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THE EXPANDING UNIVERSE
for Physical Science/ Grade 11
Quarter 4/ Week 8
NegOr_Q4_PhySci11_SLKWeek8_v2
NegOr_Q4_PhySci11_SLKWeek8_v2
2
FOREWORD
This self-learning kit will serve as a guide to determine
how speeds and distances of far-off objects like the sun,
moon, other planets, and galaxies are measured. This will
also help the learners to recognize that the universe is vast
and continues to expand.
In this learning kit, the learners will gain knowledge in
determining how celestial bodies surrounding the Earth are
measured and, the evidence on the expanding universe is
recognized.
NegOr_Q4_PhySci11_SLKWeek8_v2
3
LEARNING COMPETENCIES
• Explain how the speeds and distances of far-off objects
are estimated (e.g., doppler effect and cosmic distance
ladder (S11/12PS-Ivi-j-72)
• Explain how we know that we live in an expanding
universe, which used to be hot and is approximately 14
billion years old
(S11/12PS-Ivi-j-73)
OBJECTIVES
At the end of the lesson, the learners will be able to:
K - identify the different methods in measuring distances in the
universe;
S - calculate the distance between two far-off objects or
heavenly bodies using a particular method; and
A - show appreciation on the evidences that the universe is
expanding.
NegOr_Q4_PhySci11_SLKWeek8_v2
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I. WHAT HAPPENED
PRE-ACTIVITIES/PRE-TEST
Pre-test.
I. Multiple choice. Choose the letter of the correct answer. Write your answer
directly in the notebook.
1. which does NOT belong to the group?
A. atom B. electron C. neutron D. proton
2. Which force operates on galaxies, stars, planets, and other visible objects?
A. electromagnetic force C. strong force
B. gravitational force D. weak force
3. Planet Venus is very close to Earth. What method is used to measure its
distance from planet Earth?
A. Cosmic Radar Ranging C. Parallax Method
B. Main Sequence Fitting D. Radar Ranging
Numbers 4 – 5, write TRUE if the statement is correct and FALSE it is incorrect.
4. There is only one method used in measuring the distance of celestial bodies. Tr
5. We are living in an expanding universe.
6. The _________ of the wave is the speed that a specific part of the wave passes
a point.
A. Magnitude C. Velocity
B. Acceleration D. Force
II. Rearranging jumbled letters of the words.
JUMBLED LETTERS CORRECT WORDS
1. LNVAAATTRGOII -----------------------------
2. ROMAGEETTCCEINL -----------------------------
3. RGNOTS -----------------------------
4. AKWE -----------------------------
NegOr_Q4_PhySci11_SLKWeek8_v2
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II. WHAT I NEED TO KNOW
Scientists confirmed that molecules are formed up of atoms in the early
1900s. Around the same time, scientists discovered that atoms are made up of
much smaller particles. Electrons, protons, and neutrons were the names given
to these tiny particles. Even smaller particles were identified in the 1950s.
Subatomic particles are now understood to make up protons and neutrons.
With their knowledge on subatomic particles, atoms, stars, planets, and
galaxies, they were able to explain the behavior of matter. According to
present theories, there are four forces that hold everything together.
Gravitational force operates on galaxies, stars, planets, and most visible objects
and are best explained by the previous lesson on general theory of relativity.
Electromagnetic force operates on the level of atoms and molecules. Atoms
stick together to form molecules because of electric attraction between
negatively and positively charged nuclei. The force that holds atomic nuclei
together is called strong force. The last force is the weak force which is
associated with several types of radioactive decay. The weak force helps to
hold particles such as neutrons together.
How are speeds and distances of far-off objects estimated?
Astrometry is the study of positions and movements of celestial bodies
(sun, moon, planets, stars, etc.) It is a major subfield of astronomy.
Typical questions in astrometry are:
• How far is it from the Earth to the Moon?
• From the Earth to the Sun?
• From the Sun to other planets?
• From the Sun to nearby stars?
• From the Sun to distant stars?
On a clear night sky, a lot of stars may become visible and shine in
different magnitude and color. Some celestial bodies appear to be excessively
large and luminous just like the sun and the moon. But these characteristics of
celestial body highly depend on their distances to the observers and how fast
do they move in space.
How do we measure the speeds and distances of far-off objects?
NegOr_Q4_PhySci11_SLKWeek8_v2
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Take note that there is no single method that can be used to measure the
distances of all the celestial bodies that can be seen from the Earth.
Methods of Measuring Distances of Celestial Bodies
Cosmic Distance Ladder
The most common among the methods of measuring distances is the
Cosmic Distance Ladder, also known as extragalactic distance scale, which is
composed of different methods that are built on one another. It is the
succession of methods used by astronomers in determining the distances of
celestial objects because no single technique can measure such distances at all
ranges. Instead, one method can be used to measure nearby distances, a
second can be used to measure nearby to intermediate distances, and so on.
Each rung of the ladder provides information that can be used to determine the
distances at the next higher rung. Note that every distance is measured relative
to Earth.
Figure 1: The Cosmic Distance Ladder
Source: https://terrytao.files.wordpress.com/2010/10/cosmic-distance-ladder.pdf
Radar ranging
It is at the base of the Cosmic Distance Ladder in which the distance is
measured without any assumptions about the star's characteristics. This can
measure up to a distance of 0.0001 light-years ≈ 946 052 840 kilometers. An
electromagnetic beam, in the form of radio waves is shot towards the object of
which we want to measure the distance, such as a nearby planet. Then the time
NegOr_Q4_PhySci11_SLKWeek8_v2
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it takes before the electromagnetic waves reach us back is measured, thus the
distance of the object from Earth will be identified. Radar ranging can only be
used for extremely close objects, such as our surrounding planets.
It is not practical to measure longer distances and distances to other stars
using radar ranging. For example, Sirius, the brightest white dwarf of our Milky
Way is located at 8.61 light-years. It means that light will take 8.61 years to go
there and another 8.61 years to get back. With this technique, we’ll have to wait
more than 17 years before the measured distance of Sirius from Earth will be
obtained. So instead of waiting for more than 17 years, measuring such distance
can be done using another method.
Parallax
When we say parallax, it is the apparent change of position of an object
due to the way we perceive it depending on the perception of the viewer. It is
used in measuring the distance of stars that are approximately 300 light years.
Light year is the distance light can travel in one year. Parallax is the apparent
displacement of an object when an observer changes its point of view.
Parallax method is done by measuring the angle change when observing
the distant object at 2 separate points with 6 months apart.
Figure 2: The Stellar Parallax
Source: http://hyperphysics.phyastr.gsu.edu/hbase/Astro/para.html
The parallax can be used to measure the distance to the few stars which
are close enough to the Sun to show a measurable parallax. The distance to the
NegOr_Q4_PhySci11_SLKWeek8_v2
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star is inversely proportional to the parallax. The distance to the star in parsecs is
given by:
Figure 3 : The Parallax Diagram
Source: Properties of Stars (astronomynotes.com)
Formula (1) relates the planet-Sun baseline distance to the size of parallax
measured. Formula (2) shows how the star-Sun distance d depends on the
planet-Sun baseline and the parallax. In the case of Earth observations, the
planet-Sun distance ab = 1 A.U. so d = 1/p. From Earth you simply flip the
parallax angle over to get the distance! (Parallax of 1/2 arc seconds means a
distance of 2 parsecs, parallax of 1/10 arc seconds means a distance of 10
parsecs, etc.)
Main Sequence Fitting
To the stars whose parallax is immeasurable, a method known as
spectroscopy can be used. To do this method, we have to consider the
absolute brightness of a star (standard measure of brightness of a star that is 10
Parsec away from the Earth). The actual brightness of a star as seen from the
Earth is known as the apparent brightness.
Astronomers are able to determine this spectrum by analyzing its spectral
lines and plotting the observations in the Hertzsprung-Russell diagram. This
diagram shows star's luminosity versus its temperature. This becomes an
Conversion:
1 light year = 0.306601 Parsec
1 light year = 9.461x1015 m
NegOr_Q4_PhySci11_SLKWeek8_v2
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important tool for determining the distance of far-off objects. From the apparent
brightness and absolute brightness, one can solve for distance modulus.
m - M = 5 log d - 5 (where small m is the apparent brightness, big M is the
absolute brightness, and d is the distance to the object in Parsec)
This technique (main sequence fitting) works out to about 300,000 light
years (covering the entire galaxy).
300,000 light years = 2.8 x 1021 m = 1.8 x 1018 mi
Diameter of Milky Way = 100,000 light years
Beyond this distance, the main sequence stars are too faint to be
measured accurately.
Cepheids
Henrietta Swan Leavitt (1868- 1921) observed a certain class of stars (the
Cepheids) oscillated in brightness periodically. This method is used to measure
the distance of the other galaxies. Plotting the absolute brightness against the
periodicity, she observed a precise relationship. This gave yet another way to
obtain absolute brightness, and hence observed distances. Because Cepheids
are so bright, this method works up to 100,000,000 light years! Most galaxies are
fortunate to have at least one Cepheid in them, so we know the distances to all
galaxies out to a reasonably large distance.
Supernovae
Similar methods, using supernovae (the explosion and death of a star)
instead of Cepheids, can sometimes work to even larger scales than these, and
can also be used to independently confirm the Cepheid-based distance
measurements.
Hubble's law
Edwin Hubble (1889-1953) noticed that distant galaxies had their spectrum
red-shifted from those of nearby galaxies. With this data, he formulated Hubble’s
law: the red-shift of an object was proportional to its distance. This led to the
famous Big Bang model of the expanding universe, which has now been
confirmed by many other cosmological observations. But it also gave a way to
NegOr_Q4_PhySci11_SLKWeek8_v2
10
measure distances even at extremely large scales, by first measuring the red-
shift and then applying Hubble’s law (Tao, T., no date)
QUESTION:
When and how will you use the different methods of measuring distances
of celestial bodies?
1. Radar ranging
2. Parallax
3. Main Sequence Fitting
4. Cepheids
5. Supernovae
6. Hubble's law
The Expanding Universe
Figure 4. The Electromagnetic Spectrum
Source: https://www.bestfunquiz.com/q/-ultimate-trivia-quiz-about-the-electromagnetic-
spectrum-in-physics
V. H. Slipher, from 1912 to 1914, studied the spectrum of light emitted by
nearby spiral galaxies. He observed familiar lines of hydrogen and helium. Their
wavelengths appear longer where the yellow line appears a little orange while
the blue line appears a little green.
The phenomenon was described by Doppler as the red shift. This is also
called the Doppler shift or Doppler effect. It has been observed that luminous
objects are moving away from the observer. From the amount of red shift,
NegOr_Q4_PhySci11_SLKWeek8_v2
11
astronomers can compute the speed of the moving objects. It has been
noticed that all galaxies are moving away from the Earth. More and more
recent observations using powerful telescopes confirm these observations.
Anywhere you look, the galaxies show Doppler shift (Caintic, 2016).
The star near us (those in our galaxy) are too close to have large red shifts
caused by the expanding universe. Thus, astronomers were surprised in 1963 to
discover objects that looked like stars in our galaxy but had huge red shifts.
These objects gave off large amounts of radio waves. They are quasi-stellar (star-
like) radio sources --- quasars. Quasars have the largest red shifts known. For this
reason, they are probably, the most distant objects in the universe. Some
quasars are so far away that their light takes fifteen billion years to reach us
(Pasachoff, et. al., 1986).
Figure 5. Diagram of an expanding live universe
Source: https://room.eu.com/news/new-research-questions-the-rate-at-which-the-
universe-is-expanding
We are living in an expanding universe. Astronomers think that the
universe was once packed together in a very dense mass. It was believed to
have exploded 15 billion years ago in a big bang. The explosion had no center
and occurred everywhere in space at the same time. It sent matter and strong
radiation in all directions. Some of these matter and radiations clamped
together to form the galaxies. These galaxies as they were formed continued to
speed in space in all directions. Many evidences were found, in the advent of
very sophisticated telescopes, that the universe is expanding (Caintic, 2016).
NegOr_Q4_PhySci11_SLKWeek8_v2
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Key points
Astrometry - is the study of positions and movements of celestial
bodies.
Parallax - apparent change in the position of an object due to the
way it is perceived.
Light year - distance light can travel in one year.
Hertzprung-Russell diagram (HR) diagram - shows star's luminosity
versus its temperature.
Distance modulus - difference between apparent and absolute
magnitude of stars.
Doppler effect - shift in wavelength of the emitted light of an object
proportional to its speed.
Performance Task
Do this correctly:
Proxima Centauri (the nearest star) has a parallax angle of 0.762 arcsec.
What is the distance between Earth and Proxima Centauri using the
parallax method? Once you have the answer in Parsec, try to convert it
into Light Years. Ten points is to be given for this task.
I. Asked:
II: Given:
III: Working Formula:
IV: Solution:
NegOr_Q4_PhySci11_SLKWeek8_v2
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III. WHAT I HAVE LEARNED
EVALUATION/POST TEST
I. Multiple choice. Read the statements carefully. Choose the letter of the
correct answer and write it in your notebook.
1. Which of the following is true about Astronomical Unit or AI?
A. It is the distance from the Earth to the moon.
B. 1 AU is equivalent to 159,597,871 km.
C. 1 AU is equivalent to 92,955,807 mi.
D. This unit is also used in in measuring the distance of stars that are
approximately 300 light years.
2. What is the method used in measuring the distance of stars that are
approximately 300 light years?
A. Radar Ranging B. Parallax C. Main Sequence Fitting D. Cepheids
3. What does a Hertzsprung-Russell diagram show?
A. star's luminosity versus its temperature
B. star's density versus its temperature
C. star's temperature versus its pressure
D. star's luminosity versus its pressure
4. Which of the following best describes the red-shift?
A. It is the area in the spectrum of shorter wavelengths.
B. Red shift decreases if the galaxy is moving away from us at a greater speed.
C. Red shift increases if the galaxy is moving away from us at a slower speed.
D. The light “shifts” toward the red end of the spectrum.
5. What is the best characteristic of a quasar?
A. They have the largest blue shifts known.
B. They are the most distant objects in the universe.
C. These objects gave off large amounts of X-rays in the universe.
D. none of the above
II. Essay. Write a short essay about the expanding universe by citing examples
and evidences.
Rating criteria: Content-------------- 5 points
Cohesiveness------- 5 points
Total--------------------10 points
NegOr_Q4_PhySci11_SLKWeek8_v2
14
References
Caintic, H. E. Physical science. Quezon City: C & E Publishing, Inc.,
2016.
New research questions the rate at which the Universe is expanding.
Room The Space Journal of Asgardia.
https://room.eu.com/news/new-research-questions-the-rate-
at-which-the-universe-is-expanding.
Parallax.http://hyperphysics.phyastr.gsu.edu/hbase/Astro/para.html
Pasachoff, J. M., Pasachoff, N., Cooney, T.M. Physical science. USA:
Scott, Foresman and Company, 1986.
Properties of Stars. Astronomy Notes.
https://www.astronomynotes.com/starprop/s2.htm.
Tao, T. (no date). "The Cosmic Distance Ladder".
https://terrytao.files.wordpress.com/2010/10/cosmic-distance-ladder.pdf.
The Cosmic Distance Ladder Explained. Medium
URL: https://medium.com/axons/the-cosmic-distance-ladder-
explained-d21740ca49c6.
Ultimate Trivia Quiz About The Electromagnetic Spectrum In Physics –
BestFunQuiz. https://www.bestfunquiz.com/q/-ultimate-trivia-
quiz-about-the-electromagnetic-spectrum-in-physics.
NegOr_Q4_PhySci11_SLKWeek8_v2
15
ACKNOWLEDGMENT
DEPARTMENT OF EDUCATION
SCHOOLS DIVISION OF NEGROS ORIENTAL
SENEN PRISCILLO P. PAULIN, CESO V
Schools Division Superintendent
JOELYZA M. ARCILLA EdD
OIC - Assistant Schools Division Superintendent
MARCELO K. PALISPIS EdD
OIC - Assistant Schools Division Superintendent
NILITA L. RAGAY EdD
OIC - Assistant Schools Division Superintendent / CID Chief
ROSELA R. ABIERA
Education Program Supervisor – (LRMS)
ARNOLD R. JUNGCO
PSDS – Division Science Coordinator
MARICEL S. RASID
Librarian II (LRMDS)
ELMAR L. CABRERA
PDO II (LRMDS)
FRUSSELL V. ELTANAL
Writer
Noelyn Siapno
Lay – Out Artists
________________________________
ALPHA QA TEAM
LIEZEL A. AGOR
EUFRATES G. ANSOK
JOAN Y. BUBULI
MA. OFELIA BUSCATO
LIELIN A. DE LA ZERNA
DEXTER D. PAIRA
BETA QA TEAM
LIEZEL A. AGOR - BESAS
JOAN Y. BUBULI - VALENCIA
LIELIN A. DE LA ZERNA
PETER PAUL A. PATRON
THOMAS JOGIE U. TOLEDO
DISCLAIMER
The information, activities and assessments used in this material are designed to provide
accessible learning modality to the teachers and learners of the Division of Negros Oriental. The
contents of this module are carefully researched, chosen, and evaluated to comply with the set
learning competencies. The writers and evaluator were clearly instructed to give credits to
information and illustrations used to substantiate this material. All content is subject to copyright
and may not be reproduced in any form without expressed written consent from the division.
NegOr_Q4_PhySci11_SLKWeek8_v2
16
SYNOPSIS AND ABOUT THE AUTHOR
AUTHOR
Frussell V. Eltanal is a Registered Nurse who
graduated in Silliman University. He took a Crash
Program in Education at LCC-Bais campus. Mr.
Eltanal is a Licensed Professional Teacher who is
currently teaching at Gregorio Elmaga Memorial
High School - Senior High School Department – in
Nasig-id, Zamboanguita, Negros Oriental, Philippines.
He is currently taking up Master of Arts in Science
Teaching at Negros Oriental State University.
This lesson focuses on two major topics: how
speeds and distances of far-off objects are
measured and the universe that continues
to expand. The genius physicists and their
theories paved the way of what seems to
be a mysterious Universe.

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Physical Science-Q4-Week-8_THE EXPANDING UNIVERSEv2.pdf

  • 1. THE EXPANDING UNIVERSE for Physical Science/ Grade 11 Quarter 4/ Week 8 NegOr_Q4_PhySci11_SLKWeek8_v2
  • 2. NegOr_Q4_PhySci11_SLKWeek8_v2 2 FOREWORD This self-learning kit will serve as a guide to determine how speeds and distances of far-off objects like the sun, moon, other planets, and galaxies are measured. This will also help the learners to recognize that the universe is vast and continues to expand. In this learning kit, the learners will gain knowledge in determining how celestial bodies surrounding the Earth are measured and, the evidence on the expanding universe is recognized.
  • 3. NegOr_Q4_PhySci11_SLKWeek8_v2 3 LEARNING COMPETENCIES • Explain how the speeds and distances of far-off objects are estimated (e.g., doppler effect and cosmic distance ladder (S11/12PS-Ivi-j-72) • Explain how we know that we live in an expanding universe, which used to be hot and is approximately 14 billion years old (S11/12PS-Ivi-j-73) OBJECTIVES At the end of the lesson, the learners will be able to: K - identify the different methods in measuring distances in the universe; S - calculate the distance between two far-off objects or heavenly bodies using a particular method; and A - show appreciation on the evidences that the universe is expanding.
  • 4. NegOr_Q4_PhySci11_SLKWeek8_v2 4 I. WHAT HAPPENED PRE-ACTIVITIES/PRE-TEST Pre-test. I. Multiple choice. Choose the letter of the correct answer. Write your answer directly in the notebook. 1. which does NOT belong to the group? A. atom B. electron C. neutron D. proton 2. Which force operates on galaxies, stars, planets, and other visible objects? A. electromagnetic force C. strong force B. gravitational force D. weak force 3. Planet Venus is very close to Earth. What method is used to measure its distance from planet Earth? A. Cosmic Radar Ranging C. Parallax Method B. Main Sequence Fitting D. Radar Ranging Numbers 4 – 5, write TRUE if the statement is correct and FALSE it is incorrect. 4. There is only one method used in measuring the distance of celestial bodies. Tr 5. We are living in an expanding universe. 6. The _________ of the wave is the speed that a specific part of the wave passes a point. A. Magnitude C. Velocity B. Acceleration D. Force II. Rearranging jumbled letters of the words. JUMBLED LETTERS CORRECT WORDS 1. LNVAAATTRGOII ----------------------------- 2. ROMAGEETTCCEINL ----------------------------- 3. RGNOTS ----------------------------- 4. AKWE -----------------------------
  • 5. NegOr_Q4_PhySci11_SLKWeek8_v2 5 II. WHAT I NEED TO KNOW Scientists confirmed that molecules are formed up of atoms in the early 1900s. Around the same time, scientists discovered that atoms are made up of much smaller particles. Electrons, protons, and neutrons were the names given to these tiny particles. Even smaller particles were identified in the 1950s. Subatomic particles are now understood to make up protons and neutrons. With their knowledge on subatomic particles, atoms, stars, planets, and galaxies, they were able to explain the behavior of matter. According to present theories, there are four forces that hold everything together. Gravitational force operates on galaxies, stars, planets, and most visible objects and are best explained by the previous lesson on general theory of relativity. Electromagnetic force operates on the level of atoms and molecules. Atoms stick together to form molecules because of electric attraction between negatively and positively charged nuclei. The force that holds atomic nuclei together is called strong force. The last force is the weak force which is associated with several types of radioactive decay. The weak force helps to hold particles such as neutrons together. How are speeds and distances of far-off objects estimated? Astrometry is the study of positions and movements of celestial bodies (sun, moon, planets, stars, etc.) It is a major subfield of astronomy. Typical questions in astrometry are: • How far is it from the Earth to the Moon? • From the Earth to the Sun? • From the Sun to other planets? • From the Sun to nearby stars? • From the Sun to distant stars? On a clear night sky, a lot of stars may become visible and shine in different magnitude and color. Some celestial bodies appear to be excessively large and luminous just like the sun and the moon. But these characteristics of celestial body highly depend on their distances to the observers and how fast do they move in space. How do we measure the speeds and distances of far-off objects?
  • 6. NegOr_Q4_PhySci11_SLKWeek8_v2 6 Take note that there is no single method that can be used to measure the distances of all the celestial bodies that can be seen from the Earth. Methods of Measuring Distances of Celestial Bodies Cosmic Distance Ladder The most common among the methods of measuring distances is the Cosmic Distance Ladder, also known as extragalactic distance scale, which is composed of different methods that are built on one another. It is the succession of methods used by astronomers in determining the distances of celestial objects because no single technique can measure such distances at all ranges. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher rung. Note that every distance is measured relative to Earth. Figure 1: The Cosmic Distance Ladder Source: https://terrytao.files.wordpress.com/2010/10/cosmic-distance-ladder.pdf Radar ranging It is at the base of the Cosmic Distance Ladder in which the distance is measured without any assumptions about the star's characteristics. This can measure up to a distance of 0.0001 light-years ≈ 946 052 840 kilometers. An electromagnetic beam, in the form of radio waves is shot towards the object of which we want to measure the distance, such as a nearby planet. Then the time
  • 7. NegOr_Q4_PhySci11_SLKWeek8_v2 7 it takes before the electromagnetic waves reach us back is measured, thus the distance of the object from Earth will be identified. Radar ranging can only be used for extremely close objects, such as our surrounding planets. It is not practical to measure longer distances and distances to other stars using radar ranging. For example, Sirius, the brightest white dwarf of our Milky Way is located at 8.61 light-years. It means that light will take 8.61 years to go there and another 8.61 years to get back. With this technique, we’ll have to wait more than 17 years before the measured distance of Sirius from Earth will be obtained. So instead of waiting for more than 17 years, measuring such distance can be done using another method. Parallax When we say parallax, it is the apparent change of position of an object due to the way we perceive it depending on the perception of the viewer. It is used in measuring the distance of stars that are approximately 300 light years. Light year is the distance light can travel in one year. Parallax is the apparent displacement of an object when an observer changes its point of view. Parallax method is done by measuring the angle change when observing the distant object at 2 separate points with 6 months apart. Figure 2: The Stellar Parallax Source: http://hyperphysics.phyastr.gsu.edu/hbase/Astro/para.html The parallax can be used to measure the distance to the few stars which are close enough to the Sun to show a measurable parallax. The distance to the
  • 8. NegOr_Q4_PhySci11_SLKWeek8_v2 8 star is inversely proportional to the parallax. The distance to the star in parsecs is given by: Figure 3 : The Parallax Diagram Source: Properties of Stars (astronomynotes.com) Formula (1) relates the planet-Sun baseline distance to the size of parallax measured. Formula (2) shows how the star-Sun distance d depends on the planet-Sun baseline and the parallax. In the case of Earth observations, the planet-Sun distance ab = 1 A.U. so d = 1/p. From Earth you simply flip the parallax angle over to get the distance! (Parallax of 1/2 arc seconds means a distance of 2 parsecs, parallax of 1/10 arc seconds means a distance of 10 parsecs, etc.) Main Sequence Fitting To the stars whose parallax is immeasurable, a method known as spectroscopy can be used. To do this method, we have to consider the absolute brightness of a star (standard measure of brightness of a star that is 10 Parsec away from the Earth). The actual brightness of a star as seen from the Earth is known as the apparent brightness. Astronomers are able to determine this spectrum by analyzing its spectral lines and plotting the observations in the Hertzsprung-Russell diagram. This diagram shows star's luminosity versus its temperature. This becomes an Conversion: 1 light year = 0.306601 Parsec 1 light year = 9.461x1015 m
  • 9. NegOr_Q4_PhySci11_SLKWeek8_v2 9 important tool for determining the distance of far-off objects. From the apparent brightness and absolute brightness, one can solve for distance modulus. m - M = 5 log d - 5 (where small m is the apparent brightness, big M is the absolute brightness, and d is the distance to the object in Parsec) This technique (main sequence fitting) works out to about 300,000 light years (covering the entire galaxy). 300,000 light years = 2.8 x 1021 m = 1.8 x 1018 mi Diameter of Milky Way = 100,000 light years Beyond this distance, the main sequence stars are too faint to be measured accurately. Cepheids Henrietta Swan Leavitt (1868- 1921) observed a certain class of stars (the Cepheids) oscillated in brightness periodically. This method is used to measure the distance of the other galaxies. Plotting the absolute brightness against the periodicity, she observed a precise relationship. This gave yet another way to obtain absolute brightness, and hence observed distances. Because Cepheids are so bright, this method works up to 100,000,000 light years! Most galaxies are fortunate to have at least one Cepheid in them, so we know the distances to all galaxies out to a reasonably large distance. Supernovae Similar methods, using supernovae (the explosion and death of a star) instead of Cepheids, can sometimes work to even larger scales than these, and can also be used to independently confirm the Cepheid-based distance measurements. Hubble's law Edwin Hubble (1889-1953) noticed that distant galaxies had their spectrum red-shifted from those of nearby galaxies. With this data, he formulated Hubble’s law: the red-shift of an object was proportional to its distance. This led to the famous Big Bang model of the expanding universe, which has now been confirmed by many other cosmological observations. But it also gave a way to
  • 10. NegOr_Q4_PhySci11_SLKWeek8_v2 10 measure distances even at extremely large scales, by first measuring the red- shift and then applying Hubble’s law (Tao, T., no date) QUESTION: When and how will you use the different methods of measuring distances of celestial bodies? 1. Radar ranging 2. Parallax 3. Main Sequence Fitting 4. Cepheids 5. Supernovae 6. Hubble's law The Expanding Universe Figure 4. The Electromagnetic Spectrum Source: https://www.bestfunquiz.com/q/-ultimate-trivia-quiz-about-the-electromagnetic- spectrum-in-physics V. H. Slipher, from 1912 to 1914, studied the spectrum of light emitted by nearby spiral galaxies. He observed familiar lines of hydrogen and helium. Their wavelengths appear longer where the yellow line appears a little orange while the blue line appears a little green. The phenomenon was described by Doppler as the red shift. This is also called the Doppler shift or Doppler effect. It has been observed that luminous objects are moving away from the observer. From the amount of red shift,
  • 11. NegOr_Q4_PhySci11_SLKWeek8_v2 11 astronomers can compute the speed of the moving objects. It has been noticed that all galaxies are moving away from the Earth. More and more recent observations using powerful telescopes confirm these observations. Anywhere you look, the galaxies show Doppler shift (Caintic, 2016). The star near us (those in our galaxy) are too close to have large red shifts caused by the expanding universe. Thus, astronomers were surprised in 1963 to discover objects that looked like stars in our galaxy but had huge red shifts. These objects gave off large amounts of radio waves. They are quasi-stellar (star- like) radio sources --- quasars. Quasars have the largest red shifts known. For this reason, they are probably, the most distant objects in the universe. Some quasars are so far away that their light takes fifteen billion years to reach us (Pasachoff, et. al., 1986). Figure 5. Diagram of an expanding live universe Source: https://room.eu.com/news/new-research-questions-the-rate-at-which-the- universe-is-expanding We are living in an expanding universe. Astronomers think that the universe was once packed together in a very dense mass. It was believed to have exploded 15 billion years ago in a big bang. The explosion had no center and occurred everywhere in space at the same time. It sent matter and strong radiation in all directions. Some of these matter and radiations clamped together to form the galaxies. These galaxies as they were formed continued to speed in space in all directions. Many evidences were found, in the advent of very sophisticated telescopes, that the universe is expanding (Caintic, 2016).
  • 12. NegOr_Q4_PhySci11_SLKWeek8_v2 12 Key points Astrometry - is the study of positions and movements of celestial bodies. Parallax - apparent change in the position of an object due to the way it is perceived. Light year - distance light can travel in one year. Hertzprung-Russell diagram (HR) diagram - shows star's luminosity versus its temperature. Distance modulus - difference between apparent and absolute magnitude of stars. Doppler effect - shift in wavelength of the emitted light of an object proportional to its speed. Performance Task Do this correctly: Proxima Centauri (the nearest star) has a parallax angle of 0.762 arcsec. What is the distance between Earth and Proxima Centauri using the parallax method? Once you have the answer in Parsec, try to convert it into Light Years. Ten points is to be given for this task. I. Asked: II: Given: III: Working Formula: IV: Solution:
  • 13. NegOr_Q4_PhySci11_SLKWeek8_v2 13 III. WHAT I HAVE LEARNED EVALUATION/POST TEST I. Multiple choice. Read the statements carefully. Choose the letter of the correct answer and write it in your notebook. 1. Which of the following is true about Astronomical Unit or AI? A. It is the distance from the Earth to the moon. B. 1 AU is equivalent to 159,597,871 km. C. 1 AU is equivalent to 92,955,807 mi. D. This unit is also used in in measuring the distance of stars that are approximately 300 light years. 2. What is the method used in measuring the distance of stars that are approximately 300 light years? A. Radar Ranging B. Parallax C. Main Sequence Fitting D. Cepheids 3. What does a Hertzsprung-Russell diagram show? A. star's luminosity versus its temperature B. star's density versus its temperature C. star's temperature versus its pressure D. star's luminosity versus its pressure 4. Which of the following best describes the red-shift? A. It is the area in the spectrum of shorter wavelengths. B. Red shift decreases if the galaxy is moving away from us at a greater speed. C. Red shift increases if the galaxy is moving away from us at a slower speed. D. The light “shifts” toward the red end of the spectrum. 5. What is the best characteristic of a quasar? A. They have the largest blue shifts known. B. They are the most distant objects in the universe. C. These objects gave off large amounts of X-rays in the universe. D. none of the above II. Essay. Write a short essay about the expanding universe by citing examples and evidences. Rating criteria: Content-------------- 5 points Cohesiveness------- 5 points Total--------------------10 points
  • 14. NegOr_Q4_PhySci11_SLKWeek8_v2 14 References Caintic, H. E. Physical science. Quezon City: C & E Publishing, Inc., 2016. New research questions the rate at which the Universe is expanding. Room The Space Journal of Asgardia. https://room.eu.com/news/new-research-questions-the-rate- at-which-the-universe-is-expanding. Parallax.http://hyperphysics.phyastr.gsu.edu/hbase/Astro/para.html Pasachoff, J. M., Pasachoff, N., Cooney, T.M. Physical science. USA: Scott, Foresman and Company, 1986. Properties of Stars. Astronomy Notes. https://www.astronomynotes.com/starprop/s2.htm. Tao, T. (no date). "The Cosmic Distance Ladder". https://terrytao.files.wordpress.com/2010/10/cosmic-distance-ladder.pdf. The Cosmic Distance Ladder Explained. Medium URL: https://medium.com/axons/the-cosmic-distance-ladder- explained-d21740ca49c6. Ultimate Trivia Quiz About The Electromagnetic Spectrum In Physics – BestFunQuiz. https://www.bestfunquiz.com/q/-ultimate-trivia- quiz-about-the-electromagnetic-spectrum-in-physics.
  • 15. NegOr_Q4_PhySci11_SLKWeek8_v2 15 ACKNOWLEDGMENT DEPARTMENT OF EDUCATION SCHOOLS DIVISION OF NEGROS ORIENTAL SENEN PRISCILLO P. PAULIN, CESO V Schools Division Superintendent JOELYZA M. ARCILLA EdD OIC - Assistant Schools Division Superintendent MARCELO K. PALISPIS EdD OIC - Assistant Schools Division Superintendent NILITA L. RAGAY EdD OIC - Assistant Schools Division Superintendent / CID Chief ROSELA R. ABIERA Education Program Supervisor – (LRMS) ARNOLD R. JUNGCO PSDS – Division Science Coordinator MARICEL S. RASID Librarian II (LRMDS) ELMAR L. CABRERA PDO II (LRMDS) FRUSSELL V. ELTANAL Writer Noelyn Siapno Lay – Out Artists ________________________________ ALPHA QA TEAM LIEZEL A. AGOR EUFRATES G. ANSOK JOAN Y. BUBULI MA. OFELIA BUSCATO LIELIN A. DE LA ZERNA DEXTER D. PAIRA BETA QA TEAM LIEZEL A. AGOR - BESAS JOAN Y. BUBULI - VALENCIA LIELIN A. DE LA ZERNA PETER PAUL A. PATRON THOMAS JOGIE U. TOLEDO DISCLAIMER The information, activities and assessments used in this material are designed to provide accessible learning modality to the teachers and learners of the Division of Negros Oriental. The contents of this module are carefully researched, chosen, and evaluated to comply with the set learning competencies. The writers and evaluator were clearly instructed to give credits to information and illustrations used to substantiate this material. All content is subject to copyright and may not be reproduced in any form without expressed written consent from the division.
  • 16. NegOr_Q4_PhySci11_SLKWeek8_v2 16 SYNOPSIS AND ABOUT THE AUTHOR AUTHOR Frussell V. Eltanal is a Registered Nurse who graduated in Silliman University. He took a Crash Program in Education at LCC-Bais campus. Mr. Eltanal is a Licensed Professional Teacher who is currently teaching at Gregorio Elmaga Memorial High School - Senior High School Department – in Nasig-id, Zamboanguita, Negros Oriental, Philippines. He is currently taking up Master of Arts in Science Teaching at Negros Oriental State University. This lesson focuses on two major topics: how speeds and distances of far-off objects are measured and the universe that continues to expand. The genius physicists and their theories paved the way of what seems to be a mysterious Universe.