Download Lecture 2 Our Place in the Universe (Cont`d)

Astronomy 110 –1
Lecture 2
Our Place in the
Universe
(Cont’d)
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A few useful mathematical
skills
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Powers of ten
103 = 10 x 10 x 10 = 1000
102 = 10 x 10 = 100
101 = 10
100 = 1
10-1 = 1/10 = 0.1
10-2 = 1/10 x 1/10 = 0.01
10-3 = 1/10 x 1/10 x 1/10 = 0.001
Then:
300 = 3 x 100 = 3 x 102
2,500 = 2.5 x 1000 = 2.5 x 103
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Multiplying & dividing
101 x 101 = 100 = 102
101 x 102 = 10 x 100 = 1000 = 103
102 x 102 = 100 x 100 = 10000 = 104
 When multiplying two powers of ten, add the exponents
1000 ÷ 100 = 103 ÷ 102 = 10 = 101
10 ÷ 10 = 101 ÷ 101 = 1 = 100
10 ÷ 100 = 101 ÷ 102 = 1/10 = 10-1
 When dividing, subtract exponent of divisor from exponent
of numerator
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Powers and roots
(104)3 = 104 x 104 x 104 = 1012
 Rule of thumb: when raising to a power, multiply
exponents
What about √(104)?
√(104) = 102
 taking roots is the same as raising to a fractional
power, in this case 1/2 power:
√(104) = (104)1/2 = 102
√ is the same as raising to 1/2 power
3√ is the same as raising to 1/3 power
4√ is the same as raising to 1/4 power
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Summary
To multiply powers of ten, add exponents:
10n x 10m = 10(n+m)
To divide powers of ten, subtract exponents:
10n ÷ 10m = 10(n-m)
To raise powers of ten to other powers, multiply
exponents:
(10n)m = 10(nxm)
where m can be fractional for roots.
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Scientific notation
All numbers should be expressed as a number between 1
and 10 times whatever power of ten is required
Radius of Earth = 6,400 km = 6.4x103 km.
Galaxy diameter = 1,000,000,000,000,000,000,000 m = 1021 m.
Size of H atom = 0.000,000,000,05 m =5x10-11 m.
Rule of thumb:
• number of places decimal is moved to the left is the positive power of
ten;
• number of places decimal is moved to the right is the negative power
of ten.
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Basic units used in Astronomy
• astronomical unit (AU):
average distance between Earth and Sun
= 150 million km or 1.5 108 km
(about 108 mi or 100 million miles)
[Technically = semi-major axis of Earth’s orbit
around Sun]
• light year:
distance that light travels in 1 year
= 9.46 1012 km (about 6 1012 miles,
or 6 trillion miles)
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Calculating the distance equivalent of a
light year
[distance that light travels in 1 year]
This distance is fixed because light in a vacuum always
travels at the same speed = 300,000 km/s or 3 105
km/s (1.86 105 mi/s)
Calculation:
distance = velocity x time
1 light year = speed of light x 1 year
= 3 105 km/s x 1 yr x 365 day/yr x 24 hr/1 day x 60 min/1 hr x
60 sec/1 min
= 9.46 1012 km
[do exercise by rounding off numbers]
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Working with units
A number without a unit has no physical meaning: For
example, a salary of 1,000,000 is meaningless without
units
You cannot add or subtract numbers unless they have
the same units.
You can multiply units: area is feet x feet = (feet)2,
or, volume is meter x meter x meter = (meter)3.
You can divide units: speed = miles ÷ time = miles per
hour
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Converting Units
1. Converting speed of light from km/s to m/s
We know that 1 km =1000 m
So:
300,000 km/s = 300,000 km/s x 1000 m/1km = 3 108 m/s
2. Converting from m/s to km/hr
1 m = 10-3 km
1 hr = 60 min x 60 s = 3600 s = 3.6 103 s
Or 1 s = 1 ÷ 3.6 103 hr ≅ 2.8 10-4 hr
So:
1 m/s = 1 m x 10-3 km/m ÷ ( 1s x 2.8 10-4 hr/s) = 3.6 km/hr
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Other examples
How long is 1 light second?
1 light second = distance traveled by light in 1 second
distance = speed x time
speed of light = 3 105 km/s
1 light second = 3 105 km/s x 1s = 3 105 km
In units of miles:
1 mi = 1.6 km
1 light second = 3 105 km x 1 mi/1.6 km ≅ 2 105 mi
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Chapter 1 (Cont’d)
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How did we come to be?
Telescopic observations
of distant galaxies show
that the entire universe
is expanding
From observed rate, we
estimate that it occurred
about 14 billion years
ago
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Here is how we think
things happened …
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1. The Big Bang
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2. Stellar lives and galactic
recycling
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3. Stars manufacture the elements of
Earth and Life
Massive stars
explode when
they die,
scattering the
elements they
have produced
into space
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Stars are born in
clouds of gas and
dust; planets may
form in surrounding
disks
Stars shine with energy released
by nuclear fusion, which ultimately
manufactures all elements
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heavier than hydrogen and helium
4. Earth and Life
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How can we know what the universe
was like in the past?
• Light travels at a finite speed (300,000 km/s).
Destination
Light travel time
Moon
1 second
Sun
8 minutes
Sirius
8 years
Andromeda Galaxy
2.5 million years
• Thus, we see objects as they were in the past:
The farther away we look in distance,
the further back we look in time.
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Quick study exercise:
• Try to find the distance to these objects
in km using scientific notation
Remember:
distance = speed x time
speed of light = 3 105 km/s
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Example:
This photo shows the Andromeda Galaxy as it looked about
1/2 million years ago.
Question: When will we be able to see what it looks like now?
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M31, the Great Galaxy
in Andromeda
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• At great distances, we see objects as they were
when the universe was much younger.
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Thought Question:
Assume the universe is 14 billion years old.
Why can’t we see a galaxy 15 billion lightyears away?
A. Because no galaxies exist at such a great
distance.
B. Galaxies may exist at that distance, but their
light would be too faint for our telescopes to
see.
C. Because looking 15 billion light-years away
means looking to a time before the universe
existed.
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Thought Question:
Assume the universe is 14 billion years old.
Why can’t we see a galaxy 15 billion lightyears away?
A. Because no galaxies exist at such a great
distance.
B. Galaxies may exist at that distance, but their
light would be too faint for our telescopes to
see.
C. Because looking 15 billion light-years
away means looking to a time before the
universe existed.
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What have we learned?
• What is our place in the universe?
— Earth is part of the solar system, which is in
the Milky Way Galaxy, which is a member
of the Local Group of galaxies in the Local
Supercluster.
• How did we come to be?
— The matter in our bodies came from the Big
Bang, which produced hydrogen and helium.
— All other elements were constructed from H
and He in stars and then recycled into new
star systems, including our solar system.
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What have we learned?
• How can we know what the universe was
like in the past?
— When we look to great distances, we are
seeing events that happened long ago
because light travels at a finite speed.
• Can we see the entire universe?
— No. The observable portion of the universe is
about 14 billion light-years in radius because
the universe is about 14 billion years old.
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1.2 The Scale of the Universe
Our goals for learning:
•
•
•
•
•
How big is Earth compared to our solar system?
How far away are the stars?
How big is the Milky Way Galaxy?
How big is the universe?
How do our lifetimes compare to the age of the
universe?
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How big is Earth compared to our solar system?
Let’s reduce the size of the solar system by a factor of
10 billion; the Sun is now the size of a large grapefruit
(14 cm diameter).
How big is Earth on this scale?
A.
B.
C.
D.
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an atom
a tip of a ball point pen
a marble
a golf ball
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Let’s reduce the size of the solar system by a factor of
10 billion; the Sun is now the size of a large grapefruit
(14 cm diameter).
How big is Earth on this scale?
A.
B.
C.
D.
an atom
a tip of a ball point pen
a marble
a golf ball
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The scale of the solar system
• On a 1-to-10 billion
scale:
— Sun is the size
of a large
grapefruit (14
centimeters).
— Earth is the size
of a tip of a ball
point pen, 15
meters away.
Relative Distance of the Nearest Star
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How far away are the stars?
On our 1-to-10 billion scale, it’s just a few minutes’
walk to Pluto.
How far would you have to walk to reach Alpha
Centauri?
A. 1 mile
B. 10 miles
C. 100 miles
D. the distance across the United States (2500
miles)
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How far away are the stars?
On our 1-to-10 billion scale, it’s just a few minutes’
walk to Pluto.
How far would you have to walk to reach Alpha
Centauri?
A. 1 mile
B. 10 miles
C. 100 miles
D. the distance across the United States (2500
miles)
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Relative Distance of the Nearest Star
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How big is the Milky Way Galaxy?
The Milky
Way has
about 100
billion stars.
On the same
10 billion-to1 scale…
The Size of the Milky Way
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Thought Question
Suppose you tried to count the more than 100
billion stars in our galaxy, at a rate of one per
second…
How long would it take you?
A. a few weeks
B. a few months
C. a few years
D. a few thousand years
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Thought Question
Suppose you tried to count the more than 100
billion stars in our galaxy, at a rate of one per
second…
How long would it take you?
A. a few weeks
B. a few months
C. a few years
D. a few thousand years
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How big is the universe?
• The Milky Way is one of about 100 billion galaxies.
• 1011 stars/galaxy × 1011 galaxies = 1022 stars
It has as many stars as grains of (dry) sand on all Earth’s beaches.
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• Now let’s step through the universe in powers of 10:
Zooming Out or Zooming In 26 Orders of Magnitude
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How do our lifetimes compare to the age of
the universe?
The Cosmic Calendar: A scale on which we
compress the history of the universe into 1 year
Jan 1: Big Bang
February: Milky way forms
September: Earth forms
Fig. 1.10
 On this scale: Human civilization is just a few
seconds old, and a human lifetime lasts only a
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fraction of a second.
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What have we learned?
• How big is the Earth compared to our solar system?
— On a scale of 1-to-10 billion, the Sun is about the size of a
grapefruit. The Earth is the size of a tip of a ball point pen
about 15 m away. The distances between planets are huge
compared to their sizes.
• How far away are the stars?
— On the same scale, the stars are thousands of kilometers
away.
• How big is the Milky Way Galaxy?
— It would take more than 3000 years to count the stars in the
Milky Way Galaxy at a rate of one per second. The Milky
Way Galaxy is about 100,000 light-years across.
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What have we learned?
• How big is the universe?
— 100 billion galaxies in the observable universe
— 14 billion light-years in radius
— As many stars as grains of sand on Earth’s beaches
• How do our lifetimes compare to the age of the
universe?
— On a cosmic calendar that compresses the history of
the universe into 1 year, human civilization is just a
few seconds old, and a human lifetime is a fraction of
a second.
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1.3 Spaceship Earth
Our goals for learning:
• How is Earth moving in our solar system?
• How is our solar system moving in the Milky
Way Galaxy?
• How do galaxies move within the universe?
• Are we ever sitting still?
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Terms Relating to Motion
• rotation
– spinning of an object around its axis
• orbit (revolution)
– orbital motion of one object around another
• expansion of the universe
– increase in average distance between
galaxies as time progresses
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How is Earth moving in our solar system?
• Contrary to our perception, we are not “sitting still.”
• We are moving with the Earth in several ways, and at
surprisingly fast speeds.
Earth rotates around its
axis once every day.
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Earth orbits the Sun (revolves) once every year…
• at an average distance of 1 AU ≈ 150 million km.
• with Earth’s axis tilted by 23.5º (pointing to Polaris).
• and rotates in the same direction it orbits, counterclockwise as viewed from above the North Pole.
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Our Sun moves randomly relative to the other stars
in the local solar neighborhood…
• at typical relative speeds of more than 70,000 km/hr.
• but stars are so far away that we cannot easily notice
their motion.
… and it orbits the galaxy every 230 million years.
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More detailed study of the Milky Way’s rotation
reveals one of the greatest mysteries in astronomy…
Most of Milky Way’s
light comes from the
disk and the bulge …
…. but most of the
mass is in its halo
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How do galaxies move within the universe?
Galaxies are carried
along with the
expansion of the
universe.
But how did Hubble
figure out that the
universe is
expanding?
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• raisin_cake.htm
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Hubble discovered that…
• all galaxies outside our Local Group are
moving away from us.
• the more distant the galaxy, the faster it is
racing away.
Conclusion: We live in an expanding universe.
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Are we ever sitting still?
Earth rotates on axis: > 1,000 km/hr
Earth orbits Sun: > 100,000 km/hr
Solar system moves among stars: ~ 70,000 km/hr
Milky Way rotates: ~
800,000 km/hr,.carrying
the Sun around its
center once every 230
million years
Milky Way moves relative to others
in the Local Group (300,000 km/hr
towards Andromeda)
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Universe
expands
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What have we learned?
• How is Earth moving in our solar system?
— It rotates on its axis once a day and orbits the
Sun at a distance of 1 AU = 150 million km.
• How is our solar system moving in the Milky
Way Galaxy?
— Stars in the Local Neighborhood move
randomly relative to one another and orbit
the center of the Milky Way in about 230
million years.
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What have we learned?
• How do galaxies move within the universe?
— All galaxies beyond the Local Group are
moving away from us with expansion of the
universe: the more distant they are, the faster
they’re moving.
• Are we ever sitting still?
— No!
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