Senior High School
NOT
Physical Science
Quarter 2 - Module 5
How we come to realize that the Earth
is not the center of the Universe
(design your own cover page)
Department of Education ● Republic of the Philippines
Table of Contents
What This Module is About ................................................................................................................... i
What I Need to Know .............................................................................................................................. ii
How to Learn from this Module ...........................................................................................................ii
Icons of this Module ...............................................................................................................................iii
What I Know ........................................................................................................................................... iii
Lesson 1:
The Universe: Through the Eyes of the Ancient
Great Thinkers ................................................. .1
What I Need to Know: ………………………………………………………………..…1
What’s New: The Way I See It ........................................................................................... 2
What Is: Sphere It Is .............................................................................................................. 3
What’s More: And the Shape Is .......................................................................................... 5
What’s New : What’s Your Sense of Fashion………………………………………. 6
What Is It: Pre- Telescope Observed Phenomena ....................................................... 6
What’s More: The Phases of the Moon and Me ............................................................. 8
What I Have Learned: Synthesizing your Learning ....................................................... 9
What I Can Do: DepEd TV Live ..........................................................................................10
Lesson 2:
Thanks to Brahe
...................................................................................................................... 11
What’s In ........................................................................................................................11
What I Need to Know..................................................................................................11
What’s New: The Who .......................................................................................... 12
What Is It: Tycho Brahe’s Contribution ............................................................... 12
What’s More: The Data Says ................................................................................. 15
What I Have Learned Here’s My Take ……………………………………… 15
What I Can Do: As I Ponder On … ..................................................................... 16
Summary ………......................................................................................................................................... 17
Assessment: (Post-Test)………. ........................................................................................................... 18
What I Know
Multiple Choice. Select the letter of the best answer from among the given choices.
1. According to the Greeks, the Earth’s shape is _______.
A. elliptical
B. flat and square
C. spherical
C. cylindrical
2. Which among the Greek philosophers computed 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 seems to be moving around the Earth except for Earth
itself.
4. Which of the following is not true about the how ancient people were able to make use of
their knowledge about heavens?
A. They used their knowledge to invent the calendar
B. They used their knowledge to study more closely the origin of the universe
C. They their knowledge in their architecture.
D. They used their knowledge to navigate the ocean
5. Which time of the year did Eratosthenes observe the pillar in Alexandria casted a shadow?
A. noon time during spring
B. noon time during summer solstice
C. noon time during solar eclipse
D. noon time during winter solstice
6. Which of the following astronomical phenomenon were 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 casts a shadow on the moon during lunar
eclipse when it is observe here on Earth without the aid of a telescope?
A. Sun
B. Moon
C. North star
D. Earth
III
8. Which phase of the moon is shown in the figure below?
A. full moon
B. first quarter moon
D. last quarter moon
C. new moon
9. Which phase of the moon is shown in the figure below?
A. full moon
B. first quarter moon
D. new moon
C. last quarter 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 with respect to each other.
But there are very bright stars that change positions periodically.
B. They noticed that Mercury and Venus are bigger compared to the others 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 with respect to each other.
11. What is the major contribution of Tycho Brahe to the field of astronomy?
A. the Earth’s axis of rotation
B. measurement of Earth’ circumference
C. accurate measurement of stars’ and planets’ position
D. the invention of telescope
12. Below is Brahe’s model of the universe. Based on the figure ,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. The planets except Earth
revolve around the Sun, while
the moon revolves around the
Earth
D. Neither the Sun nor the Earth
is at the center and the others
planets do not revolve around
it.
IV
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 it position relative to the Sun. What is its speed when it is closer to the
Sun?
A. faster
C. slower
B. neither fast nor slow
D. similar to the speed when it is far
from the sun
15. What relationship between the times of revolutions of the planets and their distance
from the Sun did Kepler discover?
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 are 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 are not proportional to the
square of their average distance from the Sun.
Lesson
1
The Universe: Through the Eyes of
the Ancient Great Thinkers
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 in 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 vacation on board on a
space ship and your destination is the outer space! Isn’t it cool?
Man’s knowledge about the universe has a come a long way. Gone are the days that
people feared the occurrence of an eclipse for its means something bad is going to happen.
But it’s a different story if you were born hundreds or thousands years ago.
Ancient people perhaps did not think about aliens or parallel universe or thought of
going to Mars, but they have definitely wondered and gave a lot of thought about how object
seem to move across the sky. As they continued to observe the occurrences around them
the more they became fascinated and curios, thus, these lead them to their quest for
answers and explanations. And the knowledge they accumulated through the years about
the skies has been applied to their everyday lives. They rely on it to tell the time, in making
calendars, in navigation, in architecture, in agriculture especially on when to sow and when
to harvest and so on. And how about you can you tell the time or direction by just observing
the sky?
Apart from utilizing their knowledge about astronomy in their day to day living, they
also used this to shed light on some prevalent questions and ideas of their time. Few of the
ideas that ancient people tried to work on were on giving us the picture of the shape of the
Earth and of the universe.
As for the Earth’s shape, how did the Greeks (though they were not the only who
studied it) come into a conclusion that it’s not flat? What were the evidences that they used
support the idea?
And before we expound the concept let’s put to test first your power of observation
and reasoning by doing the activity below. As you know, observing is one of the skills that
the great ancient thinkers possessed and you too as senior high school learner is expected
to acquire.
1
What’s New
Activity 5.1.1: The Way I See It
You and your siblings are playing the game “Truth or Dare”. And it so happen that
the spinning bottle stopped and it is pointing at your direction. Since you lose by the verdict
of the spinning bottle, thus, you choose to do the “Dare”. And the dare is for you to
determine which of the five (5) shadows cannot be formed by the object below if it is lighted
from different positions. You are given 30 seconds by your sibling to figure it out. And your
timer starts now!
A
D
The shadows that cannot be formed are:
C
B
E
B (the first one is done for you),___________
Note to the Teacher
Kindly remind your students to put all their answers on the agreed activity notebook for Science.
2
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 of the Earth,
they made careful and repetitive observation of the phenomena around them.
The Mesopotamian as accounted in their mythology around 6th century BC,
described Earth as a flat disk floating in the ocean and bounded by a spherical sky. And this
idea has prevailed for hundreds of years until a new view was presented (Punzalan and
Monserrat, Science in Todays’ World,126)
As the quest for knowledge continues and civilization prospers, several models of the
universe were presented. And it is categorized as geocentric model or Earth-centred and
heliocentric
model
or
Sun-centred.
(Retrieved
from
https://www.merriamwebster.com/dictionary/communication).
In the geocentric model, the Earth was at the
center and 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 evidences to support their claim. Until Aristotle (around
320 BC), a student of Plato presented his arguments that established the claim during their
time as referenced from the DepEd CDO Learning Activity Sheet in Physical Science Shared
Option LAS
Aristotle argued that:
-
the sphere is a perfect 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: a flat disc would
cast an oval shadow
-
even in short travels northwards the Pole Star is higher in the sky.
Are there still other evidences that you know about that are not listed here? Can you name
them?
3
If it is not 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 actually a shadow
formation. This happens when
the path of light rays is blocked
by an object.
Can Earth cause an
eclipse? How about you, can
you cause an eclipse too?
Fig 1.2. When the rays shine directly above at Syene, it is
not directly overhead at Alexandria which around 800 km
north. The pillar in Alexandria casted a shadow, while the
water in the deep well at Syene directly reflected back the
sunlight.
While working as a librarian in the University of Alexandria in Egypt, he came across
an information that during summer solstice especially at noon time, sunlight shines directly
down a deep well in Syene (a city south of Alexandria ) and is reflected back up again. He
knew also that no shadow is cast by any object on a noon time. But in Alexandria at the
same date and time, a vertical pillar and other structures cast a shadow.
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 7.2 0
angle between the sun‘s rays and the vertical pillar while in Syene its 0 0. Based on his
calculation, 7.20 is equivalent to 1/50 of a circle. He reasoned 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 travelled, the distance was measure to be 5000 stadia (800 kilometers). So the
Earth’s circumference is 50 x 5000 stadia = 250 000 stadia.(Retrieved from
https://www.britannica.com/biography/Eratosthense)
Are you now convinced that indeed the Earth is spherical? Why don’t you find it for yourself?
Try doing the simple activity below.
4
What’s More
Activity 5.1.2: 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 during night time)
Question:
1. What is the shape of the shadow? ______________________________________
2. In what way that this simple activity supports Aristotle’s claim about the shape of the
Earth?
_______________________________________________________________________
_______________________________________________________________________
3. Supposed that the Earth is heart shape, what shadow would it formed when sunlight is
aligned with it? Why?
_______________________________________________________________________
_______________________________________________________________________
5
What New
Activity 5.1.3: What’s Your Sense of Fashion
Below are list of clothes, accessories and gears that you may have at home. Sort them by
season. Write your answers on the table.
umbrella
sunglasses
rain coat
swim wear
thick jacket/coat
t-shirt
flip flops
plastics boots (botas)
sun visor
layered clothing
light fabric clothing
WET/RAINY SEASON
DRY/SUMMER
SEASON
Are there things that appeared on both categories? Why?
What Is It
Pre- Telescope Observed Phenomena
Based from your answers on the activity, it shows that your sense of fashion and the
things that you used is most often also dictated by the season. It is rather unusual that you
would be wearing a raincoat when in fact the Sun is brightly shining or you’re wearing thick
socks, long sleeves and several layers of shirts while swimming in the pool.
The change in the season on Earth were already known and studied by the ancient
people even before sophisticated instruments were invented. They realized that the
changing season has something to do with the variation of Sun’s motion. And they also
found out that this variation was periodic. 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 as referenced from the DepEd CDO Learning Activity Sheet in Physical
Science Shared Option LAS
1. Phases of the Moon
Ancient people have observed that the
moon changes its path and its appearance
within a period of 29.5 days. They observe
that the moon changes appearance from
thin semi-circular disk to full circular disk.
The periodic change of moon’s phases
was the basis of ancient calendar.
Fig. 1.3.1 Moon’s relative position with respect
to the Sun as it moves around the Earth attributes
its changing appearance as viewed from the Earth
6
.
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 lunar eclipse. Lunar eclipse
occurs when Earth is between the moon
and the Sun, Earth casts a shadow on the
moon. Sometimes they would notice that
moon’s color changes into blood red color.
Fig. 1.3.2 A lunar eclipse occurs Earth’s shadow is
cast on the moon.
3. Solar Eclipse
A solar eclipse occurs when the moon is
in between the Sun and the Earth and the
moon partially or 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 to the wrath of God to
them.
Fig. 1.3.3 A solar eclipse occurs when a moon’s
shadow is cast on Earth
4. The Motion of the Stars
It was also observed that the stars appear to be attached to a celestial sphere that rotates
around an axis in one day. Also, the constellations’ positions in the night sky vary depending
on the time of the year.
5. Visibility of Planets
Astronomers have discovered that Mercury, Venus, Mars, Jupiter, and Saturn are planets
because they have noticed that the stars are in a fixed position with respect to each other.
But there are very bright stars that change positions periodically which are called
“wanderers” or planetes in Greek terms.
Now that you have learned about the different astronomical events even before an
instrument like telescope was invented. From the information that they gathered, it has
resulted to innovation and invention. One of these is the calendar.
With the use of 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.
7
What’s More
Activity 5.1.4: The Phases of the Moon and Me
Aim: To keep track of the periodic change of 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
Last
Quarter
13
Full Moon
Ex. July 2020
5
New Moon
21
First
Quarter
28
B
C
4. Then count the number of days’ interval from one phase to another.
Full moon – Last quarter
A. Ex. July
2020
8
Last quarter – New moon
8
Days interval/Month
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
B.
C.
7
July-Aug
6
29
Questions:
1. How many days would take the moon to compete 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?
______________________________________________________________________
8
What I Have Learned
Activity 5.1.5: Synthesizing Your Learning
Answer the following questions based on your learning. Be brief and concise.
1. Can you tell the time or direction by just observing the sky? How?
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
2. Of all the arguments presented by the Greeks as proof that the Earth is spherical, which
among you find more convincing? Why?
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
3. Differentiate a solar eclipse from a lunar eclipse?
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
9
What I Can Do
Activity 5.1.6: DepEd TV Live
You are a script writer 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 evidences
presented by the Greeks’ about the spherical shape of the Earth. Choose only 2 evidences
and prepare a script for it. Make a video presentation based on the script. You segment will
run for two (2) minutes.To make your presentation more convincing, it should include correct
information and must interesting and creative. The language format of your show is in
Filipino/English.
Note: Videographer and Extra casts or actors maybe recruited for this activity.
Activity Rubric
Criteria
Accuracy
Visual Appeal
Creativity
10 points
The data included
in the presentation
are well
researched.
The presentation
shows visually
appealing images
and artistic.
The presentation
is very creative
and interesting
8- 6 points
The data included
in the presentation
contain a few
minor errors.
The presentation
has a few images
that are not
visually appealing
and fairly artistic.
The presentation
is fairly creative
and interesting
5-4 points
The data included
in the presentation
contain a few
many errors.
The presentation’s
images are not
visually appealing
and not artistic.
The presentation
lacks creative and
is not interesting
SCORE
Total Score
10
Lesson
2
Thanks to Brahe
What’s In
In lesson 1, we have learned the views of the ancients when it comes to giving a
plausible explanation about the shape of the Earth, presenting to us the conflicting ideas on
the models of the universe, their capability to observe and discover 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 has a great influence to one’s way
of living. In this lesson we will delve into the brilliant mind of Tycho Brahe and the impact of
his work in the formulation of the laws that explains the motion of heavenly object especially
the planets, the moons and the Sun.
What I Need to Know
The knowledge about the universe starting from the ancient time up to the present
has proven to be a dynamic one. The new discoveries weakened the foundation of a theory
that thought 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 for several times. Just like the works of
Tycho Brahe.
As referred from Teaching Guide for SHS: Physical Science, CHED in collaboration with
the PNU, Tycho Brahe is one of the most celebrated Danish astronomers during his time. His
patron the King of Denmark, Frederick II, built him an observatory equipped with an
oversized instrument a brass protractor-like called quadrants and of course the naked eyes
of the observers. This observatory allowed Brahe to measure with high accuracy the
positions of the planets, moon and the sun. Aside from that he was able to ascertain some
mathematical errors of the data on hand based from the records that was in his possession.
Through the years Brahe continues to record every data and came up with significant results
and accurate explanations out from the voluminous data. Part of the achievement in his
lifetime was the discovery of a supernova explosion in 1572 and the passing of a comet in
Earth’s orbit in1577. Come to think of it, all of these discoveries were made even before the
telescope was invented. With the data that Tycho Brahe collected, he also made an attempt
to present a model of the universe and his assistant Johannes Kepler made use of the data
to shed light of some of the anomalies about the planet’s motion.
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 to their contribution by answering the activity in the next page. If
you are not certain of your choice, don’t worry just give it a try.
11
What’s New
Activity 5.2.1: The Who
Below is a simple matching type activity. All you have to do is 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 A
______ 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
Column B
a. proponent of the universal law of gravitation.
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 an 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. a 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
What Is It
Tycho Brahe’ Contribution
If you got all the answers in
activity 5.2.1 correctly and correlate it
with the timeline in Fig.2.1, you will see
that the geocentric universe model has
prevailed for thousands of years. Only in
the later of part in 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
Fig. 2.1 The timeline of some of the who’s who in
the field of astronomy and mathematics.
12
The conflicting ideas and
evidences in both models have pushed
Brahe to come up with his own model.
It is called the geoheliocentric model, 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.
It was also during this time that
Brahe met the young German
mathematician Johannes Kepler. Brahe
hired Kepler as sort of “research
assistant” primarily to prove that
Brahe’s model (geoheliocentric model)
Fig 2.2 Brahe’s model of the universe also called the
which emphasize that the Earth was at Tychonic model. It is considered as a hybrid of
rest, the sun went around the Earth and geocentric and heliocentric models of the universe.
the planets all went around the sun - an
intermediate picture between Ptolemy
and Copernicus. Kepler needed Brahe’s data to do mathematical analysis while Brahe
needs Kepler to make mathematical calculations to prove that the model satisfies the
observed data. Brahe died before his model is proven. Kepler inherited vast set of data that
will prove crucial for developing his Three Laws of Planetary Motion later. It took Kepler
many more years trying out many possible models to fit the available data being concerned
largely on the philosophical implication of his models and the belief that there has to be
simple numerical relationships among phenomena like the Pythagoreans. But Kepler failed
to reconcile the data on hand with the model Brahe proposed especially on the notion of the
stationary Earth. It takes another brilliant mind and his invention the telescope to prove that
Copernicus was right in proposing that Earth after all is not the center of the universe.
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 2.1 Law of Ellipses
13
Second Law: Law of Equal Areas (1609)-In their orbits around the sun, the planets sweep
out equal areas in equal times. For this to happen, the planets move fastest at the perihelion
as shown in Fig.2.1 the first shaded area from point A to B and lowest at the aphelion the
second shaded area from point C to D. When the planet is nearest to the Sun, it is called
perihelion. When it is farthest from the Sun, it is called aphelion.
Fig 2.1 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 r1 and r2 represent the mean distances from the Sun,
then
𝑻𝟏 2
=
𝑻𝟐
𝒓𝟏 3
𝒓𝟐
If we are to rewrite this
𝒓𝟑𝟏
𝑻𝟐𝟏
=
𝒓𝟑𝟐
𝑻𝟐𝟐
Meaning that r3/T2 should be the same or constant for each planet. So determine value of
proportionality constant k, the value of Earth’s known orbit could be used:
TEarth = 365.24 days
r Earth = 149 million kilometres (149 600 000 km or 149.6 x 10 6 km )
So, r3/T2 = k or proportionality constant
(149.6 𝑥 106 𝑘𝑚)3
𝒌𝒎𝟑
𝟏𝟗
=
𝟐.
𝟓𝟏𝒙𝟏𝟎
(365.24 𝑑𝑎𝑦𝑠)2
𝒅𝒂𝒚𝒔𝟐
Thus, ratio of the cube of the mean distance of Earth from the Sun and the square of its
revolution is 𝟐. 𝟓𝟏𝒙𝟏𝟎𝟏𝟗
𝒌𝒎𝟑
𝒅𝒂𝒚𝒔𝟐
.
Based on the result of the calculation, do you think this is also true for other planets and
heavenly bodies?
14
What’s More
Activity 5.2.2: 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. And 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 scientific calculator. Earth’s data is already
supplied for you.
PLANET
Mercury
Venus
Earth
Mars
Planetary Data Applied to Kepler’s Third Law
r3/T2
MEAN DISTANCE
PERIOD
𝒌𝒎𝟑
FROM THE SUN
(T in days)
in
(r in kilometers)
𝒅𝒂𝒚𝒔𝟐
57.9 x 106
88.023
6
108.2 x 10
224.623
149.6 x 106
365.24
2.51 x 1019
227.9 x 106
686.651
Show at least one of the solutions here. Just follow the example given in the previous page
for Earth.
What I Have Learned
Activity 5.2.3: 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
planetary motion?
15
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? S Comparing its period of revolution to Earth, is the imaginary
planet near or far the Sun? Show your solution.
What I Can Do
Activity 5.2.4: As I Ponder On
What important life lesson can you get from this:
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 thousands of years can become out-dated or no longer correct
when evidences especially accurate data is presented.
16
Summary
1. Ancient peoples’ knowledge about astronomy has greatly influenced their way of life.
2. The Greeks believed that the Earth is spherical.
3. 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 travelled to places nearer the equator, they noticed that the North Star is closer
to the horizon;
-During lunar eclipse, the shape of Earth’s shadow reflected on the Moon’s surface is
circular.
4. Eratosthenes estimated the Earth’ circumference by observing the shadow casts by a
pillar and correlating it the with information that while an object in Alexandria during
noontime cast a shadow, in Seyene the light rays that hits the water well is reflected back
thus, no shadow is from. This is another proof presented to support the idea that the
Earth is indeed round.
1. The following are examples of astronomical phenomena known to man even before the
invention of the telescope: different phases moon, lunar and solar eclipses, motion of
stars, the discover of planets Mercury, Venus, Mars, Jupiter, and Saturn, supernova and
the passing of a comet along the Earth’s orbit.
2. Tycho Brahe calculated with high accuracy the positions planets, moon and the Sun. He
also made correction of the discrepancies of the data gathered by his forerunners.
3. With the data on hand, he questioned the geocentric model of the universe of Ptolemy
and rejected the heliocentric model of Copernicus, instead proposed his own model the
geo-heliocentric model.
8. The idea of his geo-heliocentric model, Earth is fixed and the Sun revolves around it.
But the rest of the planets revolve around the Sun.
9. Johannes Kepler was hired by Brahe to assist him in looking for more data to support his
geo-heliocentric model.
10. 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:
Second Law:
Third Law:
Law of Ellipse
Laws of Equal Areas
Law of Period
17
Assessment: (Post-Test)
Multiple Choice. Select the letter of the best answer from among the given choices.
1. How did the Greeks especially Aristotle use the lunar eclipse phenomenon to explain that
the Earth is not flat?
A. He noticed that all things seems 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 the shadow casts by Earth on the moon is round.
.
2. Which time of the year did Eratosthenes observe the pillar in Alexandria casted a
shadow?
A. noon time during spring
B. noon time during summer solstice
C. noon time during solar eclipse
D. noon time during winter solstice
3. According to the Greeks, the Earth’s shape is _______.
A. flat and square
B. spherical
C. elliptical
D. cylindrical
4. Which of the following is not true about the how ancient people were able to make use of
their knowledge about heavens?
A. They used their knowledge to navigate the ocean
B. They their knowledge in their architecture.
C. They used their knowledge to invent the calendar
D. They used their knowledge to study more closely the beginning of the universe
5. Which among the Greek philosophers computed the Earth’s circumference?
A. Eratosthenes
B. Pythagoras
C. Plato
D. Aristotle
6. Which phase of the moon is shown in the figure below?
A. full moon
B. new moon
D. last quarter moon
C. first quarter moon
7. Which of the following astronomical phenomenon were already observed by the ancient
people even before the telescope was invented?
A. solar eclipse
B. sunspots
C. craters of the moon
D. all the moons of Jupiter
18
8. Which of the following casts a shadow on the moon during lunar eclipse when it is
observe here on Earth without the aid of a telescope?
A. Sun
B. Earth
B. North star
D. Moon
9. How did the ancient astronomers discover that Mercury and Venus are planets
not stars?
A. They noticed that Mercury and Venus are bigger compared to the others stars
B. They noticed that the constellations’ positions in the night sky vary depending
on the time of the year
C. They noticed that the stars change positions periodically. But there are very
bright stars in a fixed position with respect to each other.
D. They noticed that the stars are in a fixed position with respect to each other.
But there are very bright stars that change positions periodically.
10. Which phase of the moon is shown in the figure below?
A. full moon
B. first quarter moon
D. new moon
C. last quarter moon
11. What is the major contribution of Tycho Brahe to the field of astronomy?
A. the invention of telescope
B. the Earth’s axis of rotation
C. measurement of Earth’ circumference
D. accurate measurement of stars’ and planets’ position
12. Below is Brahe’s model of the universe. Based on the figure ,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. The planets except Earth
revolve around the Sun, while
the moon revolves around the
Earth
D. Neither the Sun nor the Earth
is at the center and the others
planets do not revolve around
it.
19
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 it position relative to the Sun. What is its speed when it is farther from
the Sun?
A. faster
C. slower
B. neither fast nor slow
D. similar to the speed when it is closer
to the Sun
15. What relationship between the times of revolutions of the planets and their distance
from the Sun did Kepler discover?
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 are not proportional to the
square of their average distance from the Sun.
C. The square of the times of revolution of the planets are proportional to the
cube of their average distance from the Sun.
D. The square of the times of revolution of the planets are not proportional to the
cube of their average distance from the Sun.