Senior High School
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Physical Science
Quarter 2 - Module 8
Einstein’s Special and General Relativity
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Physical Science- Grade 12
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Quarter 2 - Module 8: Einstein’s Special and General Relativity
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Senior
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Senior
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Physical Science
Quarter 2 - Module 8
Einstein’s Special and General Relativity
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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:
Special Relativity ......................................................................................................................... 1
What I Need to Know .......................................................................................... 1
What’s New: Observing Light ............................................................................ 2
What Is It ............................................................................................................... 3
What’s More: Special Relativity experiment ................................................... 4
What I Have Learned: Test your Analysis ........................................................ 5
What I Can Do: Reflection Paper ....................................................................... 6
Lesson 2:
Consequences of Postulate of Special Relativity .................................. 7
What’s In ....................................................................................................... 7
What I Need to Know.................................................................................... 7
What’s New: Guessing Time ..................................................................... ..9
What Is It: .................................................................................................... .10
What’s More: Perform Me Correctly .......................................................... .14
What I Have Learned: Explain Briefly……………………………………..15
What I Can Do: Reaction Paper … ............................................................ ..16
Lesson 3:
Consequences of Postulate of General Relativity................................. 17
What’s In ....................................................................................................... 17
What I Need to Know.................................................................................... 17
What’s New: Find A Partner ...................................................................... ..18
What Is It: .................................................................................................... 18
What’s More: I am Bent .............................................................................. . 21
What I Have Learned: Expound Me ……………………………………… 22
What I Can Do: Let’s React ………………………………………………22
Lesson 4:
Speeds and Distances of Far-off Objects ....................................................... 23
What I Need to Know.................................................................................... 23
What’s New: Knowing Parallax…………. ................................................. ..24
What Is It:…… ............................................................................................ ..24
What’s More: Show It To Me! ................................................................... ..30
What I Have Learned: Test Your Analysis ……………………………..…31
What I Can Do: How far? How Powerful? …………..……………………32
Lesson 5:
The Expanding Universe .................................................................................................... 35
What’s In ....................................................................................................... 35
What I Need to Know.................................................................................... 35
What’s New: Think Pair-Share ................................................................... ..36
What Is It: ................................................................................................... ..36
What’s More:The Expanding Universe- Galaxies … ...................................... ..41
What I Have Learned: Test Your AnalysisCalculating the age of the Universe ……………....42
What I Can Do: Sketch Me Up!……………………………………………42
Summary………………………………………..…………………………………………43
Assessment: (Post-Test)…………………………………………………………………...44
Key to Answers……………………………………………………………………………46
References…………………………………………………………………………………48
What This Module is About
This Module in Physical Science attempts to supplement the students’ knowledge in
Einstein’s Special and General Theory of Relativity as well as the Understanding on the
Expanding Universe and to develop their science process skills. It is designed to make
students’ study time more profitable and to provide a better understanding of Physical Science.
Each lesson should be read thoroughly before answering the activities in each topic in
order to be successful and efficient in every task given. The introductory remarks at the
beginning of lesson provide a brief review of the background upon which the activity is
predicated. The questions appearing in the activity are designed to check the student’s
understanding of the quantitative principle learned inside and outside the classroom.
The authors took into consideration the adequacy and endeavors needed as well as the
suitability of equipment and materials involved in making this module.
It is hope that this
module will not only make the activities instructional but also more enjoyable.
The following are the lessons contained in this module:
1. Einstein’s Special Relativity
2. Einstein’s General Relativity.
3. Expanding Universe
What I Need to Know
At the end of this module, you should be able to:
1. Explain how special relativity resolved the conflict between Newtonian mechanics
and Maxwell’s electromagnetic theory (S11/12PS-IVi-68);
2. Explain the consequences of the postulates of Special Relativity (e.g., relativity of
simultaneity, time dilation, length contraction, mass-energy equivalence, and
cosmic speed limit) (S11/12PS-IVi-69);
3. Explain the consequences of the postulates of General Relativity (e.g., correct
predictions of shifts in the orbit of Mercury, gravitational bending of light, and black
holes) (S11/12PS-IVi-70);
4. Explain how the speeds and distances of far-off objects are estimated (e.g., doppler
effect and cosmic distance ladder) (S11/12PS-IVi-71);
5. Explain how we know that we live in an expanding universe, which used to be hot
and is approximately 14billion years old (S11/12PS-IVi-72).
How to Learn from this Module
To achieve the objectives cited above, you are to do the following:
• Take your time reading the lessons carefully.
• Follow the directions and/or instructions in the activities and exercises diligently.
• Answer all the given tests and exercises.
Icons of this Module
What I Need to
Know
This part contains learning objectives that
are set for you to learn as you go along the
module.
What I know
This is an assessment as to your level of
knowledge to the subject matter at hand,
meant specifically to gauge prior related
knowledge
This part connects previous lesson with that
of the current one.
What’s In
What’s New
An introduction of the new lesson through
various activities, before it will be presented
to you
What is It
These are discussions of the activities as a
way to deepen your discovery and understanding of the concept.
What’s More
These are follow-up activities that are intended for you to practice further in order to
master the competencies.
What I Have
Learned
Activities designed to process what you
have learned from the lesson
What I can do
These are tasks that are designed to showcase your skills and knowledge gained, and
applied into real-life concerns and situations.
What I Know (Pre-Test)
Multiple Choice. Select the letter of the best answer from among the given choices.
1. At what rate do the EM waves travel according to Maxwell's electromagnetic wave theory?
A. 3.00 x 108ms-1
C. 3.00 x 10-8ms-1
B. 6.00 x 108 ms-1
D. 6.00 x 10-8 ms-1
2. Which among the following resolves the conflict between Newtonian mechanics and
Maxwell's electromagnetic theory?
A. Theory of general relativity
B. Theory of special relativity
C. Law of universal gravitation
D. Law of conservation of energy
3. Einstein's theory of special relativity corrected the laws of motion first proposed by:
A. Hertz
B. Galileo
C. Maxwell
D. Newton
4. One of two identical twins becomes an astronaut, while the other becomes a real estate
broker. The astronaut embarks on high-speed space travel and is gone for several years.
Upon the astronaut's return, the two twins are reunites and observe their physical
appearances. The result will be that
A. both have aged the same.
C. the real estate broker has aged less.
B. the astronaut has aged less.
D. None of the above
5. Clocks in a stationary reference frame, compared to identical Clocks in a moving reference
frame, appear to run
A. at the same rate.
B. backward in time.
C. faster.
D. slower.
6. An object that looks green in empty space is positioned near but not in a black hole. From
the black hole far from the observer, the object would appear
A. black.
C. green.
B. blue.
D. red.
7. The Principle of Equivalence in the General Theory of Relativity states that inertial and
gravitational masses are
A. identical.
B. increasing.
C. not significant.
D. varied.
8. Which of the following is not a consequence of General Theory of Relativity?
A. Black Hole
C. Precession in the Orbit of Mercury
B. Gravitational Lensing Effect
D. Time Dilation
9. The Einstein Cross is an evidence of
A. Black Hole
B. Gravitational Lensing Effect
C. Increased gravity
D. Shifting of orbit
Lesson
1
SPECIAL RELATIVITY
What I Need to Know
Relativity is not new. Galileo explained that motion is a relative way back around the year
1600. Wherever you happen to be, it seems like you are at a fixed point, and that everything
moves with respect to you. Everyone else feels the same way. With respect to a fixed point
motion is always measured. This is what we called establishing a frame of reference. In the
discussion of relativity light is always involved for theories related to electromagnetism are
inconsistent with Galileo’s and Newton’s explanation of relativity. The true nature of light was
a hot topic of discussion and controversy in the late nineteenth century and it is now explain
how special relativity resolved the conflict between Newtonian mechanics and Maxwell's
electromagnetic theory.
Newtonian Mechanics is also called as classical mechanics containing concepts that do not
entirely agree with other known theories in Physics like electromagnetic theory of Maxwell but
when Einstein presented his theory of special relativity, the conflict between the two great
physicists was resolved.
Maxwell’s theory is in fact contradicts with Newtonian Mechanics, and in trying to find the
resolution to this conflict so, Einstein, lead to his theory of special relativity. Maxwell’s
equation withstood the conflict, but it was Newtonian mechanics that were corrected by
relativistic mechanics.
But how the theory of special relativity resolved the conflict between the two famous
physicists? What is Einstein’s theory of special relativity?
1
What’s New
Activity 8.1.1. Observing Light
What can you tell about the picture below? Which theory regarding light is correct the
Newtonian’s Theory or Maxwell Theory? Why?
https://doi.org/10.1119/1.4895355
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2
What Is It
Newtonian mechanics discusses the everyday motion of the objects of normal size around us
including the force that causes these motions. The concepts under Newtonian mechanics are
mainly based on ideas of Newton about motion which correctly describes the state of motion
of an object whether at rest or moving in a straight path and the forces that maintain and can
cause changes in the body’s states of motion.
Furthermore, Newtonian mechanics is based on the assumption of absolute space and time.
This means that the distance between two points, and the time that passes between two events
don’t depend on the coordinate system you choose. Therefore, a coordinate transformation
must leave them unchanged.
Maxwell’s electromagnetic theory consists of four formulas from the different works of
Faraday and other physicists that unite all the concepts of electricity and magnetism that had
the findings that electric and magnetic fields spread as waves. In 1886, Hertz proved that these
waves really exist and the propagation speed of these waves can be calculated using the
formula:
·
https://www.facebook.com/notes/physical-science/91-theory-of-specialrelativity/3390893954260139/
Moreover, Maxwell observed that the value of the above expression is equivalent to the speed
of light c (3.0 x 108 m/s) which implies that speed of light c must also be constant in which
the conflict between Newtonian mechanics and Maxwell’s theory starts.
If we consider a moving object with the of speed 100 m/s and switched on the flashlight,
according to Newtonian mechanics the speed of the light from the flashlight would be 100 m/s
+ c and dispute what Maxwell’s theory stating that the speed of light is a constant value. Which
is true between these two concepts?
3
The theory of special relativity proposed by Einstein in 1905, is a theory in physics that concern
the relationship between space and time objects that are moving at a consistent speed in a
straight line. Simply placing an object approaching the speed of light, its mass becomes infinite,
and it is unable to go any faster than light travels. It is the generally accepted and
experimentally confirmed.
The two main postulates of special relativity are:
1. The laws of physics are the same in all reference frames that are moving at a
constant velocity (not accelerating).
2. The speed of light is the same in all of these reference frames, even if the source of
the light is moving.
The second postulate clearly tells that Maxwell’s theory is correct but does imply that
Newtonian mechanics is wrong. But not totally, the postulates of Einstein tell us that Newtonian
mechanics has limitations in terms of its application. Considering moving objects with speed
very small compared to the speed of light, Newtonian mechanics applies like the speeds of a
flying ball and running car but considering a speed that is near to the speed of light, a new
concept must be included to supply the limit of Newtonian mechanics and that is the Lorentz
transformation the counterpart of the Galilean transformation of the Newtonian mechanics.
What’s More
Activity 8.1.2. Special Relativity Experiment
Do this activity with a partner. Mrs. Yap is standing in a ground while Mr. Yap is riding on a
truck that is moving with velocity v. Mr. Yap switched on the flashlight in the direction in
which he is moving.
https://aether.lbl.gov/www/classes/p139/exp/gedanken.html
Question: What happens? What was the observation of the Mrs. Einstein on the light
as it travels? How about to Mr. Einstein what was his observation to the light? Do
they have the same observation?
Answer:
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What I Have Learned
Activity 8.1.3. Test your Analysis
Make a Table showing the conflict between Newtonian Mechanics and Maxwell Theory on the
speed of light.
Newtonian Mechanics
Maxwell Theory
5
Explain on your own words how the theory of special relativity resolved the conflicts
between Newtonian mechanics and Maxwell theory?
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What I Can Do
Activity 8.1.4. Reflection Paper
Make a reflection paper on the special theory of relativity.
Lesson
2
CONSEQUENCES OF THE
POSTULATE OF SPECIAL
RELATIVITY
What’s In
In the year 1900, most of physics seemed to be comprised in two great theories of Newtonian
mechanics and theory of electromagnetism by Maxwell. Unfortunately, there were
inconsistencies between the two theories that seemed irreconcilable. The genius Einstein sees
that the conflicts were alarmed not merely with mechanics and electromagnetism, but with
most elementary ideas of space and time as many physicists struggled with the problem,
Einstein resolved these difficulties and profoundly altered our conception of the physical
universe using special theory of relativity.
What I Need to Know
POSTULATES OF SPECIAL RELATIVITY
The first Einstein’s Postulate states, "At any frame of reference, all laws of physics
are the similar.”
These physical laws help us to understand how and why our environment reacts the way it does
allowing us to predict events and their outcomes. As a result of this postulate, we can formulate
such laws and be sure that they are independent of our current state of motion. Consider a
yardstick and a box. If you measure the length on the box, you can get the same result whether
you are standing on the ground or riding a bus. Measure the time it takes a pendulum to make
10 full swings from a height of 12 inches above its resting place. You will again get the same
results regardless whether you are standing on the ground or riding a bus, assuming that the
bus is not accelerating, but travels along at a constant velocity on a plane road. If we take the
same examples, but this time measure the box and time the pendulum swings as they ride past
us on the bus, this time we arrive at different results than our previous results. The difference
in the results of our experiments happens because it follows the first postulate of special
relativity.
The second Einstein’s Postulate states: "For all reference frames, the speed of light (c)
is the same no matter what their relative speed is."
In other words, the speed of light is ultimate constant of nature. Suppose I am in a car going 50
km/h, and I throw a baseball 10 km/h in the same direction the car is going. If you were standing
on the side of the road with a radar gun, you’d measure the baseball going 50 + 10 = 60 km/h.
That’s how we classically deal with relative motion. Now suppose I am in the car shining a
flashlight. If you could measure the speed of the light coming out of it from the side of the road,
you’d get the same speed no matter fast the car was going, or what direction I shined the
light. That is what makes light special!
As you go along this lesson, you can find answers to the following questions:
 Can you catch up with light?
 What would happen if I rode a light beam?


If you were moving at the speed of light and viewed in a mirror, can you see
your reflection?
If you are travelling on the outer space, does the time the same in the Earth?
The questions above will give you an idea on the topics you may find more interested to
know and eager to learn more.
8
What’s New
Activity 8.2.1. Guessing Time
Look at the picture below. Why the twin in a rocketship looks younger than the other twin
after 60 years? Does time on Earth differ on the time in the outer space? Why?
http://abyss.uoregon.edu/~js/cosmo/lectures/lec06.html
What Is It
The consequences of the postulate of special relativity are relativity of simultaneity, time
dilation, length contraction, mass-energy equivalence, and cosmic speed limit.
LENGTH CONTRACTION
A moving object would be shorter in length.as observe by the observer at rest that is relative to
the moving object.
Here are two identical cars, car A and car D.
http://web2.uwindsor.ca/courses/physics/high_schools/2005/Special_relativity/LENGTHCON
TRACTION.html
Car A is stopped at a stop sign and car B is moving past at an appreciable fraction of the speed
of light. Measure the length of Car B while passing at Car A and measure the length of car A.
Does the length of Car A is the same as Car B?
It turns out that the length you measure will be smaller than the value you obtained for car A.
This is the principle of length contraction. Since car B has a relative velocity with respect to
you and car A does not, you obtain two different values for their lengths.
Note that car B will only be shorter in the direction it is traveling its width and height will not
be affected. In our lives, we never detect length contraction because we move at speeds that
are very small with respect to the speed of light.
10
TIME DILATION
An observer who is in relative motion with respect to that clock determined the “slowing down”
of a clock.
Consider a light clock.
http://web2.uwindsor.ca/courses/physics/high_schools/2005/Special_relativity/TIMEDILATI
ON.html
This clock measures the speed of light by sending out a beam of light to the top plate. Call this
event A. This beam is then reflected back to the clock. Event B is when the light reaches the
clock again.
For the stationary clock on the left, the measured time interval between events A and B is ten
seconds. The clock on the right is set in motion with a given speed. To an observer traveling
on the clock, the time interval between events A and B is still ten seconds. However, to an
observer watching the clock move, it now appears that the light beam travels further than
before.
Since velocity is distance/time and the speed of this beam must be a constant, the measured
time interval between events A and B must now be greater than ten seconds.
SIMULTANEITY
Whether two spatially separated events not absolute occur at the same time but depends on
the observer's reference frame.
Imagine that you and your friend Timmy are at opposite ends of your class when you notice
your professor turns on his light at the podium. You call Timmy and ask him if he saw the
professor turn on the light. Timmy answers that he did.
11
.http://web2.uwindsor.ca/courses/physics/high_schools/2005/Special_relativity/SIMULTANE
ITY.html
The next day your professor decides demonstrate simultaneity by asking the class to go on
the special relativity bus, while he stands outside it. Once again you and Timmy are on the
opposite sides of the bus, where he is sitting in the front and you are sitting in the back.
The bus starts moving at 0.9c (where c is the speed of light, approximately 300 000 000 m/s)
the professor, who is standing in the middle turns on his flashlight. Write down the time at
which you see the light from the outside. Timmy, sitting on the front of the bus does the same
thing since both two have synchronized watches.
When the bus comes to a stop you and Timmy compare the times at which you saw the light.
Unfortunately they are different. Now that the bus was moving, its back was going into the
path of the light waves faster than the light waves were spreading out from the middle of the
bus. This enabled you to see the event sooner, whereas Timmy had to wait for the emitted light
waves to reach him.
12
MASS INCREASE
The rest energy and total energy of the body are equivalent to the rest mass (an invariant
quantity which is the same for all observers in all reference frames) and relativistic mass
(dependent on the velocity of the observer), respectively.
http://web2.uwindsor.ca/courses/physics/high_schools/2005/Special_relativity/MASSINCRE
ASE.html
Einstein cleverly suggested that when someone observes you in motion, if they measure your
mass, it would appear to increase as your speed increases.
So why does your mass seems to increase to an observer watching you if you are speeding up?
First, consider that Einstein determined that energy (E) and mass (m) are related. He stated that
the energy an object contains is simply its mass multiplied by the speed of light squared. This
is the famous equation we all know, E = mc2.
Through this equation, Einstein tells us that the energy of a body always equals mc2. We stated
earlier that when you are at rest, you have a given rest mass, and let’s call it m0. So your energy
in this case to someone observing you at rest would be m0c2. Your rest energy is a sort of basic
or minimum amount of energy you always have whether you are at rest or not
13
What’s More
Activity 8.2.2. Perform Me Correctly
Place an expanded balloon of air on a weighing scale outside your house early morning in the
morning. Assuming that the balloon stays on the scales and record changes in its weight
everyday. Does the mass of the balloon change from day 1 to day 5? Discuss the worries in
carrying out this experiment.
Day
Weight
14
What I Have Learned
Activity 8.2.3. Explain briefly
Answer the questions briefly and concisely.
1. When you riding in a commercial airplane, it appears that the plane is at rest and the Earth
is moving underneath you. Is this point of view valid? Discuss briefly.
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2. How does the elapsed time for a process seem to be longer, an observer moving with the
process or observer moving relative to the process? Which observer measures proper time?
Explain your answer.
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3. How far could you travel into the future without aging significantly? Could this method
also applied to travel into the past?
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4. To whom does an object seem greater in length, observer moving relative to the object or
an observer moving with the object? Which observer measures the object’s proper length?
Why?
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5. Assuming no molecules escape or are added, what happens to the mass of water in a pot
when it cools? Is this observable in practice? Explain.
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15
What I Can Do
Activity 8.2.4. Reaction Paper
Choose one of the consequences of the postulate of special relativity and make a reaction
paper for that topic.
16
Lesson
3
CONSEQUENCES OF THE
POSTULATES OF GENERAL
RELATIVITY
What’s In
After the publication of the theory of special relativity in 1905, the following years, Einstein
worked on the details that acceleration produced the same effect as gravitation. The General
Theory of Relativity is a generalization of the Special Theory of Relativity. It is definitely the
most remarkable achievements of science to date. It was developed by Einstein with little or
no laboratory experiment but instead he was driven by mental analysis and philosophical
questions.
What I Need to Know
The General Theory of Relativity rests on the Principle of Equivalence which states that inertial
and gravitational masses are identical. This postulate will fail if one can find a material for
which the inertial and gravitational masses have different values. One might think that this
represents a defect of the theory, its Achilles heel – its weakness in spite of overall strength. In
one sense this is true since a single experiment has the potential of demolishing the whole of
the theory which may people have tried, but all experiments have validated the principle of
equivalence.Thus, the General Theory of Relativity is a gem.
The second fundamental principle of General Relativity is that the presence of curve matter in
space. In this opinion, gravity is not classified as force, as being described by Newton, but a
curvature in the fabric of space, and objects respond to gravity by following the curvature of
space in the vicinity of a massive object as illustrated in Figure 8.3.1.
17
Figure 8.3.1 The Curvature of Space caused by a Massive Object.
https://casswww.ucsd.edu/archive/public/tutorial/GR.html
What’s New
Activity 8.3.1. Find A Partner
Pair the following terms according to their meaning:
Bend
Precess
Equivalent
Identical
Deflect
Shift
What Is It
The consequences of the postulates of General Relativity:
SHIFTS IN THE ORBIT OF MERCURY
In the study of the Solar System a long-standing problem was that the orbit of Mercury did not
behave as Newton’s equations says. Let me describe the way Mercury’s orbit looks to
understand what the problem is.
As Mercury orbits the Sun, it follows approximately an elliptical path. It was found that the
point of closest approach of Mercury to the sun changes as it slowly moves around the sun as
shown in Figure 8.3.2. This rotation of the orbit is a precession. The precession of the orbit
does not happen to Mercury only but to all the planetary orbits., The effect of being produced
by the pull of the planets on one another was predicted in Newton’s theory.
The precession of Mercury’s orbit is measured to be 5600 seconds of arc per century as seen
from Earth. Newton’s equations, considering all the effects from the other planets (as well as a
very slight deformation of the sun due to its rotation) and the fact that the inertial frame of
reference is not the Earth, the precession of 5557 seconds of arc per century where the
discrepancy is 43 seconds of arc per century is predicted. This discrepancy cannot be accounted
for using Newton’s formalism. Many ad-hoc fixes were devised (such as assuming there was a
certain amount of dust between the Sun and Mercury) but none were consistent with other
observations. Similarly, Einstein was able to predict that the orbit of Mercury should precess
by an extra 43 seconds of arc per century should the General Theory of Relativity be correct.
Figure 8.3.2. Artist’s version of the precession of Mercury’s orbit. Most of the effect is due to the pull
from the other planets but there is a measurable effect due to the corrections to Newton’s theory
predicted by the General Theory of Relativity.
http://iontrap.umd.edu/wp-content/uploads/2016/01/WudkaGR-7.pdf
GRAVITATIONAL BENDING OF LIGHT
A clear consequence of the equivalence principle is that bending of light by gravity. For two
times Einstein calculated the amount that light would be deflected passing by the sun, which is
the largest "nearby" mass. It was in his second calculation that Einstein was able to predict that
light from a distant star would be deflected by 1.75 arcseconds or less than 1/2000th of a degree.
19
The Solar Eclipse of 1919 was the first opportunity for Einstein to test
his calculations. British Astrophysicist Sir Arthur Eddington observed
the shift in position of the Hyades cluster stars behind the occulted
sun by mounting a pair of expeditions to West Africa and Brazil to.
Though not perfectly precise, Eddington's measurements clearly
showed a deflection and favored the larger value. This result made
Einstein world-famous.
An exhilarating and only very recently verified prediction of the
bending of light by gravity is the existence of gravitational lenses,
bending of light due to the change of the speed of light as it passes through a refractive medium.
Massive objects can act as lenses because gravity can bend light. This is done by focusing and
amplifying images of distant objects. Gravitational lenses differ from "normal" lenses. It
produce multiple images such as the Einstein Cross, a case of a distant quasar imaged by a
galaxy between us and the quasar, discovered by J. Huchra & colleagues as shown in Figure
8.3.3.
Figure 8.3.3 The Einstein Cross: four images of a quasar GR2237+0305 (a very distant – 8
billion light-years– very bright object) appear around the central glow. The splitting of the
central image is due to the gravitational lensing effect produced by a nearby galaxy
https://casswww.ucsd.edu/archive/public/tutorial/images/EinsteinCross.jpg
BLACK HOLES
Light is pulled by gravity just like rocks. Rocks can be put in orbits, but how about light?
Indeed, light can be put in orbits but we need a very heavy object whose radius is very small,
for example, we need something as heavy as the sun but squashed to a radius of less than about
3km.
Going farther and imagine an object so massive and compact that if we turn on a laser beam on
its surface gravity’s pull will bend it back towards the surface. This means that since no light
can leave this object it will appear perfectly black, this is a black hole. An object which comes
sufficiently close to a black hole will also disappear into it since nothing moves faster than light
if an object traps light it will also trap everything else.
The effect of a black holes, like all gravitational effects, decreases with distance. This means
that there will be a boundary surrounding the black hole that anything crossing it will not be
able to leave the region near the black hole; this boundary is called the black-hole horizon.
What’s More
Activity 8.3.2. I am Bent
Refer to the two pictures below, how does the beam of light behaves in both situations?
Situations
Behavior of light
a
Upward-accelerating
elevator
b
Elevator maybe
accelerating upward or
maybe acted by gravity
What postulate supports this behavior of light?
https://openstax.org/books/college-physics/pages/34-4-dark-matter-and-closure
21
What I Have Learned
Activity 8.3.3. Expound Me
Describe the postulate and give a consequence.
Postulate 1.
___________________________________________________________________________
___________________________________________________________________________
__________________________________________________________________________
Postulate 2
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
What I Can Do
Activity 8.3.4. Let’s React
Noting on the different consequences of General Relativity Theory, what is its great
contribution to science and humanity?
Lesson
4
SPEEDS AND DISTANCES OF FAROFF OBJECTS
What I Need to Know
Speed and distance of objects moving in different directions have been discussed in
your previous grades. It can easily be measured using different mathematical equations
depending on the given variables or factors. But how about the objects very far from us known
as far-off objects? How do we measure its speed and distance? How do astronomers make
accurate determination of its distances and what is its unit of measure?
As you go on through this module, you will be able to explain how the speeds and
distances of far-off objects are estimated (e.g., doppler effect and cosmic distance ladder)
It was discussed during the discussion of planetary motion that astronomical unit AU
is a convenient unit of expressing distances in the solar system. It is the average distance
between the Earth and the Sun. One AU is 1.5 x 108 km (9.3 x 107 mi). Using astronomical
units, one can get a relative idea of planet distances from the Sun. For example, if a planet was
5 AU from the Sun, then it would be five times as far from the Sun as is the Earth.
The ancient Greeks did some splendid measurements of the Earth and moon and they
tried to get the distance to the Sun. But even without an accurate value for the Sun-Earth
distance, later astronomers could still do some nice modeling of the solar system. In
fact Johannes Kepler found the the time it takes a planet to orbit the Sun was proportional to
its distance to the Sun (technically these orbits are ellipses). Using this, he determined the
distance from other planets to the Sun in terms of the Earth's distance and that is the distance
in AU. With the AU, it is much easier to measure distances in the solar system. For instance,
the distance from the Sun to Mars is about 1.52 AU and the distance to Pluto is around 40 AU.
To measure distances to the nearest solar system objects, scientists have developed
powerful radar to bounce signals of Venus, Mars, Mercury, and even the sun. For more distant
objects, astronomers use an aged-old technique called geometric parallax that was first devised
by the Greeks in 300 BCE
What’s New
Activity 8.4.1 Knowing Parallax
Look at the figure at the right, what have you
observed? Write your observation on the
spaces provided below.
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
__________________________________
Figure 8.4.1 Annual Parallax of a Nearby Star
What Is It
Over the course of a year, a nearby star seems to move back and forth against a
background of more distant stars. This parallax effect is due to the viewer’s position changing
as the Earth moves around the Sun. The angle p, measured in arc seconds, represents the annual
parallax of the nearby star.
The distance coordinate is usually measured in astronomical unit, light-years,, or
parsecs. Remember that AU is the mean distance of the earth from the Sun (1.5 x 108 km, or
93 million mi). A light-year (ly) is the distance traveled by light in 1 year ( 9.5 x 1012 km, 6
trillon mi.). It is calculated by multiplying the speed of light (3.00 x 105 km/s) by the number
of seconds in a year (3.16 x 107 s/y). One parsec, (pc) is defined as the distance to a star when
the star exhibits a parallax of 1 second of arc, where 1 second of arc is defined to be 1/3600
of 10. A parsec is related to a light-year by the following;
1 pc = 3.26 ly
The nearby star in Figure 4.1 as shown above, observed from two positions, appears to
move back and forth against the background of more distant stars. This apparent motion is
called parallax. The angle p measure the parallax in seconds of arc (arc seconds, or arcsec).
Defining a parsec this way provides an easy method for determining the distance to a celestial
object because taking the reciprocal of the angle p, measured in arc seconds, gives the distance
in parsecs.
1
d=
where d is the distance in parsecs and p is the parallax angle in
parsecs.
p
Figure 8.4.1 shows the the diagram of the geometric parallax technique where, if any
two angles and a baseline are known, then the other sides of the triangle can be computed.
Because stellar distances are so great, this parallax technique is accurate only to distances of
about 325 ly.
The distances to stars can also be determined by knowing their absolute and apparent
magnitudes as shown in the figure below. This technique is not easy because the distance to
the star must be known to determine the absolute magnitude of the star. Fortunately, most stars
can be classified by their spectrum and placed on the H-R diagram, which can then be used to
determine absolute magnitudes. This technique is useful for measuring stellar distances out to
35, 000 ly. Careful application of the scientific method, checking, and rechecking of distances
to the same star with different methods, significantly reduces errors.
Figure 8.4.2 Equinoxes and Solstices
25
The technique of accurately measuring distances were limited to objects within the
Milky Way galaxy, that was before 1915. A breakthrough happened when Henrietta Leavitt,
an American astronomer discovered that a certain Cepheid variable stars - an unstable red
giant stars could be used to accurately measure distances.
Leavitt found that the periods of variability of the unstable stars were directly related
to their brightness; therefore, the distances to the stars could be determined. With this important
discovery, the distance to the nearest galaxies could be accurately determined. The use of
Cepheid variable stars (Figure 8.4.3) allows accurate measurements to 50 million light years.
Figure 8.4.3 Cepheid Variable Stars. The period of variation in the brightness of a Cepeid variable star
is directly related to the brightness of the star, and the distance can be determined
How about the distances to more distant galaxies found? Astronomers in the 1970s
discovered the brighter spiral galaxies (those having more stars) rotate faster. Measuring
rotation via the Doppler shift of light allows one to determine the absolute brightness of galaxy.
Distances out to 600 million light years can be determined by comparing the absolute and
apparent brightness of these galaxies.
Supernovae are stars that explode and became incredibly bright objects, sometimes
entire galaxy of stars, although even brighter than an entire galaxy of stars, although only for a
short time. Specifically, certain types (Type I) of supernovae can be used to measure distances.
Many of these techniques use a general principle in Physics, the inverse-square law of
intensity . The inverse square law describes the intensity of light at different distances from a
light source. The intensity of light changes in the same way in every different light source.
There is an inverse proportion between the intensity of light to the square of the distance. This
implies that as the distance from a light source increases, the intensity of light is a value
multiplied by 1/d2.. The proportional symbol,
, is used to show how these relate. The formula
for this is shown below. Visible light is part of the electromagnetic spectrum, and the inverse
square law is true for any other waves or rays on that spectrum, such as, radio waves,
microwaves, infrared, ultraviolet light, x rays, and gamma rays. The intensity of visible light is
expressed in candela units, while the intensity of other waves is expressed in Watts per meter
squared (W/m2).
Proportional:
Where; I = light intensity (candela, W/m2)
means "is proportional to"
d = distance from a light source (m)
Intensity at different distances:
Where;
I1 = light intensity at distance 1
I2 = light intensity at distance 2
d1 = distance 1 from light source (m)
d2 = distance 2 from light source (m)
Example: 1) If a bright flashlight has a light intensity of 15.0 candela at a distance
1.00 m from the lens, what is the intensity of the flashlight 100.0 m from the lens?
Solution : The intensity at the farther distance can be found using the formula:
If d1 = 1.00 m from the lens, and d2 = 100.0 m from the lens, then I1 = 15.0 candela, and we
need to solve for I2. This requires rearranging the equation:
Now, substitute the values that are known in to the equation:
I2 = (0.0001)(15.0 candela)
I2 = 0.0015 candela
So, the intensity of the flashlight at a distance of 100.0 m is 0.0015 candela.
When astronomers use this principle to measure distances, they refer to the method as
standard candles. Because the brightness of the candle decreases as the square of the distance
increases, the distance to the candle is determined. The figure below shows the simple idea for
this technique.
Figure 8.4.4 The Standard Candle Technique. As the candle is moved farther away, the
brightness decreases. If the distance to the candles doubles, then the brightness of the candle decreases by a
factor of 4
The cosmic distance ladder or the extragalactic distance scale is the succession of
methods by which astronomers determine the distances to celestial objects. A
real direct distance measurement of an astronomical object is possible only for those objects
that are "close enough" (within about a thousand parsecs) to Earth. The techniques for
determining distances to more distant objects are all based on various measured correlations
between methods that work at close distances and methods that work at larger distances.
Several methods rely on a standard candle, which is an astronomical object that has a
known luminosity.
The ladder (See Figure 4.5) analogy arises because no single technique can measure
distances at all ranges encountered in astronomy. 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.
Figure 8.4.5 The Cosmic Distance Ladder






Light green boxes: Technique applicable to star-forming galaxies.
Light blue boxes: Technique applicable to Population II galaxies.
Light Purple boxes: Geometric distance technique.
Light Red box: The planetary nebula luminosity function technique is applicable to all
populations of the Virgo Supercluster.
Solid black lines: Well calibrated ladder step.
Dashed black lines: Uncertain calibration ladder step.
The fundamental distance measurements is at the base of the ladder, in which distances
are determined directly, with no physical assumptions about the nature of the object in question.
As part of the discipline of astrometry, stellar positions is done with precision.
Finally, distances to the farthest known objects in the universe can be determined by
Hubble’s Law. The figure below shows that there is a linear relationships between the velocity
of a galaxy and its. Distance. The velocity of many distant galaxies are measured with large
telescopes by observing their spectra. The absorption lines in the spectra are redshifted in direct
relation to the overall-velocity of the galaxy ( the well-known Doppler effect).
29
Figure 8.4.6 The Doppler Effect
Remember that the Doppler effect is observed whenever the source of waves is moving
with respect to an observer. This effect is produced by a moving source of waves in which there
is an apparent upward shift in frequency for observers, towards which the source is
approaching. Thus an apparent downward shift in frequency for observers from whom the
source is receding.
Hubble’s law can be written in equation form as
Vr = H x d
Where,
Vr, is the recessional velocity,
H, is the Hubble’s constant (currently estimated to
be 71 km/s/MPc), and
d, is the distance to the galaxy.
Thus, if a galaxy’s velocity is measured to be 10, 000 km/s , then
d = Vr = 10,000 km/s = 141 Mpc ≈ 460 Mly
H
71 km /s/Mpc
Take note that to determine distances to the most distant objects in the universe, a very
good determination of the Hubble constant is needed. The Hubble space telescope does that
very Task.
What’s More
Activity 8.4.2. Show It To Me!
Solve the following and show your solution. Box your final answer.
1. The intensity of a radio signal is 0.120 W/m2 at a distance of 16.0 m from a small transmitter.
What is the intensity of the signal 4.00 m from the transmitter?
30
2. Galaxy NGC 123 has a velocity away from us of 1,320 km/s and the Hubble Constant's value
is 70 km/s/Mpc. How far away is the galaxy according to Hubble's Law?
What I Have Learned
Activity 8.4. 3 Test Your Analysis
In the table below, write a summary on how to solve speeds and distances of far-off objects
(First column) and give your brief explanation in the second column.
Method/Technique in solving far-off
objects’ distances
Explanation/Equation
Method/Technique in solving speed of
far-off objects
Explanation/Equation
31
What I Can Do
Activity 8.4.4. How Far? How Powerful?
Your teacher has just gone over a calculation showing that the intensity of light
decreases as you move away from the light source. It does this with a very specific
relationship with your distance from the light – as 1/r2. You are going to prove that
relationship!
Materials

scissors

tape measure

tape

single-hole hole punch

dark orange or dark red paper (at least 7 by 7cm)

flashlight

graphing calculator or computer to perform a power regression
Procedure
1. Pick up the listed materials from your teacher.
2. Find a blank, flat wall to shine a light onto and a table or chair that can stabilize the
flashlight for this lab. If you have a blank wall near the end of a lab table, then put the
light on top of the table. You will need to be able to move the light (whether along the
table or by moving the chair) at least 1 meter closer to or away from the wall.
3. Use the hole punch to punch a hole in the center of the dark orange or red paper.
4. Tape the paper to the light end of the flashlight, making sure the hole is roughly
centered over the light.
5. Place the flashlight on the chair or table at least 10 cm from the wall. You can adjust
it with papers or books so that it is level (i.e., the light beam shines perpendicular on
the wall). Measure the distance from the wall to the hole on the front of the flashlight.
Record this distance in your data table.
6. Turn the flashlight on. You should see a distinct white circle projected on the wall.
The rest of the light emitted outside of this light should be a shade of the colored
paper taped to the flashlight.
Illustration of the lab set-up. (Credit: NASA/Imagine the Unvierse)
7. Take 3 different measurements of the diameter of the circle of white light on the wall.
HINT: Remember, the diameter of a circle is the longest measured chord from one
edge of the circle to the other. Therefore, you know you've got the diameter when you
hold one end of the tape measure on one side (edge) of the circle and get the largest
measured value by moving the other end of the tape measure along the other side.
8. Record these values in the data chart. Calculate the mean and record it as well.
9. Move the chair with the flashlight (or move along the table) about 20 cm further away
from the wall. Measure the distance from the wall to the hole on the front of the
flashlight. Record this distance on your data table.
10. Repeat steps 6-8 at least two more times.
11. Calculate the radius from each mean diameter. Record each calculation in the data
table.
12. Calculate the area of the circle formed from each calculated radius. Record each
calculation in the data table. HINT: Area of a circle equals π r2.
33
13. In your graphics calculator, enter the distance from the hole to the wall as one list and
the area of each calculated circle as another list.
14. Plot the data in the lists as a scatter plot. What kind of relationship do you see?
15. Calculate a Power Regression equation on the two lists. What is the equation?
Diameter of light circle (cm)
Measurement
Distance
(cm)
Trial
1
Trial
2
1
2
3
34
Trial
3
Radius
(cm)
Average
Lesson
5
THE EXPANDING UNIVERSE
What’s In
You have done learning on how to determine speeds and distances of the far-off objects
in the previous lesson. Using the knowledge that you have, this time, you try explain how we
know that we live in an expanding universe which is used to be hot and is approximately 14
billion years old.
One of the branches of astronomy is cosmology which study the structure and
evolution of the universe. Cosmology is the branch of astronomy that deals with the study of
the structure and evolution of the universe. The electromagnetic waves that came from galaxies
(the “building blocks” of the universe) were detected and analyzed by the astronomers in
determining the structure of the universe. Astronomers determine the structure of the universe
by detecting and analyzing electromagnetic waves that come from the galaxies, the “ building
blocks” of the universe. From the data collected, they determine the way in which these
galaxies are distributed throughout the vast volume of the universe. Astronomers estimate the
tens of billions of galaxies are within range of the optical telescopes. Even if they were inclined
to do so, astronomers would not have the time to observe the tremendous volume of the
universe to obtain information about all the galaxies. Instead, the astronomers’ model of the
structure of the universe is based on the sampling of different regions.
What I Need to Know
A team of astronomers enter the coordinates (DECs, RAs, and distances) into the
computer in 2003. They obtained an illustration showing the location and relative positions of
different galaxies. Closely every galaxy in the sample belongs to either a two-dimensional
“sheet” or a one-dimensional “thread” that is millions of light-years in length.
35
The data also revealed large spaces, millions of light-years across, that contained very
few galaxies. That is, the two-dimensional sheets were separated by vast volumes of nearly
empty space. Such a structure is reminiscent of the structure of a bunch of soap bubbles
attached to one another. Think of the galaxies as being located o the surface of intersection of
the soap bubbles, with very few galaxies being inside a given bubble. Like the galaxies, dark
matter does not seem to be present to any significant extent in the voids. It seems that galaxies
are not evenly distributed in space.
What’s New
Activity 8.5.1. Think Pair-Share
With your partner, discuss the following and write your answer on the spaces provided
below.
1. Into what is the universe is expanding?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
2. Is universe expanding into something?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
What Is It
For a long time, astronomers wrestled with the basic questions about the size and age
of the universe. Does the universe go on endlessly, or does it have an edge somewhere? How
does it existed? In 1929, an astronomer at Caltech, Edwin Hubble made a critical discovery
that soon led to scientific answers for these questions. He discovered that the universe is
expanding.
It was difficult to imagine what an infinite universe might look like as the ancient
Greeks recognized. They also wondered that if the universe were finite, where would your hand
go if you stuck out your hand at the edge? These two problems of the Greeks with the universe
is represented by a paradox - the universe had to be either finite or infinite.
Another paradox began to puzzle astronomers after the rise of modern astronomy. In
the early 1800s, Heinrich Olbers, German astronomer, argued that the universe must be finite.
If the Universe were infinite and contained, if you looked in any particular direction, your lineof-sight would eventually fall on the surface of a star. Though the apparent size of a star in the
sky becomes smaller as the distance to the star increases, the brightness of this smaller surface
remains a constant. Therefore, the whole surface of the night sky should be as bright as a star
if the Universe were infinite,. Apparently, there are dark areas in the sky, so the universe must
be finite.
However, when Isaac Newton found out about the law of gravity, he thought and
realized that gravity will always be attractive. All of the objects in the universe will be attracted
to another object. And so, if the universe turns out to be finite, the attractive force which is the
gravity may have caused the entire universe to collapse in itself. Throughout the centuries, this
has not happened which lead the astronomers with a living paradox.
As Einstein made his own theory of gravity which is included in his General Theory of
Relativity, he had the same results and problem as what Newton had. The equations he
formulated says that the universe must be expanding or collapsing, but he has a thought that
the universe might be static. This was due to the constant term in his original solution which is
called the cosmological constant. This constant cancels out the effects of gravity at very high
scales which will lead us to having a static universe. This cosmological constant soon turned
out to be Einstein’s great mistake when Hubble discovered that our universe was expanding.
In those times, large telescopes were built that were able to measure the spectra with
higher accuracy. These new data gathered has been the key for the astronomers to understand
those nebulous formations that they were studying. In between the years 1912 to 1922, an
astronomer named Vesto Slipher in Arizona discovered that these spectra of lights from these
nebulous formations were shifted to longer wavelengths or in other terms, redshifted.
Sometime later, other astronomers define that these nebulous formations were called galaxies.
Some physicist and mathematicians who worked on Einstein’s theory of gravity found
out that the equations had some formulas that described the expanding of the universe. In the
solutions, the light from a distant object would be shifted to longer wavelengths as it travels
through the expanding universe. The redshift will increase in proportion to the distance to the
object.
In 1929 Edwin Hubble, worked at the Carnegie Observatories in
Pasadena, California, measured the redshifts of a number of distant
galaxies. He also measured their relative distances by measuring the
apparent brightness of a class of variable stars called Cepheids in each of
the galaxy. When he plotted redshift against relative distance, he found
out that the redshift of distant galaxies increased as a linear function of
their distance. The only explanation deduced for this observation is that
the universe was expanding.
Edwin Hubble
Once scientists understood that the universe was expanding, they immediately realized
that the universe would have been smaller in the past. At some point in the past, the entire
universe would have been a single point of entity. This point, later called the big bang, was the
beginning of the universe in its entirety as we understand it today.
The expanding universe is finite in terms of both time and space. The reason that the
universe did not collapse, as Newton's and Einstein's equations said it might be, is that it had
been expanding from the time it was created. The universe is in a constant state of change and
evolution. The expanding universe, which is the idea based on modern physics, put out the
paradoxes that troubled many astronomers from ancient times until the early 20th Century.
The expanding universe is somewhat related to the expanding dough in a loaf of a
raisin bread (See figure below). The raisins (galaxies)are carried along with the dough (space)
as it expands. The number shows that the farther the observer “raisin”, the faster the former is
moving.
Figure 5.1 Analogy of the Expanding Universe
Let us use the baking of a loaf of raisin bread (Figure 5.1). Imagine all of the raisins
represent the galaxies and the dough will be the space. When the loaf bakes and expands, the
raisin remains the same size but moves away from another raisin. No matter which raisin an
observer might be “riding”, the other raisins would move away. The greater the initial distance
of a specific raisin was from an observer’s raisin, the faster and farther the observed raisin
would move (study Fig. 5.1). Note that the raisins which represents the “galaxies” stay the
same size, but the expansion of the dough (space) carries them. Essentially, the raisins behave
according with Hubble’s law.
How Old Is the Universe?
Astronomers estimated that the Big Bang happened between 12 and 14 billion years
ago. To put this in a perspective, the Solar System is about 4.5 billion years old and humans
have only existed as a genus for only a few million years. Astronomers estimate the age of our
universe in two ways: 1) by looking and examining for the oldest stars; and 2) by measuring
the rate at which the universe expands and extrapolating back to the Big Bang; just like those
detectives which can trace the origin of a bullet from the holes in a wall.
The expansion or contraction of the universe will depend on the containments and the
events in the past. The expansion will slow or even become a contraction given with enough
matter. The Big Bang model was an outcome of Einstein's General Relativity which is applied
homogeneous universe. However, in 1917, the thought that the universe was expanding was an
absurd one, so Einstein invented this so called cosmological constant as a term in his General
Relativity theory which allows for a static universe.
In 1929, Edwin Hubble announced his study about other galaxies which showed that
they were moving away from us with a speed proportional to their distance from us. The more
distant the galaxy, the faster it is to move away from us. The universe was really expanding,
just as General Relativity originally predicted! Hubble observed that the light from a given
galaxy was shifted away toward the red end of the light spectra the further that galaxy was from
our galaxy.
The Hubble's expansion law is important in specific form:
the speed of recession is proportional to distance. Hubble
stated this idea in an equation - distance/time per
megaparsec. A megaparsec is a truly big distance (3.26
million light-years). The expanding raisin bread model at
left shows why this proportion law is important. If every part
of the bread expands by the same amount in a given interval
of time, then the raisins would recede from each other with
exactly a Hubble type expansion law. In a given time
interval, a adjacent raisin would move relatively slight, but a
distant raisin would move relatively farther which results in
a same behavior with the other raisin in the loaf. Thus, the
Hubble law is just what one would expect for
a homogeneous expanding universe, as predicted by the Big
Bang theory. Furthermore, no raisin, or galaxy, occupies a
special place in this universe - unless you get too close to the
edge of the loaf where the analogy breaks down. Besides,
dark energy drives the universe towards increasing rates of
expansion. The Hubble Constant (in units of kilometers per
second per Megaparsec, or just per second) is the current rate
of expansion.
Hubble found that the universe was not static, but rather was expanding!
Astronomers can use a simple technique in determining the age of the universe by using
Hubble’s law (See Fig. 5.4) The slope of the graph shows the assumed constant rate at which
the universe is expanding. Astronomers now, can calculate the rate at which the universe is
expanding, and the result of that calculation is the age of the universe.
39
Figure 5.4 Hubble’s Law- This graph shows the relationship between how fast a cluster
of galaxies is moving away ( it’s recessional velocity) and its distance from the Milky Way.
If the slope of the line is H (the Hubble constant), then the age of the universe is
Age of the universe (in years) = 9.78 x 1011
H
where;
H is the Hubble constant (currently estimated to be 71 km/second/Mpc)
The number 9.78 x 1011 is a conversion factor for the time and distance units used in
the problem. The best estimate of the constant H is about 71 km/s/Mpc ( 1 Mpc = 1 megaparsec, 1 million parsecs). This calculation gives abut 13.8 billion years for the age of the
universe.
Astronomers agreed that our universe is expanding. Does the universe expand forever?
Recent evidence strongly indicates that we live what we call a flat universe that continues to
expand with time. Contrary to those ideas that gravity will slow down the expansion, recent
findings have confirmed that the expansion of the universe is actually accelerating. The
acceleration is thought to be due to the repulsive effect of an enigmatic dark energy that seems
to make up 68% of the mass-energy of the universe (E=mc2). The remaining mass energy is
about 5% ordinary matter in 27% dark matter.
The Big Bang
If the galaxies are moving away from one another at the present time, the galaxies must
have been closer to one another in the past. That is, the universe must have been more
compressed. Carrying this idea to each logical conclusion, most astronomers think that the
universe began in a small, hot, dense state, the rapid expansion of which is called the Big Bang.
The Big Bang hypothesis was first proposed in 1927 by Georges Lemaitre, a Belgian
catholic priest and cosmologist. Since then, scientist have focused great efforts on
investigating the Big Bang model. Our knowledge of the structure of the universe and of
subatomic particles is able take us back to within 10-43 second of the Big Bang. Before that
time, the universe also compressed and opaque that our present understanding of the laws of
relativity and quantum mechanics is inadequate.
When the universe was 30 minutes old, it had cold so much that nuclear reaction
ceased; the matter in the universe consisted, by mass, of about 25 % helium nuclei and 75 %
hydrogen nuclei. By the time the universe was about 400, 000 years old, it was cool enough
for the helium and hydrogen nuclei to capture electrons and become neutral atoms. Photons
were now able to move freely through space, and matter was able to be influenced by gravity
and begin forming galaxies and stars.
What’s More
Activity 8.5.2. The Expanding Universe- Galaxies
Follow the step-by-step instructions.
1, take a round balloon and draw on it six more galaxies, each about 5 mm across. Make your
galaxies roughly evenly spaced around the balloon.
2. Choose any one of the galaxies, and mark it “ A” so that you remember which it is. Make a
mental note of the distances from this galaxy to its nearest neighbors.
3. The balloon represents Space itself. Blow up the balloon to represent the expansion of
space.
4. Again, check the distances from galaxy A you selected to its nearest neighbors.
5. Answer the following questions( in complete sentences):
a. Sketch the balloon with its galaxies before and after you blew it up. Observe and record
your observation.
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
b. If people living somewhere in galaxy A. observe the motion of their neighbor galaxies,
what will they notice? Why might they think their own galaxy is the center of the universe?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
c. Would people in a different galaxy observe the same over all effect, or something
different?
________________________________________________________________________
________________________________________________________________________
______________________________________________________________________
d. As time goes by, the real universe behaves rather than like this balloon. What do you think
our astronomers must have observed about the motion of our neighboring galaxies?
_________________________________________________________________________
_________________________________________________________________________
What I Have Learned
Activity 8.5.3 Test Your Analysis- Calculating the age of the Universe
In a clean sheet of paper, calculate the age of the universe if the constant rate of expansion is
71 km/s/Mpc. Show your solution.
What I Can Do?
Activity 8.5.4. Sketch Me Up!
Using 1/8 sized illustration board, draw an expanding universe. Make it colorful and
presentable.
42
SUMMARY
1. Black Hole. A region of spacetime where gravity is so strong that nothing—no
particles or even electromagnetic radiation such as light—can escape from it.
2. First Postulate of special relativity. At any frame of reference, all laws of physics
are the similar.
3. Gravitational Lensing. The bending and focusing of light and especially the
formation of multiple images of a more distant object by a celestial object acting
as a gravitational lens.
4. Length of Contraction. A moving object would be shorter in length.as observe by
the observer at rest that is relative to the moving object.
5. Mass Increase. The rest energy and total energy of the body are equivalent to the
rest mass (an invariant quantity which is the same for all observers in all reference
frames) and relativistic mass (dependent on the velocity of the observer),
respectively.
6. Maxwell Theory. The light in a vacuum travel at a constant speed regardless of the
motion of source or the observer.
7. Newtonian Mechanics. The speed of light depends on the motion of the observer
and the light source.
8. Precession. The change in the orientation of the rotational axis of a rotating body.
9. Second Postulate special relativity. For all reference frames, the speed of light (c)
is the same no matter what their relative speed is.
10. Simultaneity. Whether two spatially separated events not absolute occur at the
same time but depends on the observer's reference frame.
11. Time Dilation. An observer who is in relative motion with respect to that clock
determined the “slowing down” of a clock.
43
Assessment: (Post-Test)
Multiple Choice. Select the letter of the best answer from among the given choices.
1. Einstein theory of special relativity is based on what two postulates? Choose all that apply.
I. The laws of physics are the same in all inertial frames of reference moving with
constant velocity relative to one another.
II. The laws of physics application change based on the condition of the observer.
III. The speed of light is constant in all inertial frame of reference.
IV. The speed of light depends on the speed of the observer.
A. I only
C. II and IV
B. I and II
D. I and III
2. Which of the following describes the speed of light according to Newtonian mechanics?
A. The light speed depends on the speed of the observer.
B. The speed of light is constant.
C. The speed of light depends on its source.
D. The speed of light is infinite
3. Which of the following correctly describes the statement: The speed of light is constant?
A. The statement is sometimes true.
C. The statement is never true.
B. The statement is always true
D. The statement is sometimes false.
4. woman on the ground sees a rocket moving past her at 99% the speed of light. Compared
to when the rocket is at rest, the women measures the length as being:
A. longer
B. shorter
C. the same length
D. all of the above
5. Starship "Alpha" travels at 0.9c past an identical starship "Beta," which is at rest. Both a
cabin boy on the "Alpha" and a cook on the "Beta" measure the time required for the other
ship to pass by their respective windows. Who measures the longer time?
A. Both measure the same time.
B. The cabin boy
C. The cook
D. The measured times cannot be compared
6. Two identical clocks are made. One is placed in interstellar space, and the other is placed on
the surface of a massive planet. Which runs faster?
A. Both clocks will run at the same rate.
B. The planet clock
C. The space clock
D. None of the above
7. Which of the following describes the first postulate of General Relativity Theory?
A. Inertial and gravitational masses have different values
B. Inertial and gravitational masses are identical
C. Inertial and gravitational masses are inversely proportional
D. Both inertial and gravitation masses are zero
8. Which of the following phenomena are consequences of the General Theory of Relativity?
A. Black hole
B. Precession of Mercury’s orbit
C. The existence of gravitational lenses
D. Weightlessness
9. Why is black hole black?
A. All colors are absorbed in that hole.
B. All colors are reflected from the hole
C. No light can leave this hole
D. No light is absorbed by the hole
References
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https://www.facebook.com/notes/physical-science/91-theory-of-specialrelativity/3390893954260139/
Dangel, Mercygel, Gorre, Dyna F, Udarbe, Leneth. DepEd Shared Options Learning
Activities.
Egdall, Ira Mark, “Teaching Special Relativity to Lay Students”, accessed last June 15,
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2020,
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“Postulates of Special Relativity’, accessed last May 22, 2020,
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OSTULATE.html
“Relativity”, accessed last June 16, 2020,
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https://aether.lbl.gov/www/classes/p139/exp/gedanken.html
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2020,
Schaltegger, Joris, “How does special relativity resolve the conflict between Newtonian
mechanics and Maxwell’s electromagnetic theory?”, accessed last June 9, 2020,
https://www.quora.com/How-does-special-relativity-resolve-the-conflictbetween-Newtonian-mechanics-and-Maxwell-s-electromagnetic-theory
Smith, James H, Introduction to Special Relativity, accessed last June 16, 2020,
https://www.perlego.com/book/109844/introduction-to-special-relativity-pdf
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