SHS

PHYSICAL SCIENCE
Quarter 2 – Week 8
Module 8A: Speeds and Distances of
Far-off Objects
Physical Science
Grade 11/12 Quarter 2 - Module 8A - Speeds and Distances of
Far-off Objects
First Edition, 2020

Copyright © 2020
La Union Schools Division
Region I

All rights reserved. No part of this module may be reproduced in any form
without written permission from the copyright owners.

Development Team of the Module

Author: Asteria B. Oyando

Editor: SDO La Union, Learning Resource Quality Assurance Team

Illustrator: Ernesto F. Ramos Jr., P II

Management Team:

Atty. Donato D. Balderas, Jr.

Schools Division Superintendent

Vivian Luz S. Pagatpatan, PhD

Assistant Schools Division Superintendent

German E. Flora, PhD, CID Chief

Virgilio C. Boado, PhD, EPS in Charge of LRMS

Rominel S. Sobremonte, Ed.D., EPS in Charge of Science

Michael Jason D. Morales, PDO II

Claire P. Toluyen, Librarian II

 Physical Science
Quarter 2 – Week 8
Module 8A - Speeds and
Distances of Far-off Objects
 Target

The Earth is considered a tiny dot in comparison to the immense space of the
universe where it belongs. In a clear night sky, a lot of stars become visible and shine
in different magnitude and color. Some celestial bodies appear excessively large and
luminous such as the sun and the moon. However, these characteristics highly
depend on their distances to the observer and how fast do they move in the space.
Distance in the universe can be measured in light years. A light year is a unit
used to express the length traveled by light in a year and is approximately 9.5 x 1015
m. If the light coming from heavenly bodies needs to travel billions of light years,
then that means these bodies are very far from the Earth.
Astronomers used numerous distance-measuring schemes, which overlapped
over a range of distance. This is significant for astronomers to calibrate and
corroborate their measurements with various approaches.
This module will provide you with information and activities that will help you
understand better How the Speeds and Distances of Far-off Objects Are Estimated
(e.g., cosmic distance ladder and Doppler Effect).

After going through this module, you are expected to:

1. Explain how the speeds and distances of far-off objects are estimated
(e.g.,doppler effect and cosmic ladder) (S11/12PS-IVj-72)

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 Jumpstart

For you to understand the lesson well, do the following activity.

Have fun and good luck!

Activity 1 . CURVATURE OF SPACETIME

Materials: box
clothed stretched over box
different balls
ruler
marker

Procedure:

1. Place the tennis ball on top of the box with a stretched cloth down towards
the center of the box.

2. Roll a pingpong ball in a straight line past the tennis ball at various speeds
and record the result.

Note the curve paths and orbits created.

3. Repeat step 2 by replacing it with various size of balls.

4. Remove the tennis ball and draw a straight line on the cloth then place the
black ball down.

Notice: The straight line bends just like the light would from distorted
space-time.

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 Discover

The branch of astronomy that deals with the study of motions of celestial
bodies is called Celestial Mechanics. Astronomers studying celestial mechanics
usually estimates the speed and distance of celestial objects.
Take note, however, that there is no single method that can be used to
measure the distances of all celestial bodies that can be seen on earth.
How do astronomers measure the distance of heavenly bodies from the Earth?
Also, how are their speeds measured? The following discussions will concentrate on
the several methods to determine distances of objects in the universe.

Cosmic Distance Ladder

https://www.daviddarling.info/encyclopedia/C/cosmic_distance_ladder.html

The most common method of measuring distances is the Cosmic Distance

Ladder. This method is composed of several methods that are built on one another.
The data obtained in the first step of the ladder are used in the succeeding steps and
so on.
The base of the ladder, is a measurement without any assumptions about
stars’ characteristics. For example, the measurement of one astronomical unit (AU),
which is the measure of the distance of Earth from the Sun, is considered the base.
One AU is approximately 1.50x 1011m. This value is used in measuring the parallax
of a star.
Parallax
Parallax is the apparent change in the position of an object due to change in
the way it is perceived, depending in the perception of the viewer. It is used in
measuring the distance of the stars that are approximately 300 light years away. 8
How are these stars parallax measured? Usually, astronomers take a picture
of a specific star, in this example PLEIADES, wait for six months to pass so that the
Earth has moved two AU and then take a photo of the same star to compare the
change in its position.

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 The image of the star in the two photos will appear to shift slightly due to the
change in the position of how the star was seen. These shifts serve as the angles of
an isosceles triangle, formed in the perception of the viewers from earth.

https://cdn.mos.cms.futurecdn.net/KUhXyrLdXw8qpXULApiLWX.jpg

Here in the figure, it forms a parallax angle measured in arc seconds.

Remember that,
1 degree = 1/360 degree of a circle
1 arc second= 1/3600 of a degree
We, can establish the relationship between a star’s distance and its parallax
angle as:
Distance [d]= 1 [p]
angle
Usually, this distance is expressed in units of parsec. Parsec (parallax second) is
the distance of a star that has a parallax of two arcsecond. Arcsecond is the 60th
part of one arcminute and one arcminute is the 60th part of one degree.
But, a more common unit used to denote distances of celestial objects is light year.
A light year is defined as a distance light can travel in one year. The conversion
factor is presented below:
One light year= 0.306601 PARSEC, which is equal to 9.461x 1015 m

Let us compute this by applying a formula.

Example problem 1:
Alpha Centauri has a parallax angle, of 0.742 arcsec. What is the distance between
the Earth and Alpha Centauri using the parallax method?

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 What is asked in the problem, is the distance of Earth and Alpha Centauri

and the given is the parallax angle of the Alpha Centauri.

To compute this problem, we can use the formula:
1 1
d= , substitute the value of parallax angle as d= = 1.35 parsec
𝑝 0.742 𝑎𝑟𝑐𝑠𝑒𝑐
Therefore, the distance is computed as 1.35 parsec. Now, express this in light year,
which is the most common unit in measuring astronomical distance or in meters, in
order to have a better idea.
First, multiply the computed distance which is 1.35 parsec to the conversion factor.
1 𝑙𝑖𝑔ℎ𝑡𝑦𝑒𝑎𝑟
Thus, 1.35 parsec x
𝑜.306601 𝑝𝑎𝑟𝑠𝑒𝑐
Cancel the unit parsec leaving only the lightyear.
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1 𝑙𝑖𝑔ℎ𝑡𝑦𝑒𝑎𝑟
Hence, 1.35 parsec x = 4.403 Lightyear
𝑜.306601 𝑝𝑎𝑟𝑠𝑒𝑐

To further convert this to meters, multiply it to the conversion factor of

9.461x1015 meters

I. Asked? - distance [d]

II. Given? - parallax angle [p]= 0.742 arcsec.
III. Working Formula: d=1/p
IV. Solution:

1
d= = 1.35 parsec
0.742 𝑎𝑟𝑐𝑠𝑒𝑐

Convert to lightyears and meters:

1 𝑙𝑖𝑔ℎ𝑡𝑦𝑒𝑎𝑟
1.35 parsec x = 4.403 Lightyear x 9.461x1015 meters = 4.16 x 1015 m
𝑜.306601 𝑝𝑎𝑟𝑠𝑒𝑐
Lightyear
Therefore, the distance between the Earth and the Alpha Centauri is 1.35 parsec or
4.403 LY or
4.16 x 1015 m
Spectroscopic Method

For stars whose parallax cannot be measured using the ladder, the
spectroscopic method is used. Spectroscopic method requires that the star’s
apparent brightness and spectrum be first observed. To do this method we have to
consider for absolute brightness of star.
Astronomers measure the brightness of the stars thru the process known as
photometry. Based on Physics concepts, the brightness and distance have an
inverse-square relationship. Mathematically it can be expressed as

In the equation, brightness decreases proportionally to the square of the

distance or when distance is doubled, the brightness of the star will be quartered of
its original.
The standard measure of the brightness of a star in astronomy is the
brightness of a star that is 10 parsec away from earth. This brightness is called
absolute brightness while the actual brightness of the star that we see here on earth
is known as its apparent brightness.
How do we measure the distance of the star from us using the measurement
of their brightness?

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 By looking at their spectral lines under the process known as spectroscopy,
astronomers analyze the spectra of nearby stars whose parallax are known to those
which are not. Astronomers are able to determine the spectral type of a star’s
spectrum by analyzing its spectral lines and plotting the observations in the
Hertzsprung - Russell diagram.
Hertzsprung-Russell (HR) Diagram is a graph that shows star’s luminosity
versus its temperature. It is an important tool in determining the distance of far-off
objects because astronomers believe that the stars near Earth are similar to the stars
far from earth.

https://www.space.fm/astronomy/starsgalaxies/hrdiagram.html

If the star’s location can be plotted on HR Diagram, its absolute brightness

can be read off. Knowing the absolute brightness of a cluster of stars and comparing
this to the absolute brightness of the stars with known distance enables astronomers
to roughly estimate the distance of the cluster form Earth. The observed cluster is
shifted vertically in the HR diagram until it overlaps with the model stars (stars with
known distance).
The difference in the magnitude that was used to join the two groups is called
distance modulus which is the difference between apparent and absolute magnitude
(m – M) and is the direct measure of the distance in the formula:

where:
m is the apparent magnitude
M is the absolute magnitude
d is the distance to the object in parsec.
Manipulating this will give the formula for distance:

Example:
A star in a certain constellation was found to have an apparent magnitude of
3.5 with a spectral class of G8. According to HR Diagram, the star shows an
absolute magnitude of 5.7.
I. Asked: distance [d]
II. Given: Apparent magnitude [m]= 3.5 Absolute magnitude [M]=5.7
III. Working Formula:
d=10(m-M+5)/5
d=10(3.5-5.7+5)/5
d=100.56 or
d=3.63 parsecs

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 Doppler Effect

Doppler Effect is used by astronomers to estimate the speeds of far-off

objects. It is the shift in the wavelength of the emitted light of an object which is
proportional to the speed with which the object moves. Doppler Effect occurs when
the star emitting light is moving with respect to an observer. But it has significantly
helped the astronomers in identifying the other celestial objects in our solar system.

where:
λ is the measured wavelength
λo is the original or rest wavelength
v is the speed of the object
c is the speed of light

Example:
The measured wavelength of emitted light from a celestial object is
5.05x1010 km and the rest wavelength is 5.00x1010 km. What is the velocity of the
celestial object?

I.Asked: Velocity [v]

II. Given : initial wavelength [𝜆0 ]=5.00x1010 km
Emitted wavelength [𝜆]= 5.05x1010 km
III. Working Formula:
V=C 𝜆 − 𝜆0 [ 5.05x1010 -5.00x1010 ]km
𝜆0 = 3x108 m/s 5.00x1010 km

= 3x108 m/s [0.01]

= 3x106 m/s

Other methods to determine distances of objects in the universe:

1. Distances up tp 13,000,000 light years

Leavitt noted Cepheid stars in the HR diagram that brighten and dim
periodically . Aside from measuring the period of brightness, Leavitt also measured
the maximum brightness on Earth and used HR method to determine the distance
of these stars from Earth. She found out that the brighter the Cepheid is, longer its
period is.

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 Cepheid stars are very abundant and bright in the galaxy. If somebody
obtains the distance to a given galaxy, Cepheid variables must be located first.
Cepheid variables have certain periods associated with brightness and this can be
plotted at a distance of one light year. It is also important to measure Earth’s
brighness. The brightness at the distance if one light year is larger than the observed
brightness because its quantity drops like a square of the distance. Based on these
numbers, the distance to the stars can be obtained and work up to 13 million light
years.

2. Distances up to 1,000,000,000 light years

In order to measure such huge distance (1,000,000,000 light years) supernova
can be used. Supernova is a star that usually blows themselves apart at the end of
their life and become so bright for a period of time.
To measure the distance, the distance of supernova to Earth must be known.
Then the periodic brightness and dim must be obtaianed. A specific supernova
known as type Ia brightens and dims regularly at a distance of 1 light year. Once this
is calculated, it is found to be the same for all cases.

3. Distances beyond 1,000,000,000 light years

For every far objects, the General Theory of Relativity must be used to
measure distances.
Indeed the cosmic ladder distance can be used to estimate the distances of
objects in space and it also allowed astronomers to reach conclusion that our
universe is composed of vast collections of galaxies.

Key Points
• Cosmic distance ladder is a succession of methods used by astronomers to
estimate the distance of far-off objects. The ladder evolved from the fact that
there is no single method that can measure all the distance of star or galaxy
that can be seen from earth.
• The measure of the distance from Earth to Sun is called astronomical unit
(AU) and is approximately 1.50 x 1011m. This value is used in measuring the
parallax of a star that is at least 300 lightyears away
• Parallax is the apparent change in the position of an object due to change in
the way it is perceived. It is used to measure distance of stars that are
approximately 300 lightyears away.
• Standard candles are those objects with known luminosity.
• Luminosity of a star is the measure of the total energy it emits per
unit of time. It depends on both radius and temperature of the star and is also
the measure of the star’s absolute brightness. Doppler Effect is the shift in the
wavelength of the light emitted by a star and is used to measure the star’s
speed.

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 Explore

Here are some enrichment activities for you to work on

to master and strengthen the basic concepts
you have learned from this lesson.

Enrichment:
Activity 1. “What’s that Word?”
Direction:
Arrange the following jumbled letters to form the words related to the methods of
determining the speeds and distances of far-off objects.

1. L A A P X A R L
2. S T Y L M I N U I O
3. P L E O D P R F F E T C
4. L O S M U U D
5. T O H O P R E Y M T
6. S P E C A R
7. L H I G T A R E Y
8. C C O S I M
9. P S C E R T S O C Y P
10. E C S C A R

Activity 2:

Tell Me:
Provide the answers for the following questions. You may use different materials as
a reference for the articulation of your points.

1. What is the difference between parallax technique and Cepheids variables

technique when determining distance?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________

2. What is the reference point when two or more values are being measured?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________

3. How can we know that objects are closer to us or further away in the sky?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________

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4. What is parallax and how do we use it?

__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________

5. How many light years away must be a star for the parallax angle to be one
second?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________

6. What do we call the apparent motion of an object when observed from 2 different
perspective?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________

Activity 3.

Match Me:
Choose the answer that best matches the definitions below. Write the letter of your
answer on the column entitled “Match”.

Definition Key Terms Match

1. The measure of the distance from Earth to A. Cosmic ladder
Sun
2. It is the shift in the wavelength of the B. Luminosity
emitted light of an object which is
proportional to the speed with which the
object moves
3. which is the difference between apparent C. Doppler Effect
and absolute magnitude (m – M)
4. is a succession of methods used by D. Astronomical
astronomers to estimate the distance of far- unit
off objects
5. is the measure of the total energy it emits E. distance modulus
per unit of time
6. It is used to measure distance of stars that F. parallax
are approximately 300 lightyears away.

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 Deepen

ACTIVITY: What Is a Light-Year?

1. Record the distance you walk, at a normal pace, in 10 sec.

A. Trial 1 _____________m
B. Trial 2 _____________m
C. Trial 3 _____________m

2. Average the distances for your trials by adding the values from A, B, and C and
dividing by the number of values, which in this case is 3.
D. Average distance ______________m

3. Calculate the speed (distance over time) of your travel by dividing the time (10 sec)
into the distance traveled (D).
E. Your speed ______________m/sec

4. Calculate the distance traveled in 1 min if you were to keep your speed the same
by multiplying your speed (E) by the number of seconds in a minute (60 sec/min).
F. Your distance traveled per minute _____________m

5. Calculate the distance traveled in 1 hr if you were to keep your speed the same by
multiplying the distance traveled per minute (F) by the number of minutes in an
hour (60 min/hour)
G. Your distance traveled per hour _______________m

6. Calculate the distance traveled in 1 day if you were to keep your speed the same
by multiplying the distance traveled per hour (G) by the number of hours in a day
(24 hr/day).
H. Your distance traveled per day _______________m

7. Calculate the distance traveled in 1 yr if you were to keep your speed the same by
multiplying the distance traveled per day (H) by the number of days in a year (365
days/yr).
I. Your distance traveled per year _______________m

8. Calculate how many kilometers you could travel in 1 yr if you were to keep your
speed the same by dividing your distance traveled per year (I) by the number of
meters in a kilometer (1,000 m/km).
J. Your distance traveled per year ______________km

9. The speed of light is about 300,000,000 m/sec. What is the distance light travels
in 1 sec in meters?
K. _______________m

10. Calculate the distance light travels in 1 min in meters.

L. _______________ m

11. Calculate the distance light travels in 1 hr in meters.

M. ______________ m

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12. Calculate the distance light travels in 1 day in meters.
N._______________ m

13. Calculate the distance light travels in 1 year in meters.

O.___________ m

14. Calculate the distance light travels in 1 year in kilometers.

P. _______________ km

15. Calculate how much faster light travels compared to your walking speed by
dividing the distance light travels in 1 year (P) by your distance traveled per year
(J).
Q. ______________ times faster

16. Calculate how many years it would take you to walk a distance of 1 light-year.
R. ______________ year

17. Why do you think astronomers use light-years instead of kilometers to measure
distances in the universe?

___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________
___________________________________________________________________________________

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 Gauge

Read and analyze each question then choose the letter of the answer of your choice.
Use a separate sheet of paper in writing your answer.

1. What is an astronomical unit?

A. the average speed of Earth around the Sun
B. the length of time it takes Earth to revolve around the Sun
C. the average distance from Earth to the Sun
D. the diameter of Earth's orbit around the Sun

2. What method can be used to determine the distance of stars that are less than
300 light years away?
A. parallax C. spectroscopy
B. photometry D. standard candles

3. The term observable universe refers to

A. that portion of the universe that we have so far photographed through
telescopes.
B. the portion of the universe that can be seen by the naked eye.
C. the portion of the universe that is not hidden from view by, for example, being
below the horizon.
D. that portion of the universe that we can see in principle, given the current age
of the universe.

4. It is the shift in the wavelength of the emitted light which occurs when the
source of light is moving relative to an observer.
A. Astronomical Unit C. parallax
B. Doppler Effect D. light years

5. What is cosmic distance ladder?

A. method used in determining the distance of far-off objects which involves
several processes that are not related to one another.
B. method used in determining the distance of far-off objects which involves
several processes that builds on one another.
C. method used in determining the distance of far-off objects which involves one
process only.
D. method used in determining the distance of far-off objects which involves
several processes that can only measure limited distances

6. Which of the following correctly defines one astronomical unit?

A. the distance of the Earth from the Sun
B. the distance of the earth to the nearest planet in the solar system
C. the distance of the earth from the nearest galaxy
D. the distance that the earth travels in a year

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7. If the distance of the star is increased three times what will happen to its
brightness according to the inverse square law?
A. The brightness of the star will decrease 9 times.
B. The brightness of the star will increase 8 times.
C. The brightness of the star will decrease 3 times.
D. The brightness of the star will increase 9 times.

8. Which of the following correctly describes the luminosity of a star?

I. Measure of the apparent brightness of a star.
II. Total amount of energy emitted by a star per unit time.
III. Measure of the absolute brightness of a star.
IV. Depends on both radius and temperature of the star.
A. I and II C. III and IV
B. II, III and IV D. All of the above

9. What does the inverse – square relationship between star’s brightness and
distance mean?
A. the star’s brightness decreases proportionally to the square of the distance.
B. the star’s brightness increases proportionally to the square of the distance.
C. the star’s brightness decreases proportionally when distance is doubled.
D. the star’s brightness increases proportionally when distance is doubled.

10. How do we call this variable where there is expanding and contracting of stars
causing their brightness to change in a very regular way?
A. Cepheid C. parallax
B. Doppler D. Supernova

11. If a star’s radius is 3 solar (3 times that of the sun) and its temperature is 2
solar, what is its luminosity relative to that of the sun?
A. 100 times that of the luminosity of the sun
B. 36 times that of the luminosity of the sun
C. 144 times that of the luminosity of the sun
D. 108 times that of the luminosity of the sun

12. If a certain photon emitted by an object has a rest wavelength of 2x1010km and
a measured wavelength of 3x1010km. What is the speed of the object relative to
the speed of light?
A. 0.5 times the speed of light C. 2 times the speed of light
B. 5 times the speed of light D. 0.2 times the speed of light

13. Which among the stars blow themselves apart at the end of their life and
become so bright for a period of second?
A. Alpha Centauri Cepheid C. Rigel
B. Cepheid D. Supernova

14. How can we know that the objects are closer to us or further away in the sky?
A. parallax angles C. stellar parallax
B. parallax shift D. parallax triangulation

15. What method is used by astronomers to estimate the distance of nearby objects
in space?
A. parallax angles C. stellar parallax
B. parallax shift D. parallax triangulation

17 with this module.

Great job! You are done
 18
1. A
2. A
3. C
4. B
5. B
6. A
7. C
8. D
9. A
10. A
11. C
12. D
13. D
14. B
15. A
Answer may vary
Gauge: Deepen:
Activity 1:
1. parallax
2. luminosity
3. Doppler
Effect
Activity 3 4.modulus
5. photometry
1. D 6. parsec
2. C 7. light year
3. E 8. cosmic
4. A Answer may vary 9. spectroscopy
5. B 10. arsec
6. F
Explore Activity 3 Explore: Activity 2 Explore: Activity 1
Answer Key
References:

Printed Materials:

Borra-Cudera, R., Carreon, H. and Morales, N. (2016). Physical Science for Senior
High School (pg. 210-212). Malabon City, Mutya Publishing House, Inc.

Ungson, O. and Teope, F. (2016). Physical Science (pg. 310). Quezon City, Trinitas
Publishing Inc.

Internet:

pearson.com/us/higher-education/program/Bennett-Modified-Mastering-
Astronomy-with-Pearson-e-Text-Standalone-Access-Card-for-Cosmic-Perspective-
The-9th-Edition/PGM2016873.html?tab=resources

Links:

https://www.daviddarling.info/encyclopedia/C/cosmic_distance_ladder.html
https://cdn.mos.cms.futurecdn.net/KUhXyrLdXw8qpXULApiLWX.jpg
https://www.space.fm/astronomy/starsgalaxies/hrdiagram.html
https://www.youtube.com/channel/UC5VjpHGXA5xyIexkkhFtCLw

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