aristarchus, however, was the first to propose a serious model of
the heliocentric model using mathematical/physical evidence. It is notable
that according to Plutarch, a contemporary of Aristarchus accused him of
impiety for "putting the Earth in motion." This is important because
it is stated that one reason Copernicus may not have cited Aristarchus in his
published version of De revolutionibus orbium coelestium, was
because Copernicus had no desire to inform or remind anybody that the religious head of an influential philosophical school had "thought that
the Greeks ought to bring charges of impiety against Aristarchus." In other words, he did not want to take a strong stance on any side of the issue. One other reason Copernicus may have removed the citing of Aristarchus was because of how
unpopular he was at the time of his publications.
Aristarchus' work on
the geocentric model (On the Sizes) was the only one that remained while his
supposed work of the heliocentric model was destroyed or 'lost.' Multiple
different scholars cite his heliocentric model/work and because of that we can
accredit Aristarchus with the first logical model of the heliocentric system.
Aristarchus and Copernicus still included epicycles in their models because
they could not explain retrograde (keep in mind that their hypotheses revolved around the idea that the planets orbited in a uniform circular motion).
Anyway, should have Copernicus cited Aristarchus (keep his citations in
the final draft)? I think that would have been the right thing to do, ethically.
Even during their era, scholars cited other scholars' work. Even though
their system was not as meticulous as ours today, attributing a hypothesis or a
theory to someone was considered a citation. Even though I believe that
Copernicus should have cited Aristarchus in his final text for ethical reasons,
it is understandable why Copernicus did not cite Aristarchus in the final
draft. For one, although his hypotheses revolve around Aristarchus' ideas,
Copernicus put in time and effort and modified/built off of Aristarchus'
original idea. Copernicus did not reuse the same idea. Also, if Copernicus
truly did not include a citation for Aristarchus because he feared that no one
would read or take his work seriously, it may have been a better idea for him
to remove Aristarchus' name. Even though Copernicus' work was popular among
his friends and some people of the public, the Catholic Church banned his work
and put it on the forbidden list (a list of books not RECOMMENDED to read).
Copernicus published De revolutionibus the same year he died.
When Copernicus started receiving positive feedback and popularity, he was
already dead. Who knows if he would have stated that Aristarchus was the
first to propose a heliocentric model.
Conclusion
Conclusion
To conclude, although Aristarchus
was known by others to be the first to propose a heliocentric model, Copernicus extended, modified and included his own evidence to
support this new heliocentric hypothesis. Aristarchus' work isn't physically
available (except for On the Sizes, which although contains a great amount of
detail and measurements on the sizes of the Moon, Sun and Earth, it still
describes a geocentric viewpoint). However, Copernicus' work survived and after
his death, it was given to his pupil, Rheticus, who for publication had only
been given a copy without annotations. Via Heidelberg, it ended up in Prague,
where it was rediscovered and studied in the 19th century. Having a physical
book is easier to trust than citations from scholars. Because of these reasons,
Copernicus is known for the heliocentric model, but, he should be known as the
one who revised it to the point where Kepler stated that Copernicus' model was
the closest to the truth. Even though Copernicus was not the first to propose a
hypothesis on a heliocentric model (many of his hypotheses, although edited
came from Aristarchus' original proposition), he was still a great scientist. He
worked his whole life using mathematics to find the truth. Inspired by his predecessors, he sought to prove that the sun was truly at the center of our Solar System. Even though he knew that he would probably get heat from the
Catholic Church, he published anyway. His book was banned during his era,
however when Kepler came along, he used Copernicus' ideas and his own
mathematical evidence to prove that we truly live in a heliocentric system.
Without scholars such as Aristarchus and Copernicus, Kepler wouldn't have been able to build off of existing hypotheses, Galileo may not have been influenced to
observe the night sky, Newton would have never proposed his laws of motion (to
answer Kepler's question) and Einstein may have never proposed a theory of general
relativity and gravitational waves (to finish Newton's work). This domino effect is what is
important in science. One person might not get the credit for a certain
discovery because multiple scientists/scholars contribute in a direct/indirect
way. Discoveries are still being made, theories are being
challenged, and more information is added to existing hypotheses today. Cooperation, open-mindedness, being able to take criticism, skepticism, etc. are all important characteristics that these scholars had and what everyone should want to have and acquire if they want to be successful, especially if you're interested in diving into the fascinating world of science.
References
10) Aristarchus
Archimedes & Aristarchus
Plutarch
Vitruvius
4) Scaphe
Copernicus & Aristarchus
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