Galileo Galilei and Constant Uniform Acceleration
For nearly over a millennium, Humans and civilizations turned from the teaching and
observations focusing on reality and rationality choose to focus spirituality and the teachings of
living a life pure and humble for the afterlife. These Middle Ages (around fifth century to around
the fifteenth century A.D.) provided little scientific improvement and discovery for civilization.
Yet around the end of the fifteenth century, a resurgence started to form in Italy with better
trading between Europe and the Middle East. Though many goods followed these trades, the
influence of ideas, cultures, and technologies also followed leading to Europe in a trend or
“rebirth” of learning known as the Renaissance.
The Renaissance came into fruition with events such as the “increasing multiple failure
on the Roman Catholic Church and Holy Roman Empire” and turn in philosophy from
spirituality towards Humanism.1 With less focus on spirituality, scholars began to focus on the
understanding of the natural world expressing the world through art, philosophies, and scientific
discoveries. These scientific discoveries came to influence a surge in mathematical advancement
as scholars were able to study, print and debate mathematical discussion and discoveries with
ease. The Renaissance provided many famous mathematicians such as Copernicus, Kepler, Da
Vinci, and Pitiscus, but of these scholars, the one who help set the foundation for many modern
day discoveries and mathematicians was Galileo Galilei.
Galileo Galilei, born February 15, 1564 in Pisa, Italy, came to become one of the most
influential figures of the scientific revolution sweeping during the Renaissance. “Originally sent
to be taught medicine at University of Pisa”2, he found the allure of mathematics and “decided to
make mathematical subjects and philosophy his profession.”3 Though often credited with the
discovery of the telescope, Galileo did not invent the instrument itself. However, Galileo
“improvised and improved a three-powered spyglass towards an eight-powered spyglass”4 that
lead to many successes in his career. Galileo was able to “draw the Moon’s phases, discovered
that Jupiter has four revolving moons, and there were countless more stars” indicating new
discoveries previously unknown about the universe.5 From his discoveries, Galileo holds a title
of a hero for mapping and showing a universe relatively unknown before his influences and
observations. Though regarded for his astronomy discoveries, Galileo contributed and paved a
way that “fundamentally changed the study of motion”6 and the “early development of the
scientific method.”7
Galileo had a curiosity to understand why and how objects moved in the world. Driven
by “linking theory with experiment”8, Galileo became curious of how and what laws of motion
governed all objects. From this desire comes one of Galileo’s most important experiments, The
inclined plane experiment. Galileo describes his experiment as follows:
A piece of wooden molding or scantling, about 12 cubits long, half a cubit wide, and three
finger-breadths thick, was taken; on its edge was cut a channel a little more than one finger
in breadth; having made this groove very straight, smooth, and polished, and having lined it
with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth,
and very round bronze ball. Having placed this board in a sloping position, by lifting one
end some one or two cubits above the other, we rolled the ball, as I was just saying, along
the channel, noting, in a manner presently to be described, the time required to make the
descent. We ... now rolled the ball only one-quarter the length of the channel; and having
measured the time of its descent, we found it precisely one-half of the former. Next we tried
other distances, comparing the time for the whole length with that for the half, or with that
for two-thirds, or three-fourths, or indeed for any fraction; in such experiments, repeated a
full hundred times, we always found that the spaces traversed were to each other as the
squares of the times, and this was true for all inclinations of the plane, i.e., of the channel,
along which we rolled the ball.9
Essentially, Galileo, without any reliable timing device and his own realization, discovered that
as the ball was allowed to roll freely on the ramp, the ball covered more distance that the
previous recorded time interval suggesting a change in the balls velocity. However, Galileo
discovered that the ball was constantly increasing its distance with a proportion of time squared
which indicates a constant force on the ball while on the ramp. Galileo proved that the ball had
an additional force that affected its velocity that was constant. Galileo had come to understand
every object had “forces acting upon objects could be broken into independent components,”10
but he also proved that the planet had a constant uniform acceleration acting on all objects.
Enforcing his thoughts and beliefs from the experiment, Galileo had paved the foundation
to modern mechanic. From his findings, Galileo theorized that all objects fall the same regardless
of its mass at a constant acceleration. “He surmised that if they fell in a vacuum, where there was
no air resistance to slow some objects more than others, even a feather and a cannon ball would
descend at the same rate and reach the ground at the same time.”11 This theory became Galileo’s
law of falling bodies which stated that without any outside forces affect an object, any object
would fall the distance of the acceleration multiplied by time squared or x=at^2. (A theory that
would not be proven true until the Apollo Eleven mission to the moon.) Galileo further seized his
law of falling bodies and applied the theory to all projectiles “stating that projectile’s trajectory
follow one of a parabola.”12 From his works, Galileo built the foundations to expand the
understand of the world and its mechanics leading the ideals which influenced Sir Isaac Newton
to develop the laws of motion and the foundations of calculus.
Galileo Galilei will forever be regarded as a renowned astronomer, mathematician,
philosopher, and scientist; however, Galileo became a victim of clashing philosophy and political
powers. Galileo found great discrepancies “of interpreting biblical passages with regard to
scientific discoveries but, except for one example, did not actually interpret the Bible.”13
Galileo’s discoveries strongly enforced and encouraged the heliocentric model produced by
Copernicus; a model that strongly undermined the ideals of the Catholic church which held
strong political power. From his belief and findings, Galileo was found guilty of heresy and was
force into house arrest by order of the Inquisition. Despite his later life troubles, Galileo Galilei
provided a new understanding of the physical world through experimentation and building
theories to support his finding serving as a foundation to study the physical world and universe.
1
Renaissance. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/event/Renaissance
2
Galileo. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/biography/Galileo-Galilei
3
Galileo. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/biography/Galileo-Galilei
Galileo. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/biography/Galileo-Galilei
5
Galileo. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/biography/Galileo-Galilei
6
Galileo. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/biography/Galileo-Galilei
7
Galileo. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/biography/Galileo-Galilei
8
MacDougal, D. W. (2012). Newton's gravity: An introductory guide to the mechanics of the universe. New York:
Springer.
9
MacDougal, D. W. (2012). Newton's gravity: An introductory guide to the mechanics of the universe. New York:
Springer.
10
MacDougal, D. W. (2012). Newton's gravity: An introductory guide to the mechanics of the universe. New York:
Springer.
11
MacDougal, D. W. (2012). Newton's gravity: An introductory guide to the mechanics of the universe. New York:
Springer.
12
Galileo. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/biography/Galileo-Galilei
13
Galileo. (n.d.). Retrieved October 7, 2016, from https://www.britannica.com/biography/Galileo-Galilei
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