Senior High School
Physical Science
Quarter 2 - Module 1
How we Come to Realize that the
Earth is Not the Center of the Universe
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Physical Science- Grade 11/12
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Quarter 2 - Module 1: How we Come to Realize that the Earth is Not
the Center of the Universe
First Edition, 2020
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Senior
High
School
Senior
High
School
Physical Science
Quarter 2 - Module 1
How We Come to Realize that the Earth
is Not the Center of the Universe
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Table of Contents
What This Module is About ………………………………………………………………………………………..…….
What I Need to Know ............................................................................................................................................... i
How to Learn from this Module………………………………………………………………………………………..... ii
Icons of this Module …………………………………………………………………………………..……………………… ii
What I Need to Know………………………………………………………………………………………………………...
Lesson 1:
How the Greeks Knew that the Earth is Spherical ………..………….……
What I Need to Know: ………………………………………………….………………………….…….…….
iii
1
1
What’s New: And the Shape Is ………………………………………………..………………..….…….. 1
What Is It: Sphere It Is ……………………………………………………………………………….....….…. 2
What’s More: What is the Evidence Again?........................................................................
3
What I Have Learned: Synthesizing your Learning……………………………………….……
4
What I Can Do: DepEd TV Live ……………………………………….………………………………...
4
Lesson 2:
Astronomical Phenomena Known to Astronomers
Before the Advent of Telescopes …………………………….………….………..…………
What’s In ……………………………………………………………….…………………………….…….
6
6
What I Need to Know………………………………………………………………………….……..
6
What’s New: What’s the Word ……………………………….……………………….…..……
6
What Is It: Pre- Telescope Observed Phenomena ………………….………………
7
What’s More: The Phases of the Moon and Me……………………………………….
8
What I Have Learned: Synthesizing your Learning ……………………………….…
9
What I Can Do: The Sun’s Movement……………………………………………………….. ...9
Lesson 3:
Brahe’s Innovations …………………………………………………………………………………………..
10
What’s In …………………………………………………………………………………………………...
10
What I Need to Know………………………………………………………………………………...
10
What’s New: The Who .............................................................................................................. 10
12
What Is It: Tycho Brahe’s Contribution……………………………………………………….. 11
2
What’s More: The Data Says……………………………………………………………………... 13
What I Have Learned: Here’s My Take ………………………………………..…………… 13
What I Can Do: As I Ponder On …………............................................................................ 13
………............................................................................................................................................................
14
Assessment: (Post-Test)…………………………………………………………………………………….………….….
15
Summary
Key to Answers ………................................................................................................................................................. 17
References ………........................................................................................................................................................... 19
7
What This Module is About
Physics is everywhere it comprises all the laws that govern minute objects to a
matter of cosmic proportion. That is why it is considered basic science.
This module covers the first three ideas of the second part of this two-part Physical
Science core subject which is Physics. This particularly dwells on the views and ideas of the
ancient philosophers on the spherical shape of the Earth. This also covers the discoveries of
other planets and cosmic happenings even before the invention of the telescope including
the utilization of the vast data collected by Brahe in the formulation of laws of planetary
motion by Kepler.
Together, let us scan the next few pages of this module for us to appreciate the work
of the ancient great thinkers. Through their wit and keen observation, the foundational ideas
on how this universe worked have been laid out, built upon and refined as time goes by.
This module contains varied activities that can help you as a Senior High School
student to not just gain knowledge on how they came about ideas of the Earth and the
cosmos but most importantly learn from them on how they utilize this knowledge and
information in making their lives better.
This module covers the following lessons:
1. How the Greeks knew that the earth is spherical
2. Astronomical phenomena known to astronomers before the advent of telescopes
3. Brahe’s innovations
What I Need to Know
At the end of this module, you should be able to:
1. Explain how the Greeks knew that the Earth is spherical (S11/12PS-IVa-38)
2. Cite examples of astronomical phenomena known to astronomers before the advent of
telescopes (S11/12PS-IVa-41)
3. Explain how Brahe's innovations and an extensive collection of data in observational
astronomy paved the way for Kepler’s discovery of his laws of planetary motion
(S11/12PS-IVb-44)
i
How to Learn from this Module
To achieve the objectives cited above, you are to do the following:
•
Take your time to read the lessons carefully.
•
Follow the directions and/or instructions in the activities and exercises diligently.
•
Answer all the given tests and exercises.
Icons of this Module
What I Need to
Know
This part contains learning objectives that
are set for you to learn as you go along the
module.
What I know
This is an assessment as to your level of
knowledge of the subject matter at hand,
meant specifically to gauge prior related
knowledge
What’s In
This part connects the previous lesson with
that of the current one.
What’s New
An introduction to the new lesson through
various activities, before it will be presented
to you
What is It
These are discussions of the activities as a
way to deepen your discovery and
understanding of the concept.
What’s More
These are follow-up activities that are
intended for you to practice further to
master the competencies.
What I Have
Learned
Activities designed to process what you
have learned from the lesson
What I can do
These are tasks that are designed to
showcase your skills and knowledge gained
and applied to real-life concerns and
situations.
ii
What I Know
Multiple Choice. Select the letter of the best answer from among the given choices.
1. Which of the shapes below represents the belief of the Greeks about the shape of the
Earth?
A
B
C
D
2. Which among the philosophers measured the Earth’s circumference?
A. Aristotle
B. Pythagoras
C. Plato
D. Eratosthenes
3. How did the Greeks especially Aristotle use the lunar eclipse phenomenon to explain that
the Earth is not flat?
A. He noticed that the shadow casts by Earth on the moon is round.
B. He argued that since the shape of the moon appears to be round then the Earth
must also be round.
C. He argued that lunar eclipse only happens when a round opaque object blocks the
passage of sunlight.
D. He noticed that all things seemed to be moving around the Earth except for Earth
itself.
4. Which of the following is true about how the Greeks knew that the Earth is not flat?
A. They observed that Earth is rotating on its axis.
B. They noticed that even in short travels northwards the Pole star is higher in the
sky.
C. They have seen Earth from outer space.
D. They observed that during a solar eclipse, Earth is temporarily covered with
darkness during the daytime.
5. Which time of the year did Eratosthenes observe the pillar in Alexandria cast a shadow?
A. noontime during spring
B. noontime during the summer solstice
C. noontime during solar eclipse
D. noontime during the winter solstice
6. Which of the following astronomical phenomena was already observed by the ancient
people even before the telescope was invented?
A. sunspot
B. solar eclipse
C. craters of the moon
D. atmosphere of Mars
7. Which of the following objects would most likely cast a shadow on the moon during a lunar
eclipse when it is observed here on Earth without the aid of a telescope?
A. Sun
B. Moon
C. North star
D. Earth
8. Which phase of the moon is shown in the figure below?
A. full moon
C. new moon
B. first quarter moon
D. last quarter moon
Iii
9. Which phase of the moon is shown in the figure below?
A. full moon
B. first quarter moon
C. last quarter moon
D. new moon
10. How did the ancient astronomers discover that Mercury and Venus are planets not stars?
A. They noticed that the stars are in a fixed position to each other. But they have
observed that there are very bright stars wherein its positions periodically change.
B. They noticed that Mercury and Venus are bigger compared to the other stars.
C. They noticed that the constellations’ positions in the night sky vary depending on
the time of the year.
D. They noticed that the stars change positions periodically. But there are very bright
stars in a fixed position to each other.
11. Which of the concept below is Tycho Brahe’s major contribution to the field of
astronomy?
A. the Earth’s pull of gravity on the moon
B. measurement of Earth’ circumference
C. accurate measurement of stars’ and planets’ position
D. the invention of the telescope
12. Kepler’s first law of planetary motion is known as ________.
A. Law of Ellipses
B. Law of Gravity
C. Law of Periods
D. Law of Equal Areas
13. Which of the following statements bests describe Brahe’s model?
A. The planets except Earth revolve around the Sun, while the moon and the Sun
revolve around the Earth.
B. The Sun and the Earth are both at the center and the other planets revolve around
it.
C. All the planets revolve around the Sun while the moon revolves around the Earth
D. Neither the Sun nor the Earth is at the center and the other planets do not revolve
around it.
14. Kepler discovered that planets do not go around the Sun at a uniform speed but it
depends on its position relative to the Sun. What is its speed when it is closer to the
Sun?
A. faster
B. neither fast nor slow
C. slower
D. similar to the speed when it is far
from the sun
15. What relationship did Kepler discover between the times of revolutions of the planets and
their distance from the Sun?
A. The square of the times of revolution of the planets are proportional to the cube of
their average distance from the Sun.
B. The square of the times of revolution of the planets is not proportional to the cube
of their average distance from the Sun.
C. The cube of the times of revolution of the planets are proportional to the square of
their average distance from the Sun.
D. The cube of the times of revolution of the planets is not proportional to the square
of their average distance from the Sun.
iv
Lesson
1
How the Greeks Knew that the
Earth is Spherical
What I Need to Know
You have probably gazed at the sky on a clear night and wonder about whether there
are aliens or parallel universes out there. With the advent of space explorations, the notion
of living on Mars has already been entertained by some people just in case Earth ceased to
be a habitable planet in the future. Or maybe you imagined taking a vacation on board on a
space ship and your destination is outer space! Isn't it cool?
Ancient people perhaps did not think about aliens or the parallel universe or thought
of going to Mars, but one thing is sure they too were curious about their surroundings and
tried to seek answers and explanations.
In this lesson, you will be able to explain how the Greeks knew that the Earth is
spherical.
What’s New
Activity 1.1.1 And the Shape Is
Aim: To find out the shape of the shadow
Materials: - Actual Flashlight or use the flashlight app of the mobile phone (if both materials
are not readily available, you may use a lighted candle .Caution: Be sure to put
off the candle immediately after use)
- Two spherical objects; 1-big, 1-small (alternative: make your own balls using
crumpled used papers;1-big, 1-small)
- ruler
Procedure:
1. Align the flashlight
and the balls
horizontally.
2. Point the flashlight
to one of the balls.
3. Observe the
shadow it casts on
the ball behind it.
(Note: Perform the
activity in a
darkened room or
Fig.1.1.1. The flashlight and the two balls are ligned
with each other.
during night time)
Questions:
1. What is the shape of the shadow cast by Ball 1?
2. Which of the two balls represents the Earth? the Moon?
3. Supposed that the moon or Earth is a heart shape, what shadow would it form when
sunlight is aligned with it? Why?
1
What Is It
Sphere It Is
Did your careful observation prove you right? Just like you, before the Greeks and
the rest of the ancient people were able to formulate theories of the sky and the Earth, they
made a careful and repetitive observation of the phenomena around them.
The Mesopotamians as accounted in their mythology around 6 th century BC
described Earth as a flat disk floating in the ocean and bounded by a spherical sky. This
idea has prevailed for hundreds of years until a new view was presented.
As the quest for knowledge continues and civilization prospers, several models of the
universe were presented. And it is categorized as a geocentric model or Earth-centered
and heliocentric model or Sun-centered. In the geocentric model, the Earth was at the
center and the rest of the planets and heavenly bodies revolved around it. While in the
heliocentric model, the Sun was at the center and the rest of the heavenly bodies including
the Earth moved around it.
In all of the geocentric models of the universe, the Earth and other heavenly bodies
were assumed to be spheres. They were convinced that the shape of the Earth was not flat
instead it was spherical. This idea was already entertained by Pythagoras and Plato
however they do not have concrete evidence to support their claim. Until Aristotle (around
320 BC), a student of Plato presented his arguments that established the claim during their
time.
Aristotle argued that:
- the sphere is perfectly solid and the heavens are a region of perfection
- the Earth's component pieces, falling naturally towards the center, would press
into a round form
- in an eclipse of the Moon, the Earth's shadow is always circular thus, if Earth is a
flat disc, it would cast an oval shadow
- even in short travels northwards the Pole Star is higher in the sky.
Another phenomenon considered by Greeks in their claim of Earth's spherical shape
was navigation. They observed that when ships sails away, it seems that it gradually
disappears behind the horizon.
Is there still other evidence that you know about that are not listed here? Can you
name them?
If it is not a sphere then why measure its circumference
One of the astronomical events that fascinated the early civilization was the eclipse.
And the recorded information about eclipses was used by Eratosthenes (about 235 BC) to
approximate the circumference of the Earth. This was another proof presented about the
spherical shape of the Earth. As you know an eclipse is a shadow formation. This happens
when the path of light rays is blocked by an object.
While working as a librarian at the University of Alexandria in Egypt, he came across
information that during summer solstice especially at noontime, sunlight shines directly down
a deep well in Seyene, a city south of Alexandria and reflected up again and no shadow is
cast by any object on a noontime.
But in Alexandria at the same date and time, a vertical pillar and other structures cast
a shadow.
2
And so, Eratosthenes measured the shadow cast by a vertical pillar in Alexandria
and he found out that it is 1/8 of the height of the pillar.
This is roughly equivalent to
a 7.20 angle between the sun's rays
and the vertical pillar while in
Syene it's 00. Based on his
calculation, 7.20 is equivalent to
1/50 of a circle. Thus, it follows that
the distance between Alexandria
and Syene must be 1/50 the
circumference of the Earth. Or the
Earth's circumference is 50 times
the distance between the two cities.
Since these two cities are
frequently traveled, the distance Fig 1.1.2. When the rays shine directly above at Syene, it is not
directly overhead at Alexandria which around 800 km
was measured to be 5000 stadia
north. The pillar in Alexandria cast a shadow, while the
(800 kilometers). So the Earth's
water in the deep well at Syene directly reflected the
circumference is 50 x 5000 stadia
sunlight.
= 250 000 stadia.
Are you now convinced that indeed the Earth is spherical?
What’s More
Activity 1.1.2: What are the Pieces of Evidence Again?
Aim: To share the information about the pieces of evidence of Earth's spherical shape through a
graphic organizer.
Materials: 1- long size bond paper/ cartolina of any color cut into long size bond paper
a pair of scissors
coloring materials
ruler
Instructions:
Make a trifold foldable using the long size bond paper. Just follow the word and
graphic instructions below.
a. Fold lengthwise the long size bond paper (8.5 x 13 inches bond paper/cartolina.) Using a
ruler, measure around 4.3 inches from the long side of the bond paper and fold the paper
from the 4.3 inches mark then fold again so that you can create the tri-fold foldably. Cut
down the two folds to the centerfold. In each flap, write down the evidence of the
spherical shape of the Earth. Organize the pieces of evidence by the philosopher. To
make the organizer more creative, illustrate your interpretation of the pieces of evidence.
4.3 in
b. Fold the three flaps down. In the flap write the name of the astronomer where the evidence
is credited to. If the evidence is not credited to a philosopher, simply write other
evidence/s. Then fold the two side flaps toward the center panel. Write the concept title
onto the front flap. An appropriate design on the title flap may also be added.
3
Front
flap
c. Paste your tri-fold foldable in your answer sheet.
What I Have Learned
Activity 1.1.3: Synthesizing Your Learning
Answer the following questions based on your learning. Be brief and concise.
Of all the arguments presented by the Greeks as proof that the Earth is spherical, which
among you find more convincing? Why?
What I Can Do
Activity 1.1.4: DepEd TV Live
You are a scriptwriter and at the same time actor of a production outfit for an
educational television show. You will feature in your show's next episode the evidence
presented by the Greeks about the spherical shape of the Earth. Choose only 2 pieces of
evidence and prepare a script for it. Make a video presentation based on the script. Your
segment will run for two (2) minutes. To make your presentation more convincing, it should
include correct information and must be interesting and creative. The language format of
your show is in Filipino/English.
Note: Videographer and extra casts or actors may be recruited for this activity but it should
be limited to the members of your family.
DepEd TV Live Activity Rubric
Criteria
Accuracy
10 points
The data included in
the presentation are
well researched.
8- 6 points
The data included in
the presentation
contain a few minor
errors.
5-4 points
The data included in
the presentation
contain a few errors.
Visual Appeal
The presentation
shows visually
appealing images
and artistic.
The presentation
has a few images
that are not visually
appealing and fairly
artistic.
The presentation's
images are not
visually appealing
and not artistic.
SCORE
Total Score
4
Creativity
The presentation is
very creative and
interesting
The presentation is
fairly creative and
interesting
The presentation
lacks creativity and
is not interesting
Lesson
2
Astronomical Phenomena
Known to Astronomers Before
the Advent of Telescopes
What’s In
In lesson 1, we have learned about how the Greeks knew that the Earth is spherical.
The presented evidence like the arc shape of the shadow cast by Earth on the moon during
a lunar eclipse and mathematical evidence given by Eratosthenes when he measured the
circumference of the Earth.
What I Need to Know
In this lesson, we will learn more about the examples of astronomical phenomena
discovered by astronomers even before the invention of the telescope.
What’s New
Activity 1.2.1: What’s the Word
Aim: To identify the words from the puzzle that has something to do with astronomical
phenomena.
Instructions:
Encircle 10 words about the phenomena or things discovered by ancient astronomers
before the advent of the telescope. The words can be read horizontally, vertically or
diagonally.
Search for the following words:
 lunar eclipse
 solar eclipse
 full moon
 new moon
 first quarter moon
 shadow
 stars
 sunset
 Mercury
 Venus
What Is It
Pre- Telescope Observed Phenomena
In this modern time, we come to know of the things around us because there are
appropriate instruments or gadgets used to study or analyze such an event or phenomenon.
6
Taking for example the telescope, it is one of the instruments invented by mankind that is
very useful in studying the cosmos. But despite the absence of the telescope in ancient
times, still they were able to discover some astronomical phenomena. Just like the periodic
motion of the sun across the sky, they noticed that the sun rises from the east and sets in
the west. Below is the list of other pre-telescope astronomical events studied by ancient
people.
1. Phases of the Moon
The appearance and
path of the moon were
observed
by
ancient
people to change within
29.5 days. They observe
that the moon changes
appearance from a thin
semi-circular disk to a full
circular disk. The periodic Fig.1.2.1 Moon's relative position to the Sun as it moves around the
Earth attributes its changing appearance as viewed from
change of the moon's
the Earth
phases was the basis of the
ancient calendar.
2. Lunar Eclipse
One of the things that caught the attention of the ancient people was the time in a
month when the moon or part of it seemed to be covered by a shadow for a brief moment.
A phenomenon such as this is known as a lunar eclipse. A lunar eclipse occurs when
Earth is between the
moon and the Sun,
Earth casts a shadow
Fig. 1.2.2
A lunar eclipse occurs
Earth’s shadow is cast on
the moon.
on the moon.
3. Solar Eclipse
A solar eclipse
happens when the moon
Fig. 1.2.3
is in between the Sun
and the
Eartheclipse
and occurs
the
A solar
a moon’s shadow
moon whenpartially
or
is
cast
on
Earth
completely blocks out
the Sun. This caused
temporary darkness on a
day time, thus, ancient
people feared the occurrence of a solar eclipse since they associate it with the wrath of God.
7
4. The Motion of the Stars
The astronomers noticed that the constellations’ positions in the night sky vary
depending on the time of the year. It was also observed that the stars seem to be
attached to a celestial sphere that rotates around an axis in one day.
5. Visibility of Planets
They noticed a few stars in heaven are relatively brighter than the rest of the stars.
The distant stars seemed to be fixed in their position but these stars change positions
periodically, thus the Greeks called it "wanderers" or planets. These wandering stars are
named Mercury, Venus, Mars, Jupiter, and Saturn which later discovered to be planets,
not stars.
Now that you have learned about the different astronomical events even before an
instrument like a telescope was invented. From the information that they gathered, it has
resulted in innovation and invention. One of these is the calendar.
With the use of a calendar at home, how about you try tracking the change of phase of
the moon without necessarily looking at the sky at night time. In most of the modern
calendars, the moon's movement is indicated.
What’s More
Activity 1.2.2: The Phases of the Moon and Me
Aim: To keep track of the periodic change of the phase of the moon for three months.
Materials: Calendar of the current year that indicates the movement of the moon
Procedure:
1. Choose three consecutive months of the current year (ex. January – March or
February to April).
2. For every month, check out the dates of the four major phases of the moon (1 st
quarter, full moon, last quarter and new moon).
3. Using the table below, list down the dates.
Month/ Phases
A
B
C
Ex. July 2020
Full Moon
5
Last
Quarter
13
New
Moon
21
4. Then count the number of days’ interval from one phase to another.
First
Quarter
28
8
Days interval/Month
Full moon – Last quarter
Last quarter – New moon
New moon- First Quarter
First Quarter of the current month and
the full moon of the next month
Total no. of days to complete the cycle
A
B
C
Ex. July 2020
8
8
7
July-Aug
6
29
Questions:
1. How many days would take the moon to complete the cycle for:
Month A_____________
Month B_____________ Month C_____________
2. What have you noticed with the time interval as the phase changes from one phase to
another within three months? What is the average time to complete the cycle?
What I Have Learned
Activity 1.2.3: Synthesizing Your Learning
Answer the following questions based on your learning. Be brief and concise.
1. How is a solar eclipse different from a lunar eclipse?
2. How did the ancient astronomers identify the visible planets from the rest of the stars?
What I Can Do
Activity 1.2.4: The Sun’s Movement
Aim: To keep track of the movement of the Sun particularly during sunrise and sunset.
Instructions:
1. Listen to the announcement over the radio or watch TV for the weather bulletin a
day before you make your observation on the expected time that the sun will rise
in the morning and sets in the afternoon the following day.
2. Be sure to rise early on the next day.
3. Choose a location that you can have a good vantage point for both the sunrise
and sunset.
4. Observe the movement of the Sun during sunrise for 1 hour. For the sunset
watching, do it 40 minutes before the expected time that the sun will set.
5. Draw or illustrate the pattern of the sun's movement within 1 hour in the morning
and 40 minutes before sunset.
6. Use any size of bond paper for your illustration.
7. Give a short description of the observation you have made.
8. Paste the output in your science activity notebook.
Sample layout
Name:
Grade and section:
Date:
Subject:
THE SUN’S MOVEMENT
During sunrise
During sunset
Drawing
Drawing
Brief description
Brief description
9
3
Lesson
Brahe’s Innovation
What’s In
In lesson 2, we have learned about the discovery of astronomical wonders even
without the aid of an instrument especially the telescope. Aside from that they also made us
realize that our surroundings not only heavens have a great influence on one's way of living.
What I Need to Know
In this lesson, you will be able to explain how Brahe's innovations and an extensive
collection of data in observational astronomy paved the way for Kepler's discovery of the
laws of planetary motion.
The knowledge about the universe starting from the ancient time up to the present
has proven to be a dynamic one. The discoveries weakened the foundation of a theory that
thought to be correct and widely accepted for quite a long time. And in the process of
revolutionizing the idea, one must be able to back the claim with proof. The best proof one
could present is data that is verified and tested several times. Just like the works of Tycho
Brahe.
But before we discuss further the concept, let’s try to look back and look ahead of the
who’s who in the field of astronomy by associating the names of astronomers,
mathematicians or scientists and their contributions by answering the activity on the next
page. If you are not certain of your choice, don’t worry just give it a try.
What’s New
Activity 1.3.1: The Who
Match the names in column A with their corresponding contribution in column B. Write the
letter that corresponds to your answers on the space provided.
Column B
Column A
a. proponent of the universal law of gravitation.
______ 1. Eudoxus
______ 2. Tycho Brahe
______ 3. Aristotle
______ 4. Claudius Ptolemy
______ 5. Johannes Kepler
______ 6. Galileo Galilie
______ 7. Eratosthenes
______ 8. Aristarchus of Samos
______ 9. Nicolaus Copernicus
______ 10. Isaac Newton
b. invented his own telescope and discovered the craters of the
moon and gathered proof that supports the claim of
Copernicus
c. proposed the geo-heliocentric universe model
d. proposed the first idea of a heliocentric universe.
e. proponent of the laws of planetary motion
f. calculated the Earth’s circumference
h. proposed a geocentric model of the universe where Earth is at
the center and is layered with earth, water, air and fire.
i. proponent of a heliocentric universe wherein a moving
Earth is revolving around the Sun
j. proponent of the Earth-centered model universe where Earth
lies stationary at the center of the celestial sphere.
k. proposed a homocentric and concentric universe
10
What Is It
Tycho Brahe’s Contribution
If you got all the answers in Activity 1.3.1 correctly and correlate it with the timeline
in Fig.1.3.1., you will see that the geocentric universe model has prevailed for thousands of
years.
Fig. 1.3.1
The timeline
of some of
the who’s
who in the
field of
astronomy
and
mathematics
Only in the latter part of the 16th century that this idea was questioned by Copernicus
wherein he proposed that it's the Sun, not the Earth is the center of the universe.
The conflicting ideas and
pieces of evidence in both models
have pushed Brahe to come up with
his own model. Backed with his
accurate measurement of the
distance and positions of the
planets and stars, he proposed the
geoheliocentric model of the
universe, a hybrid of the geocentric
model of Ptolemy and the
heliocentric model of Copernicus. In
his model, the Sun orbited Earth,
while the other planets orbited the
sun.
Fig. 1.3.2 Brahe's model of the universe is also called the
Tychonic model. It is considered as a hybrid of geocentric and
heliocentric models of the universe.
It was also during this time that Brahe met the young German mathematician
Johannes Kepler. Brahe hired Kepler as a sort of "research assistant" primarily to prove that
Brahe's model the geoheliocentric model is the right model. Kepler's task is to fit in the data
collected by Brahe into the model he proposed by doing the mathematical calculation.
Unfortunately, Brahe died before his model is proven. Kepler inherited a vast set of data that
will prove crucial for developing his Three Laws of Planetary Motion later. Kepler spent many
more years trying out many possible models to fit the available data that he inherited.
But Kepler failed to reconcile the data on hand with the model Brahe proposed
especially on the notion of the stationary Earth. It took another brilliant mind and his
invention of the telescope to prove that Copernicus was right in proposing that Earth after all
is not the center of the universe.
11
But despite everything still, something good came out of his persistence, after about
20 years or so working with the data he got from Brahe; the Three Laws of Planetary Motion
were published in two different years:
First Law: Law of Elliptical Orbit or Law of Ellipses (1609)- The planets move in
elliptical orbits with the Sun at a focus (F1). The other focus (F2) is empty.
Fig. 1.3.3 Law of
Ellipses
Second Law: Law of Equal Areas (1609)-As the planets orbit around the sun, the
planets cover equal areas in equal times. For this to happen, as shown in the
figure below the point A to B when the planets are nearest to the Sun it moves
and lowest at point C to D when the planets are farthest from the Sun. When the
planet is nearest to the Sun, it is called perihelion. When it is farthest from the
Sun, it is called aphelion.
Fig 1.3.4 Law of Equal Areas
Third Law: Law of Periods (1619)-The ratio of the squares of the periods (the time
needed for one revolution about the Sun) of any of the two planets revolving around the Sun
is equal to the ratio of the cubes of their mean distances from the Sun. That is if T 1 and T2
represent the periods for any two planets, and r 1 and r2 represent the mean distances from
the Sun, then
2
If we are to rewrite
this
Meaning that r3/T2 should be the same or constant for
each planet. To determine the value of proportionality
constant k, the value of Earth’s known orbit could be
used:
TEarth = 365.24 days
r Earth = 149 million kilometres or
149 600 000 km or 149.6 x 106 km
r 31 r 32
= 2
2
T1 T2
So, r3/T2 = k or proportionality constant
( 149.6 x 106 km )
3
¿¿
Thus, the ratio of the cube of the mean distance of Earth from the Sun and the square of its
km3
revolution is 2.51 x 10
.
days 2
19
12
Based on the result of the calculation, do you think this is also true for other planets and
heavenly bodies?
What’s More
Activity 1.3.2: The Data Says
Now that you know that the data left by Brahe to Kepler proved to be accurate that is
why he was able to discover the three laws of planetary motion. So to verify it yourself, why
don't you complete the table below with your own result of the calculations applying the law
of periods. For easy calculation, please use a scientific calculator. Earth's data is already
supplied to you.
PLANET
Mercury
Venus
Earth
Mars
Planetary Data Applied to Kepler’s Third Law
r3/T2
MEAN DISTANCE
PERIOD
3
FROM THE SUN
km
¿
(T in days)
(r in kilometers)
days2
6
57.9 x 10
88.023
6
108.2 x 10
224.623
149.6 x 106
365.24
2.51 x 1019
6
227.9 x 10
686.651
Show at least one of the solutions here. Just follow the example given for Earth.
Note: For the computations, use a scientific calculator.
What I Have Learned
Activity 1.3.3: Here’s My Take
Answer the following questions based on your learning.
1. In what way that the data collected by Brahe paved the way in the discovery of the laws of
planetary motion?
2. According to the Law of periods that the ratio of r3/T2 is the same for each planet, so what
do you think is the period of revolution of an imaginary planet if its mean distance from
the Sun is 337.9 x 106 km? Comparing its period of revolution to Earth, is the imaginary
planet near or far from the Sun? Show your solution.
What I Can Do
Activity 1.3.4: As I Ponder On
As you go through the lesson, it can be noted that there are prominent ideas that
many thought to be true and correct for hundreds or even thousands of years can become
out-dated or no longer correct when pieces of evidence especially accurate data are
presented. What important life lesson can you get from this?
13
Summary

The Greeks believed that the Earth is spherical.

Aristotle argued that the Earth is spherical based on the following:
 Every object on Earth is compressed and converged toward the center
forming a sphere;
 The North Star was believed to be at a fixed position in the sky. However,
when the Greeks traveled to places nearer the equator, they noticed that the
North Star is closer to the horizon;
 During a lunar eclipse, the shape of Earth's shadow reflected on the Moon's
surface is circular.

Eratosthenes estimated the Earth's circumference by observing the shadow casts by
a pillar and correlating it with the information that while an object in Alexandria during
noontime cast a shadow, in Seyene the light rays that hit the water well is reflected
back thus, no shadow is formed. This is another proof presented to support the idea
that the Earth is indeed round.

Examples of astronomical phenomena known to man even before the invention of the
telescope are the different phases of the moon, lunar and solar eclipses, the motion
of stars, the discovery of planets Mercury, Venus, Mars, Jupiter, and Saturn.

Tycho Brahe calculated with high accuracy the positions of planets, moon and the
Sun. He proposed a geo-heliocentric model, Earth is fixed and the Sun revolves
around it. But the rest of the planets revolve around the Sun.

Johannes Kepler was hired by Brahe to assist him in looking for more data to support
his geo-heliocentric model.

The data that Brahe collected did not help in proving his idea of a stationary Earth,
instead, Kepler discovered its importance in explaining the elliptical path of the
planets and moon, varying speed of planets motion and the harmony of the distance
of the planet and its motion. Which was later called Kepler's Laws of Planetary
Motion.
 First Law:
Law of Ellipse
 Second Law: Laws of Equal Areas
 Third Law:
Law of Period
14
Assessment (Post Test)
Multiple Choices. Select the letter of the best answer from among the given choices.
1. Which of the observations below was used by Aristotle to prove his claim that Earth is not
flat?
A. He noticed that all things seem to be moving around the Earth except for Earth
itself
B. He argued that since the shape of the moon appears to be round then the Earth
must also be round.
C. He argued that lunar eclipse only happens when a round opaque object blocks the
passage of sunlight.
D. He noticed that during a lunar eclipse the shadow casts by Earth on the moon is
round.
.
2. Which of the statements below refers to the information gathered by Eratosthenes about a
phenomenon that happened at the same date and time during the summer solstice in
Seyene and Alexandria?
A. In Seyene, sunlight shines directly down a deep well and is reflected back, while in
Alexandria the vertical pillar did not cast a shadow at all.
B. In Seyene, a vertical pillar cast a shadow, while in Alexandria sunlight shines
directly down a deep well and is reflected back.
C. In Seyene, sunlight shines directly down a deep well and is reflected back, while in
Alexandria the vertical pillar cast a shadow.
.
D. Both in Seyene and Alexandria that the structures cast a shadow.
3. Which of the following is also presented by the Greeks to prove that the Earth is
spherical?
A. solar eclipse
B. sunrise and sunset
C. ships sailing seemed to be gradually disappearing in the horizon
D. passing of the comet in Earth’s orbit
4. Aside from Aristotle who among the philosophers below believed that Earth is spherical?
A. Pythagoras and the Mesopotamians
B. Pythagoras and Plato
C. Plato and the Mesopotamians
D. Mesopotamians and Egyptians
5. Based on Eratosthenes' calculation, the circumference of the Earth is equivalent to ____.
A. 250 000 stadia
B. 5 000 stadia
C. 2 500 000 stadia
D. 500 000 stadia
6. Which phase of the moon is shown in the figure?
A. full moon
B. new moon
C. first quarter moon
D. last quarter moon
7. The following are astronomical phenomena that were already observed by the ancient
people even before the telescope was invented except _______.
A. solar eclipse
B. phases of the moon
C. craters of the moon
D. planet like Venus
8. Which of the statements below describes a lunar eclipse?
A. A lunar eclipse occurs when the Earth is behind the Sun and the moon is in front
of the Sun.
B. A lunar eclipse occurs when the moon is between the Earth and the Sun
C. A lunar eclipse occurs when the moon is forming ninety degree-angle with the
Earth.
D. A lunar eclipse occurs when the Earth is between the moon and the Sun.
15
9. Based on the observation made by ancient astronomers, the Sun rises in the _____
and sets in the _____ direction.
A. west, east
B. south, west
C. north, south
D. east, west
10. Refer to the figure below, “phases of the moon”. Which among the numbered figure
represents the full moon?
A. 1
B. 2
C. 3
D. 4
11. The accurate measurement of the positions and distances of stars and planets in the
major contribution of _________ to the field of astronomy.
A. Johannes Kepler
B. Tycho Brahe
C. Copernicus
D. Ptolemy
12. Below is Brahe’s model of the universe. What is the implication of
Brahe’s model when it comes to the idea of the center of the
universe?
A. There are two centers the Earth and the Sun.
B. The Earth, not the Sun is the center of the universe.
C. The Sun, not the Earth is the center of the universe.
D. Neither the Earth nor the Sun is the center of the
universe
13. Based on Kepler's First Law, which of the figures below describes the path of a
planet as it moves around the Sun?
A
B
C
D
14. Kepler discovered that planets do not go around the Sun at a uniform speed but it
depends on its position relative to the Sun. What is its speed when it is farther from
the Sun?
A. faster
B. neither fast nor slow
C. slower
D. similar to the speed when it is closer to the Sun
15. Kepler’s third law of planetary motion states that the ratio of ______________.
A. the cube of the times of revolution of the planets are proportional to the square
of their average distance from the Sun.
B. the cube of the times of revolution of the planets is not proportional to the
square of their average distance from the Sun.
C. the square of the times of revolution of the planets is proportional to the cube
of their average distance from the Sun.
D. the square of the times of revolution of the planets is not proportional to the
cube of their average distance from the Sun.
16
Key to Answers
PRE-TEST
1. B
2. D
3. A
4. B
5. B
6.
7.
8.
9.
10.
B
D
C
A
A
11.
12.
13.
14.
15.
C
A
A
A
A
POST TEST
1. D
2. C
3. C
4. B
5. A
6. C
7. C
8. D
9. D
10. A
11.
12.
13.
14.
15.
B
A
C
C
C
Lesson 1
Activity 1.1.1
1. Round or circular
2. Ball A – moon since it is smaller, Ball B – Earth since it is bigger
3. Since the sunlight is aligned with the heart-shape Earth, then the casted shadow is heartshape also. Shadow formation depends on the position of light especially if the shape is
irregular.
Activity 1.1.2. Out put of this activity may vary.
Activity 1.1.3. Answer may vary
Activity 1.1.4. The output will be appraised based on the rubric provided
Lesson 2
Activity 5.2.1
Activity 1.2.2
1. The data on the table depends on the months chosen by you.
2. The time interval is not uniform, it varies within the range of 6-8 days. But the cycle can be
completed in an average of 29-30 days.
Activity 1.2.3
1. A solar eclipse happens when moon cast its shadow on Earth. While lunar eclipse happens
when Earth cast its shadow on the moon
.2. Planets appear to very bright and change position periodically. While the rest of the stars are
not as bright compared to the planets and seemed to be fixed in its position
Activity 1.2.4
Output may vary
key terms in the description:
Sunrise from the east
Sunset in the west
Lesson 3
Activity 5.3.1
1. k
2. c
3. h
4. j
5. e
6. b
7. f
17
8. d
9. i
10. a
Activity 1.3.2
Sample Computation for Mercury
3
( 57.9 x 106 km )
¿¿
Activity 1.3.3
1. The data collected by Brahe on position and movement of planets and stars is voluminous and
accurate, thus out of these accurate measurement Kepler discover important relationships such as
2
the speed of the planet with respect to its distance from the sun.
T
=
2. Solution:
km
Based from Activity 5.3.2, the derived constant value ( k ) for the ratio is 2.51 x 1019
3
T
days 2
The given distance ( r ) from the Sun of the imaginary planet is 337.9 x 106 km
You are asked to find the period of revolution ( T )around the Sun in days.
Using the relationship that k = r3/T2 , rearranging the formula T2 = r3 / k
Substitute the given value
Thus,
T
2
2
(337.9 x 106 km)3
km
2.51 x 1019
3
days 2
3.86 x 1025km3
2.51 x 1019
km3
days 2
3.85 x 1025 km3
T2
=
days2
2.51 x 1019 km3
1.54x106 days2
√ T 2= √ 1.54 x 106 days 2
T
=
√ 1.54 x 106 days 2
T= 1 239.78 days ≈ 1240 days
The period of revolution of the imaginary planet around the Sun is 1 240 days while Earth’s
revolution is 365.25 days , thus, the imaginary planet is farther from the Sun.
2. According to the Law of period that the ratio of r3/T2 is the same for each planet, so what do you
think is the period of revolution of an imaginary planet if its mean distance from the Sun is 337.9 x
106 km? Comparing its period of revolution to Earth, is the imaginary planet near or far the Sun?
Activity 1.3.4. Answer may vary
=
=
18
References
DepEd CDO Learning Activity Sheet in Physical Science Shared Option LAS nos.
38,41,44.(DepEd Cagayan de Oro,2019) https://bitly/3dF9Kdb
Teaching Guide for SHS: Physical Science, CHED in collaboration with the PNU
QuezonCity:2016
accessed
last
June
20,2020
https://drive.google.com/file/d/0B869YF0KEHr7SHFGVG5MVFFhcXc/view?
usp=drivesdk
Punzalan, Jervee M. and Monserrat, Richard C., Physical Science in Today’s World
(Quezon City: SIBS Publishing House,2016)
“Eratosthenes”, accessed last June 20, 2020, https://www.Britannica.com/biography/
Eratosthenes
"How
to
make
foldable",
accessed
last
July
11,
http://www.dazzleonadime.com/index.php/strategies/foldables/
2020,
"Earth
Rise",
accessed
last
July
http://www.publicdomainpictures.net/en/view-image.php?
image=86453&picture=earth-rise
2020,
15,
19
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