Source: http://solar-center.stanford.edu/galileo/
https://sciencing.com/list-discoveries-galileo-galilei-8249749.html
400th Anniversary of Galileo's Astronomical Discoveries
Who was Galileo?
Galileo Galilei (1564-1642) was a Tuscan (Italian) astronomer, physicist, mathematician, inventor, and
philosopher. He was born in Pisa, and was the oldest of six children in his family. When he was a young
man, his father sent him to study medicine at the University of Pisa, but Galileo studied mathematics
instead. He later became professor and chair of mathematics at the University. Until about 1609 he taught
mathematics, and made several discoveries in physics. He helped to mathematically describe ballistics,
and the force of friction as it relates to motion. After experimenting with moving objects, he established his
"Principle of Inertia", which was similar to Newton's First Law.
Galileo then became interested in optics and astronomy, and in 1609 he built his first telescope and
began making observations. The following year he published his first results, where he described the
highlands and "seas" of the Moon, four of Jupiter's largest moons, and many newly discovered stars. He
also discovered the phases of Venus and sunspots, thereby confirming that the Sun rotates, and that the
planets orbit around the Sun, not around the Earth. But Galileo thought that most planetary orbits are
circular in shape, when in fact they are elliptical, as shown by Johannes Kepler. Still, Galileo's
observations have confirmed Copernicus' model of a heliocentric Solar System. They refuted the basic
principles of Ptolemean cosmology, and put to rest Aristotle's theory that the heavens were "perfect and
unchanging", which was supported by the Catholic Church. But the Church still allowed Galileo to conduct
his research, as long as he did not openly advocate his findings.
In 1632 Galileo angered the Pope when he published a book in which he openly stated that the Earth was
moving around the Sun. He was put on trial by the Inquisition in Rome, where he was found suspect of
heresy, and forced to say that all of his findings were wrong. He was first imprisoned, and later confined
to his house near Florence.
During the last ten years of Galileo's life, the Church monitored his travel and communications with
others, and his writings were censored and placed in the Index of Prohibited Books. Galileo continued to
write about physics, and in 1632 he put forward his concept of Basic Relativity in physics, which may be
stated as follows: "the laws of mechanics will be the same for all observers moving at the same speed
and direction with respect to one another." This fundamental concept later formed the basis for Einstein's
Special Theory of Relativity.
Until the time of Galileo, European scientists relied largely on Aristotle's approach of philosophical
analysis to explain physical phenomena. Galileo demonstrated the advantages of experimentation, and
argued that physics should be a mathematics-based science. Galileo was among the scientists, including
Kepler, Newton and others, who began the Scientific Revolution in Europe. Galileo's work was
instrumental in advancing the scientific method. His experimentational and mathematical approach to
physics was revolutionary and ahead of his time.
Did you know?

Galileo became completely blind by the age of 74, though he probably never looked at
the Sun directly through his telescope. Remember, you should NEVER look directly at
the Sun!

Galileo's telescopes had a magnification of only about 30x. He observed Neptune in
1612, but thought that it was a distant star. Galileo also observed Saturn's rings, but to
him they appeared as two separate bodies attached to the planet.

It is commonly believed that Galileo dropped balls of different mass from the leaning
tower of Pisa, to demonstrate that they fell at the same speed. There is no historical
evidence that Galileo actually did this. But it is possible that he suggested this experiment
as a way to disprove Aristotle's erroneous belief that heavier objects always fell faster
than lighter ones.

Galileo attempted (unsuccessfully) to measure the speed of light by placing observers
with lanterns about a mile apart.

Galileo is credited with making the first working thermometer, though it was not very
accurate.

Galileo's father, Vincenzo Galilei, was a musician and music theorist. He helped to invent
a new style of early Baroque music.

Earth's Orbit

Shortly after the telescope was invented in the Netherlands, Galileo fashioned his
own from makeshift spectacle lenses. He learned how to make increasingly
powerful telescopes, which he eventually used to to monitor the solar phases of
the planet Venus. After noticing Venus went through similar phases to the moon,
he concluded the sun must be the central point of the solar system, not the Earth
as was previously assumed.

The Principle of the Pendulum

At just 20 years of age, Galileo was in a grand cathedral and noticed that a lamp
swinging overhead took exactly the same period of time for each swing, even as
the distance of a swing got progressively shorter. This principle of the pendulum
made Galileo famous, and was eventually used to regulate clocks. The law
states that a pendulum will always take the same amount of time to finish a swing
because there is always the same amount of kinetic energy in the pendulum -- it
is merely transferred from one direction to the other.

The Law of Falling Bodies

This law states that all objects will fall at an equal rate, when accounting for
relatively minor differences in aerodynamics and weather conditions. Galileo
demonstrated this theory by climbing to the top of the Leaning Tower of Pisa and
dropping items of various weight off the side. All items hit the ground at the same
time. Contrary to the conventional wisdom established by Aristotle, the speed of
a heavy object's fall was found to not be proportional to its weight.

Astrological Discoveries

Galileo made several astronomical discoveries that people today simply accept
as common sense. He discovered that the surface of the moon is rough and
uneven as opposed to smooth as people had thought, and in 1610 he discovered
four moons revolving around Jupiter. More important than either of these was his
finding that many more stars exist than are visible to the eye, an assertion that
came as a shocking surprise to the scientific community at the time.

Mathematical Paradigm of Natural Law

For centuries, natural philosophy, which at that time encapsulated such fields as
physics and astronomy, was discussed and theorized from a qualitative
standpoint. Galileo didn't just discover specific laws of the universe, he reformed
the qualitative standpoint and established mathematics as the language of
scientific discovery. He pioneered the scientific method and ushered in the
modern practice of experimentation and calculated laws of nature. His doing so
led to the revelations that many of the laws of Greek philosophers such as Plato
and Aristotle were incorrect.
https://www.quora.com/What-astronomical-observation-of-Galileo-has-helpedweaken-the-Ptolemaic-model
The heliocentricity of Copernicus, Kepler and Galileo, explained the strange orbit of the
inner planets, Mercury and Venus. As observed from earth, they describe an 8-shaped
orbit. It is easy to understand why when plotting the orbits of all planets being around
the sun and not the earth.
Kepler became famous for finding that the earth's orbit was elliptical and not a perfect
circle, something that irritated the Vatican: How could a perfect God put the earth on an
orbit that was not a perfect circle?
Galileo Galilei was the first one to really observe the planets with a telescope and find
out, for example, that Jupiter had several moons. Those were, incidentally, later used as
a time table to compute the latitude when at sea.
Galileo
Galileo Galilei was the first astronomer to use a telescope to study the heavens. Galileo made a
number of observations that finally helped convince people that the Sun-centered solar system
model (the heliocentric model), as proposed by Copernicus, was correct. These arguments can be
divided into two kinds: Those that proved that the Ptolemaic model was incorrect; and those that
undermined the broader philosophy of Aristotelianism that included the Ptolemaic model. We'll
first consider some philosophically important observations and then the ones that proved Venus,
at least, goes around the Sun and not around Earth.
Sun and Moon
One of the ideas that made Aristotelianism popular with the church during the middle ages was
that the heavens are perfect. This also meant that they were unchanging, because if they change
then either they weren't perfect before or they won't be perfect after the change.
Galileo discovered spots on the Sun and also saw that the surface of the Moon was rough. People
really tried hard to account for these observations without making the heavens imperfect; one
suggestion was that over the mountains of the Moon there was a layer of clear crystal so the final
surface would be smooth and perfect!
Jupiter’s Moons
Galileo saw near Jupiter what he first thought to be stars. When he realized that the stars were
actually going around Jupiter, it negated a major argument of the Ptolemaic model. Not only did
this mean that the Earth could not be the only center of motion, but also it knocked a hole in
another argument. The supporters of the Ptolemaic model argued that if the Earth were moving
through space, the Moon would be left behind. Galileo’s observations showed that the moons of
Jupiter were not being left behind as Jupiter moved.
Phases of Venus
One observation definitely disproved the Ptolemaic model, although it didn't prove that
Copernicus was right (as Tycho Brahe pointed out). This was the observation that Venus has
phases, much like our Moon does.
To the naked eye, Venus always appears as a bright dot in the sky. With a telescope, however, it
is fairly easy to see the phases of Venus. Just as the Moon has phases, Venus too has phases
based on the planet’s position relative to us and the Sun.
There was no way for the Ptolemaic model (Earth centered solar system) to account for these
phases. They can only occur as Galileo saw them if Venus is circling the Sun, not the Earth.