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Eratosthenes
Born around 276 BCE; died around 194 BCE. He lived in northern
Africa, which was at that time part of the Roman Empire.
Eratosthenes was an ancient Greek writer, geographer, music
theorist, mathematician, astronomer, poet, teacher, and librarian.
(Quite an overachiever, huh? In fact, he was considered to be the
inventor of geography!)
Since Eratosthenes was involved in so many different fields, his
critics claimed he wasn’t the best at any particular discipline. They
made up a derisive nickname for him, “Beta,” which is the second letter of the Greek alphabet,
implying that he was always “second best.” His supporters had a different nickname, though.
They called him “Pentathlos,” after the Olympic athletes who were so talented they could
compete in five different Olympic events.
Eratosthenes is known for his many accomplishments, including calculating the tilt of the earth’s
axis, devising the first calendar with a Leap Day, and making the first map that showed lines of
longitude and latitude. However, Eratosthenes is most famous for something pretty amazing,
considering the times in which he lived. He was the first man known to have calculated the
Earth's circumference. And, surprisingly, considering his only tool was a primitive device for
measuring angles, he was only off by a very small percentage.
Eratosthenes is not in the textbook, but I have added him because his accomplishments illustrate
the fact that – contrary to much modern misunderstandings – people of the western world
understood that the earth is round since ancient times – at least the 6th Century BCE! How did
they know? They made inferences based on their observations (evidence!):
For example, when a ship approaches over the horizon, it doesn’t appear all at once. First you see
the top of the mast, then more and more of the ship. This shows the ship is approaching over a
curved surface.
So, just how did Eratosthenes measure the earth’s circumference over 2,000 years ago?
Eratosthenes had been told that at noon on the June Solstice, if someone looked down into a deep
well in a city called Syene (now Aswan, Egypt), located on the Tropic of Cancer, their reflection
blocked the reflection of the sun on the water at the bottom of the well. This indicates the sun’s
rays fall exactly vertically at that date and time in that location. Meanwhile, in Alexandria, which
was 500 miles northwest of Syene and was where Eratosthenes was living, he measured the sun’s
on that same date and time and found that they fall about 7 degrees from the vertical. He
correctly assumed the Sun's distance to be very great and concluded that because of this, the
sun’s rays are practically parallel by the time they reach Earth.
Since 7 degrees is approximately 1/50th of a circle(which has 360 degrees), and assuming that
Alexandria and Syene were on the same line of longitude, Eratosthenes concluded that
the distance from Alexandria to Syene must therefore be 1/50th of the earth’s circumference.
(See diagram, below.) The distance between these two cities was reported to be 5,000 stadia
(singular, stage), an ancient unit of distance.
He rounded the result to a final value of 700 stadia per degree, which implies a circumference of
252,000 stadia. Some claim Erathostenes used the Egyptian stade of 157.5 meters, which would
imply a circumference of 39,690 km, an error of 1.6%, but at that time, most people in the Greek
Empire would have used the Attic stade, which is equivalent to 185 meters. This would imply a
circumference of 46,620 km, an error of 16.3% -- still pretty impressive! We know now that the
earth is not a perfect sphere, but it is obvious that ancient Greeks such as Eratosthenes had a
fairly accurate understanding of its shape and definitely did not believe it was flat.
At the age of 81, Eratosthenes suffered an inflammation of the eyes, which rendered
him blind. It is said that he became so depressed at no longer being able to read or to
observe the beauty and wonders of nature that he committed suicide by self-starvation
after one year of sightlessness.
Ptolemy (Claudius Ptolemaeus)
(90 – 168)
Even though other ancient Greek astronomers, including Aristarchus (310 –
230 BCE) and Hipparchus (190 – 120 BCE), Ptolemy was so influential
that his insistence on his geocentric model of the known universe
dominated western thought for almost 1500 years. In fact, the geocentric
model he proposed is often referred to as the Ptolemaic System.
One of the reasons that Ptolemy’s model was so compelling is that people
could make accurate predictions based on the math he used.
Since in reality, the solar system (along with the stars visible from Earth,
the known universe at that time), is in actuality heliocentric, the planets sometimes seem to
change directions when seen from the earth. (In fact, this is how the planets earned their name.
“Planetes” means “wanderer” in Greek. Unlike the “fixed” stars, which seemed to rotate the
Earth in very reliable circles, the planets appeared to wander about the sky. Note: The planets
past Saturn were unknown at this time in history.) This is because Earth in its orbit sometimes
passes up the slower moving, farther planets, which also have a longer path to travel. Venus and
Mercury, closer to the sun than Earth and faster moving, sometimes pass us, leading to the same
illusion of backward motion. Ptolemy devised an elaborate system of small circles which he
termed “epicycles,” to explain this apparent motion. (See diagram, below.)
Three main ideas that Ptolemy and others
believed must be true (and are included in his
model) are as follows:
1. All motion in the heavens is uniform,
perfectly circular motion.
2. All objects in the heavens are made from
perfect material and are shaped in perfect
spheres. In addition, their properties, such as
brightness, were permanent and never
changing.
3. The Earth is at the center of the Universe.
Not much is known about Ptolemy’s personal
life, but we do know he had a major influence on astronomical thought.
Nicolaus Copernicus is the
Latinized name of Polish astronomer and mathematician
Mikolaj Kopernik. Born in 1473, he is credited with the
heliocentric model of the solar system. However, it is
important to note he was not the first person to figure out
that the sun is at the center of what was then thought to be
the entire universe. However, he was the first to calculate
the math that was needed to explain the model.
Copernicus’s model did have several shortcomings. Like the
astronomers before him, he assumed the planets orbit in
perfect circles. Since they do not, the only way he could
make his math fit celestial observations was to include
epicycles, as Ptolemy before him had done.
Remember, at this time, the majority of astronomers continued to accept Ptolemy’s geocentric
model. Another big problem was that the Holy Roman Empire was the law of the land. Claiming
the sun was at the center of the universe was deemed heresy by the Church. Copernicus was
reluctant to incite controversy and therefore did not publish his work until shortly before his
death in 1543.
Galileo Galilei
(1564 – 1642)
The terms physicist, astronomer,
mathematician, engineer, and
philosopher can all be used to
describe Galileo Galilei, commonly
referred to by his first name only. He
was truly an amazing individual and
his list of scientific accomplishments
is astounding. As Stephen Hawking
has said, "Galileo, perhaps more
than any other single person,
was responsible for the birth of modern science."
Galileo originally studied medicine, intending to become a physician, but while at university he
found himself drawn to mathematics and physics.
While it is true he formulated many of the foundational ideas about gravity and motion, and is
even referred to as the “father” of modern astronomy, Galileo did not invent the telescope, as is
often mistakenly believed. No one is certain who the first person to make a telescope was, but a
German eyeglass maker, Hans Lipperhey, was the first to apply for a patent on a telescope, in
1608.
Having heard of this wonderful new contraption that could make distant objects appear closer,
Galileo set about constructing his own telescope – without ever actually seeing one. He also
figured out how to increase the magnification, from only three times to as great as 30 times.
Galileo has long been believed to be the first person to turn the telescope to the sky and use it for
astronomical purposes. Recently, it has been made known that an Englishman named Thomas
Harriot viewed the moon through a telescope several months before Galileo, but Harriot did not
publicize his findings. In contrast, Galileo published a book called Starry Messenger in 1610
which outlined his discoveries. Here is a reproduction of one his actual drawings of the moon
(left) and an artist’s sketch of Galileo using his telescope (right):
Some of the phenomena Galileo observed flew in the face of accepted thought in the 1600s. His
observations of craters and mountains on the moon revealed that it was not a smooth, perfect
sphere, as had been assumed. Similarly, his discovery of sunspots showed the sun was not
perfect, either. Witnessing four small satellites (moons) revolving around the planet Jupiter was
proof that not everything in the heavens revolves around Earth. Most telling of all, the phases
that the planet Venus goes through simply could not occur unless Venus was traveling around
the sun, and at a closer orbit than Earth.
If Ptolemy’s model were correct, we would only see Venus as either a waxing or waning
crescent of the same size (left). However, Galileo observed Venus pass through an entire set of
phases of different sizes (right). Galileo’s observations proved that the sun is indeed at the center
of the solar system.
Unfortunately, Galileo ran into trouble with the Catholic Church for agreeing with Copernicus.
Saying that the earth is not the center of the Universe contradicts some statements in the Bible,
which was at that time taken quite literally. To cast doubt on the Bible’s veracity was considered
heresy. Galileo was brought before the Inquisition and made to recant his claim that the earth
orbits around the sun. During the last ten years of his life, he was kept under “house arrest” and
not allowed to leave his estate. Although prohibited from pursuing astronomy, he was still
allowed visitors, including scholars from other nations and pupils whom he taught mathematics
and physics. His final book detailed his ground-breaking discoveries in physics, including the
concept of inertia. Blind and deaf at the very end of his life, Galileo spent his final months
playing the lute.
In 1992, the Catholic Church issued an official apology to Galileo.
(1546 – 1601)
Tycho Brahe, or as I like to
think of him, The Man with the Golden
Schnozzola, was certainly an interesting
person. Tycho Brahe was born into a
wealthy noble family and purportedly was
inspired to become as astronomer after
witnessing a solar eclipse at the
impressionable age of 14.
A few years later, while at university,
Tycho and a fellow student got into an argument about math. Some say they were arguing over
who was the better mathematician; others say they were arguing about a mathematical concept.
At any rate, they decided to settle the argument in a duel – with swords! Tycho’s opponent sliced
off his nose. The rest of his life he wore a gold-plated nose, which he attached to his face with a
little bit of paste – carrying the paste with him at all times just in case. (Some sources say he had
a nose made of copper for every day and saved the gold schnozz for special occasions.)
Tycho became the official astronomer to the King of Denmark, who funded an observatory
designed by Tycho to resemble a castle, below, left:
Tycho designed and built
new instruments to make
precise astronomical
observations (left) , but
seeing as he died in 1601,
never had the opportunity to
use a telescope. Nevertheless,
his twenty year accumulation
of thorough, accurate
observations proved
invaluable to his
assistant and successor, Johannes Kepler, who would take his boss’s data and finally unlock the secrets of
the solar system.
Rich and eccentric, Tycho lived in a castle with a pet moose, which sadly died after falling down the stairs
after drinking too much beer at a friend’s party. (I am not making this up!)
As far as the structure of the universe goes, Tycho didn’t think the heliocentric model could be
correct because of the parallax problem. To understand parallax, hold your thumb over a distant
object, such as the clock, and close one eye. Now switch eyes. Did the object appear to “jump” to
a different position so our thumb was no longer covering it? That’s due to parallax, the apparent
change in position of an object when viewed from two different locations. (Your two eyes are in
two different locations!) Try a little experiment to find out if parallax increases or decreases with
distance.
Astronomers figured that if the Earth were traveling around the sun, then the stars would appear
to change positions at different times of the year, depending on our location along the orbit, but
they don’t. What astronomers didn’t understand was the VAST distances the stars are from the
rest of our solar system. As you should have discovered, parallax decreases with distance. The
stars are so far away that the parallax is too small to see with the naked eye.
Since Tycho thought the lack of parallax showed the heliocentric model to be false, he came up
with his own solar system model:
Even though his model was incorrect, Tycho Brahe's made huge contributions to astronomy. The
astronomical instruments he designed and built, as well as his meticulous calibrations and checks
for accuracy were revolutionary. In addition to being the most accurate observations of the sky
ever made, his were also the most thorough. Astronomers before Tycho typically made
observations of the positions of planets and the moon only at certain key points of their orbits.
Tycho, in contrast, observed these objects throughout their entire orbits, which revealed
previously unknown aspects.
After a falling out with the King of Denmark, Tycho left for Prague, where he was named
Imperial Mathematician and continued his methodical observations. It was there that Johannes
Kepler became one of his assistants. Although Tycho refused to share all his data in life, after his
mentor’s death, Kepler would make excellent use of the records of over twenty years of
astronomical observations.
At the time of Tycho’s death at age 54, he was thought to have succumbed to an infection
resulting from a burst bladder. In 1901, his body was exhumed and scientists announced that
Tycho actually died of Mercury poisoning, leading to speculation that he had been murdered. In
2010, his body was once again exhumed. This time, modern forensic tests ruled out mercury
poisoning. Even though the nose itself was not buried with its owner, researchers performed tests
on a small sample of the nasal bones, which revealed the famous golden schnozz was really
brass.
Johannes Kepler (1571 – 1630)
Kepler grew up in a poor family in Germany. At one point,
he quit school and worked as a waiter to help support his
family. When he went to university, he originally planned to
become a Lutheran minister, but possessing an extraordinary
gift for mathematics, he instead began a career as a teacher
of math and astronomy. Before signing on as assistant to
Tycho Brahe in 1600, Kepler had written several
astronomical publications and had come to embrace the
Copernican model of the solar system.
Even though the two men held different beliefs and
sometimes didn’t get along, Kepler’s association with Brahe
would be the key to his best-known accomplishments. Tycho
may have felt threatened by the young Kepler, perhaps fearing the student would surpass the
teacher. It is thought that Tycho gave Kepler his most difficult assignment to keep him occupied
-- to work out the orbit of Mars mathematically. (The Mars observations were especially
complicated.)
Like all astronomers before him, Kepler assumed Mars’s orbit was a perfect circle, but the math
wouldn’t work out. It was then Kepler realized that planetary orbits are actually ellipses!
This discovery is now referred to as Kepler’s First Law of Planetary Motion. Altogether, Kepler
formulated three Laws of Planetary Motion, which for the first time provided a truly accurate
model of the solar system: heliocentric with elliptical planetary orbits.
Here are simplified versions of Kepler’s Three Laws of Planetary Motion:
1. Planetary orbits are elliptical.
2. When a planet is closer to the sun in its orbital path it moves faster than when it is farther
from the sun in its orbital path.
3. Planets closer to the sun travel faster than planets farther from the sun.
At first reading, Laws #2 and #3 may seem to be the same, but #2 is referring to the same planet
at different points in the elliptical orbit while Law #3 is referring to different planets.
While he is most famous for these laws, Kepler made many other contributions to science,
including figuring out that the moon causes tides and making up the word, “satellite.”
By the way, if you wear glasses, you have Kepler to thank, seeing as he was the first person to
figure out how to make lenses to correct for nearsightedness and farsightedness.