Physical Science

Quarter 2

Department of Education • Republic of the Philippines

Lesson

1 MODELS OF THE UNIVERSE

The model of the solar system

today traces its history back to the
ancient Greek astronomy.

What’s In

You have studied the sun, moon,

stars, and other celestial bodies in your
Elementary Science. As you move to
Junior High School, you came to
understand the occurrence of eclipses,
solar system, and constellations.
Likewise, in the previous quarter, you
have learned how the elements in the
universe originated from the Big Bang. In
this module, we will look at the views of
the ancient Greeks about the universe
and understand how the model of the
Solar System originated.
 What is It

HOW GREEKS KNOW THAT THE EARTH IS ROUND

Even before Plato, the Greeks have deduced that the Earth is spherical
based on the observation that the shadow cast by the Earth during a lunar eclipse
is circular and that the only shape that can cast a circular shadow at whatever
direction it is pointed is a sphere. The Greeks were also able to measure the
diameter of the Earth. The Greeks also noted that the stars are viewed differently
as they travel north and south.
Eratosthenes, a Greek Mathematician, told
that no vertical shadow was cast as the
sun rays fall vertically in the city of Syene
in Egypt during summer solstice.
Eratosthenes noted that at the same time
a shadow was cast as the sun rays fell at
an angle of 7.2° [one fiftieth (1/50) of a
circle in ancient Greek writings] in the city
of Alexandria. He assumed that the sun
was so distant that the rays fall parallel to
each other on the Earth’s surface and that
the difference in the shadows cast in the
two cities was due to the curvature of
Earth’s round surface. The distance

Figure 2 Eratosthenes’ between Syene and Alexandia was found

measurement of the Earth’s to be 5000 stadia (approx. 800 km). Thus,
circumference Eratosthenes thought the Earth’s
From Ch. 2 Observing the Sky: The Birth of circumference must be 50 x 5000 stadia or
Astronomy—Astronomy p. 44 | OpenStax. (2016).
Download for free at
250,000 stadia (40,000 kilometers). Now,
https://openstax.org/details/books/astronomy. what is the significance of the spherical
shape of Earth? The sense of symmetry by
Greeks demands a spherical Earth located
at the center of the sphere of heavens.
ASTRONOMICAL EVENTS KNOWN TO MEN BEFORE THE ADVENT OF
TELESCOPES
Before the advent of telescopes, humans depended on their senses to grasp
the universe. Ancient Babylonian, Assyrian, and Egyptian knew the length of the
year and Egyptians, adopted a calendar based on 365 days a year. The Egyptians
also kept track of the yearly cycle of the star Sirius which corresponds to the
flooding of Nile. Early Chinese civilizations kept track of the comets, meteors, and
dark spots of the Sun. Mayan civilization also developed a calendar based on the
movements of Venus. Meanwhile, the Polynesians utilized the stars for navigation.
Below are astronomical events before telescope was invented.
Diurnal Motion
In modern astronomy, diurnal motion is defined as the apparent daily
motion of stars and other celestial bodies across the sky due to Earth’s rotation.
Man has observed the sun rising from the east and set in the west. The Greek
astronomers have described ‘fixed stars’ moving in the sky at the same
arrangement and speed as most of the stars are. Stars whose movements deviate
from what seems to be fixed stars were called ‘planetes’ which means ‘wandering
stars’ in Greek. The seven wandering stars are the Sun, moon, Mercury, Venus,
Mars, Jupiter, and Saturn.
Annual Motion
Annual motion is the apparent yearly motion of stars and other celestial
bodies across the sky due to Earth’s revolution. Below are events under annual
motion.
Zodiac and the Ecliptic
If we trace the path the sun takes in the celestial sphere as we see on Earth,
we would have traced the ecliptic. A band of thirteen constellations collectively
called zodiac can be seen in the ecliptic. Ancient civilizations have observed that
these constellations changes through months as constellations are visible at
different times in a year. These constellations served to mark the time for planting
and used by astronomers to develop a chart called horoscope.
Equinoxes and Solstices
Equinoxes are the two days in a year in which the sun crosses the celestial
equator occurring near March 20 (vernal equinox) and near September 22
(autumnal equinox). Midway between these two equinoxes is the solstices. Solstices
are the two days in a year in which the Sun is at the farthest declination (north or
south) from the celestial equator. Ancient Greeks and Early Chinese civilizations
have recorded solstices by observing the declination of the sun for several days
before and after the solstice. The calculated half-way between the days with the
equal declination of the sun at noon would be the solstice. This method also applies
for equinoxes.
Precession
Hipparchus in 150 BCE has discovered based on his observation that the
north celestial pole has changed during the period of a half - century. He noticed
that the slow and continuous
change in the direction in which
the sky is moving. We understand
at present that precession is the
slow ‘wobbling’ of Earth’s axis of
rotation due to the gravitational
pull of the Moon and Sun. Figure 3
illustrates the 26,000-year cycle of
precession. About 5,000 years ago
the north celestial pole is located at
the star Thuban. At present, the
Figure 3 Precession of the Earth
From Ch. 2 Observing the Sky: The Birth of Astronomy—Astronomy
p. 47 | OpenStax. (2016). Download for free at
https://openstax.org/details/books/astronomy
north celestial pole is located near the star Polaris and will be located at the star
Vega after 14,000 years.
Eclipse
Eclipses occur when either the Earth or moon cast a shadow into each other.
A solar eclipse occurs when the moon passes between the Earth and sun with the
moon casting a shadow on the Earth’s surface. A lunar eclipse occurs when the
Earth is directly aligned between the sun and moon with the Earth casting a
shadow on the moon. Take note that a solar eclipse may occur only during the new
moon phase, while a lunar eclipse may occur only during the full moon phase.
MODELS OF THE UNIVERSE
Throughout the history of astronomy, models of the universe have been
projected. The table below describes the model of the universe.
Ptolemaic system Copernican system Tychonic system
Proponent Claudius Ptolemy Nicholas Copernicus Tycho Brahe
Center of Earth Sun Earth
universe
Orbits All other celestial All planets including The moon and sun
bodies revolve Earth revolves around revolve around
around the Earth. the Sun. Only the moon Earth. All other
revolves around the planets revolve
Earth. around the sun.
Stars The stars are located The stars are located The stars are
and fixed in the and fixed in the located and fixed in
outermost celestial outermost celestial the outermost
sphere. sphere. celestial sphere.
Explanation Utilized the epicycles Differences in the orbital Same as the
of and deferent to speed of the planets Copernican
retrograde explain the apparent explained the retrograde System.
motion westward motion of motion of the planets.
the planets. (See Planets nearer to the
figure 7a) Sun revolves faster than
those that are far from
the Sun.
Illustration

Figure 4 Geocentric Figure 5 Heliocentric Figure 6 Geo-

model according to model according to heliocentric model
Ptolemy Copernicus according to Brahe
https://upload.wikimedia.org/wik https://commons.wikimedia.org/w/in https://commons.wikimedia.o
ipedia/commons/8/8f/Ptolemaic_ dex.php?curid=12353176 rg/w/index.php?curid=53903
system_%28PSF%29.png 3
 (a) (b)

Figure 7 (a) Retrograde motion of Mars as seen in the celestial sphere (b) epicycle
used by Ptolemy to explain retrograde motions.
From Ch. 2 Observing the Sky: The Birth of Astronomy—Astronomy (a) p. 47 (b) p.48 | OpenStax. (2016). Download for free at
https://openstax.org/details/books/astronomy

Planets usually rise from east to west as we see in the celestial sphere.
However, it was observed by the ancient astronomers that the planets seem to
move westward for several weeks and move eastward again in the succeeding
weeks. In our current situation, we can explain that these retrograde motions were
due to the difference in the period of revolution of the planets around the sun as
seen in figure 7a. With Earth being closer to the sun, it moves faster than the
planets farther from the Sun. Ptolemy in his time held the belief that the Earth
does not revolve and is the center of the universe. The epicycle was used to explain
these retrograde motions. Here, a planet revolves in an orbit called epicycle while
the center of the epicycle revolves around Earth. This path of revolution of the
epicycle is called deferent.
TYCHO BRAHE AND JOHANNES KEPLER
Tycho Brahe, a Danish astronomer continuously and precisely recorded the
position of the sun, moon, and planets for over 20 years using instruments that are
like giant protractors. He noted based on his observations that the positions of the
planets differ from those that were published. However, he was not able to develop
a better model than Ptolemy’s as he didn’t have the ability to analyze his data.
Years before his death, he hired Johannes Kepler as a research assistant to aid in
analyzing his data. Brahe was reluctant to provide such data to Kepler, but at his
death, the observational data was possessed by Kepler. Being knowledgeable in
geometry, Kepler was able to derive from Brahe’s data that the orbital path of Mars
was elliptical contrary to the previous investigators who were trying to fit the
planetary paths in circles. Generalizing his results, he was able to formulate the
three laws of planetary motion:
1. Law of Ellipse: orbits of all the planets are elliptical with the Sun at one
focus of the ellipse. An ellipse is a somewhat flattened circle. It is a closed
curve in which the sum of the distances from any point on the ellipse to foci
(two points inside) is constant.
2. Law of Equal Areas: a line joining a planet and the Sun sweeps out equal
areas in space in equal intervals of time. Thus, a planet moves fastest when it
is nearest to the sun
 3. Law of Harmony: the square of a planet’s orbital period (years) is proportional
to the cube of the semimajor axis of its orbit (in astronomical units or AU) or
𝑃2 = 𝑎3. Thus, the larger the orbit’s size, the longer it takes to orbit the sun.

Physical Science
Quarter 2
Investigating Principles Governing
Motion
“The physics of motion provides one of the clearest examples of the intuitive and
unexpected nature of Science.” -Lewis Wolpert

What’s In
In the previous lesson, you have learned how ancient Greeks presented the concept of spherical
Earth, cited different astronomical phenomena known before the advent of the telescope, and
explained Brahe’s inventions and discoveries which paved the way to the development of Kepler’s
laws of planetary motion. In this module, you will examine Aristotelian and Galilean conceptions
regarding motion, describe a body in motion exhibiting uniform acceleration, explain the
distinction between Newton’s first law of motion to Galileo’s assertion, and identify the practical
applications of the aforementioned topics in our day to day living.

Galilean Conceptions vs. Aristotelian Conceptions

According to Aristotle, motion is classified as natural or violent motion. He explained that
in a natural motion, a body will move and will return to its natural state based on the
body’s nature and composition. In contrast, a body moving in a violent motion needs an
external force for it to move. However, Galileo disproved Aristotle’s claims and stated that
the motion of a body is not due to its composition. He further asserted that the motion of
a body can be described by measurement and the changes in quantifiable variables such
as time and distance. Lastly, he further asserted that:
1. A body who is in uniform motion will move a distance that is proportional to the time it
will take to travel;

2. A uniformly accelerating body will travel at a speed proportional to time; and

3. An object in motion will keep moving; and the external force is not necessary to
maintain the motion.

With regards to the concept of vertical motion, Aristotle pointed out that the velocity of a
body is inversely proportional to the time it covers to travel a certain height. On the other
hand, Galileo emphasized that if two objects of different weights are dropped from a high
point, both will hit the ground at the same time.
In terms of horizontal motion, Aristotle mentioned that bodies require force to maintain
horizontal motion. In the contrary, Galileo asserted that if there is no interference, a body
in motion will keep moving in a straight line forever. He further added that there is no
need to apply force for it to continuously move. The external force will act upon the body
not to keep it from moving, but for it to stop moving.
Lastly, with regards to projectile motion, Aristotle coined the concept of antiperistasis
which is the resistance of a medium in response to the movement of a body; while Galileo
explained that projectiles follow a curved path with a horizontal and vertical component.
Galileo and his Uniform Acceleration
Galileo asserted using his cannonball experiment that when objects are dropped
simultaneously at the same height, they will reach the ground at the same time
regardless of mass, size, and air resistance. This experiment paved the way for the
discovery of the principle of uniform acceleration. 8
Furthermore, he noticed that falling objects increases their speed as they go down and he
coined this change in speed as acceleration. His observations lead to remarkable
conclusions that regardless of the mass, size, and shape of an object, and air resistance,
falling objects will always have uniform acceleration and that, force is not necessary to
sustain the horizontal motion of a body. He further asserted that the speed of a body is
directly proportional to the time it travels a path and that the distance covered by a
moving body is directly proportional to the square of time interval which implies that the
speed of a falling object does not depend on a body’s weight but on the time of fall. Lastly,
using his inclined plane experiment and cannonball experiment, he came up with the
following observations and conclusions:
➢ A body moving down an inclined plane increases its acceleration by the same value
after every second.
➢ The maximum acceleration of a body is attained when the inclined plane is positioned
vertically as if the body is falling.
➢ Using the law of parabolic fall, he concluded that bodies fall with constant
acceleration on the surface and that gravity pulling all
bodies downward is a constant force. In this regard, he found out that force is not
necessary to sustain horizontal motion.

Galileo’s Assertion and Newton’s Laws of Motion

Galileo Galilei proposed the first accurate principle governing motion and masses in his
experiments wherein, remarkable findings such as bodies accelerate at the same rate
regardless of their respective masses and sizes and that force is not needed to sustain
horizontal motion were emphasized. He stated that the mass of an object is proportional
to its resistance to move and that force is not necessary to keep an object in motion.
However, Sir Isaac Newton proposed Laws on Motion anchored on the findings of Galileo
and expounded his assertions. In his first law of motion, he mentioned that an object at
rest will remain at rest unless acted upon by an external force and a body in motion will
keep moving unless external force is acted upon it. Lastly, he stated that a body will only
accelerate if an external force is acted upon it.
Newton’s first law states that, if a body is at rest or in motion, it will remain at rest or keep in
motion unless an external force is acted upon. This postulate is known as inertia which was
proposed by Galileo in his experiment about horizontal motion wherein, he stated that a body
requires an external force to move and that an external force must be acted upon for a body to rest.
On the other hand, the second law states that the change in momentum of a body is equal to the
magnitude and direction of force acting upon it. He further added that force is the product of the
mass of an object and its acceleration. Lastly, the third law also known as the law of interaction
states that when two bodies interact, both will apply equal amount of forces to one another in the
opposite direction.

What I Have Learned

1. The motion of a body can be described by the measurement and the changes in
quantifiable variables such as time and distance.
2. Objects dropped simultaneously at the same height will hit the ground at the same
time regardless of mass, size, and air resistance.
3. Force is not necessary to sustain horizontal motion.
4. Inertia refers to the ability of a body to resist change in motion.