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Chapter 3
The Universal Context of Life
Foundations
Angles
1 circle = 360 degrees (º), 1º = 60 arc minutes (‘), 1’ = 60 arc seconds (“)
Angles are subdivided just like time!
Average time to run a marathon:
4 hours 32 minutes 8 seconds
Separation between two stars in the sky:
4 degrees 32 arc minutes 8 arc seconds(4º 32’ 8”)
Angular Separation Angular and Linear Sizes
Sun and Moon have same angular size (½º) but different linear sizes!
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In astronomy we have to deal with both very large and very small numbers….
Distance to nearest star
40000000000000000 meters
Size of a hydrogen atom
0.0000000001 meters
Scientific ‘Powers of 10’ Notation
10y
10 is called the base
y is called the exponent – it tells us how many times to multiply 10 by itself
101 = 10
102 = 10 x 10 = 100
103 = 10 x 10 x 10 = 1,000
104 = 10 x 10 x 10 x 10 = 10,000
etc.
At the end of a large number is a decimal point, even though it is not normally written:
40000000000000000.
Converting Large Numbers into Scientific Notation
Move decimal point y places to the left:
Large # → # between 1-10 x 10y
40000000000000000.
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4 x 1016
Negative Exponents
10-y
10-1 = 1 / 10 = 0.1
10-2 = 1 / 10 x 10 = 0.01
10-3 = 1 / 10 x 10 x 10 = 0.001
10-4 = 1 / 10 x 10 x 10 x 10 = 0.0001
etc.
Converting Small Numbers into Scientific Notation
Move decimal point y places to the right:
Small # → # between 1-10 x 10-y
0.0000000001
1 x 10-10
Write the following numbers in scientific notation:
a. 55000
b. 480
c. 0.000005
d. 0.00014
e. 0.00785
f. 670000
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Converting from Scientific Notation to Standard Notation
Move decimal point in opposite direction!
Fill spaces with zeros!
1.234 x 108
123400000
Write the following as standard numbers:
a. 1.2 x 104
b. 8.25 x 10-2
c. 4 x 106
d. 5 x 10-3
The Scale of the Universe
The Universe is huge!
Direct measurement virtually impossible!
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How can we know anything about the Universe when we can’t make
direct measurements?
By collecting and analyzing the information carried across the
Universe by light!
light = electromagnetic (EM) radiation
Not just visible!
Very fast – travels at 3 x 108 m/s
Can travel through a vacuum (a volume of space containing no matter) unlike
sound
Astronomical distances are so huge normal units not meaningful!
The Solar System The Solar System
1 Astronomical Unit (AU) = average Sun-Earth distance
= 150 million km = 1.5 x 108 km
Sun-Mercury = 5.79 x 107 km = 0.39 AU
Sun-Neptune = 4.5 x 109 km = 30 AU
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The Stars – much further!
Closest star (excluding Sun) > 270,000 AU away!
The Light Year
1 light year (ly) = distance light travels in one year at 3 x 108 m/s
= 9.46 x 1012 km = 63,240 AU
Proxima Centauri – the nearest star
Distance = 3.87 x 1013 km = 4.22 ly
Light Travel Time
Light year = how many years light takes to travel from the
object
Example
Light takes 4.22 years to travel from the nearest star!
Significant delays!
Result
We see the nearest star not as it is now but how it was 4.22 years
ago!
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Important implications for communicating over interstellar
distances!
The Milky Way Galaxy
The Size of the Milky Way The Local Group
The Milky Way and its neighboring galaxies
Over 8 million light years across!
The Andromeda Galaxy
A member of the Local Group
The Virgo Supercluster
The Local Group and its neighboring clusters
Over 100 million light years across!
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The Large-scale Structure of the Universe
The most distant galaxies are billions of light years away!
Hubble Ultra Deep Field Image
The Nature of Radiation
Newton’s Experiment
Light is made of different colors!
A Rainbow Light behaves like a wave!
Interference
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Light has similar properties to water waves
Wave-like Properties of LightWavelength, λ
Visible light λ = 4-7 x 10-7 m
Units of Wavelength
1 nanometer (nm) = 10-9 m
1 Ångstrom = 10-10 m
Visible light = 400-700 nm = 4000-7000 Å
Frequency, υ
Visible light υ = 4-7 x 1014 Hz
υ = 2 Hz
υ = 12 Hz
Equation of Light
λ = c / υ or υ = c / λ
where:
λ = wavelength
υ = frequency
c = 3.00 x 108 m/s = constant
λ ↑ υ ↓ c = constant
Light also has the properties of a particle!
The Photoelectric Effect
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Wave-Particle DualityA Wavepacket (Photon)
Light carries energy!
Planck Formula
E = hυ
where:
E = energy carried
υ = frequency
h = Planck’s constant
υ ↑ E ↑
Summary
c = speed of light = constant
The Electromagnetic Spectrum
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Longer wavelengths than visible
Infrared (IR) Radiation
visible → infrared (IR) → microwaves → radio
Microwaves
visible → infrared (IR) → microwaves → radio
Radio Waves
visible → infrared (IR) → microwaves → radio
Shorter wavelengths than visible
Gamma rays ← X-rays ← Ultraviolet (UV)
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X-Rays
Gamma rays ← X-rays ← Ultraviolet (UV)
Gamma Rays
Gamma rays ← X-rays ← Ultraviolet (UV)
ThermonuclearExplosions
Radioactivity
The Inverse Square Law
b = 1/d2 d ↑ b ↓
All matter produces EM radiation!
Variations:
1. Amount of radiation
2. Type of radiation
Depends on temperature!
Temperature is related to atomic and molecular motion!
Temp ↑ speed ↑
Common Temperature Scales
Make temperatures meaningful!
1. Fahrenheit Scale (ºF)
2. Celsius Scale (ºC)
Not reliable! Vary with location!
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Cool Matter - temp ↓ speed ↓
Absolute zero - at -273 ºC or -460 ºF atomic and molecular motion essentially stops!
Properties of Absolute Zero1. The coldest possible temperature
2. Matter can never be cooled to absolute zero
The Kelvin Scale (K)
Temperatures measured relative to absolute zero = 0 K
There are no negative temperatures on the Kelvin scale!
Note: the unit is written K and not ºK
Objects in the Universe produce radiation over a range of wavelengths!
Spectroscopy = separate radiation into its components to produce a spectrum
Example – a prism!!
Types of Spectra
Continuous Spectrum
Range of wavelengths with no gaps or colors missing
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Emission (bright line) Spectra
Elements have unique patterns of lines!
Absorption (dark line) Spectra
Range of wavelengths with gaps or colors missing
Kirchoff’s LawsContinuous Spectrum
Hot solids or high density gases
Light Bulb Filament
A Neon Sign
Emission SpectrumHot, low density gas
Absorption SpectrumCooler gas in front of continuous source
The Sun and stars!
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Why do atoms emit (create) and absorb (destroy) radiation in
characteristic patterns?
The Structure Matter
Matter is made of atoms
Very small ~ 10-10 m = 1 Å
Chemical Elements – different kinds of atoms (~ 115 currently known)
The Periodic Table of Elements First predicted by the Ancient Greeks around 500 BC!
Only recently seen directly using electron tunneling microscopy
Atoms can be broken into smaller subatomic particles!
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Subatomic Particles
Particle Symbol
Proton p+ or p
Electron e-
Neutron n or n0
The Nuclear Model of the Atom
Atoms are mostly empty space!
If an atom were the size of a football stadium the nucleus would be about the size of a golf ball placed in the
center of the field!
The Four Fundamental Forces of Nature
1.Gravity
2.Electromagnetism
3.The Strong Nuclear Force
4.The Weak Nuclear Force
The Electrostatic Force
Force of interaction between charges
Atoms are held together by the electrostatic force of attraction
between the positive nucleus and the negative electrons!
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Problem:
If positive protons repel each other how can the nucleus stay together? Solution:
The protons and neutrons in the nucleus are held together by another
fundamental force of nature!
The Strong Nuclear Force
How do we distinguish atoms?
Atomic Number, Z = # protons in nucleus
Different elements have different Z’s
Z is placed above each element in the Periodic Table
Neutral Atoms
Contain equal numbers of protons and electrons whose charges cancel
each other out!
Z is also equal to the number of electrons!
How do we count the number of neutrons?
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Mass Number, A
Total number of protons and neutrons
The electron has a mass of 1/1800 of a proton or a neutron so it does not contribute much to the mass of an
atom and can be ignored!
Given:
Z = # of protons
A = # of protons + neutrons
Then:
# of neutrons?
Given:
Z = # of protons
A = # of protons + neutrons
Then:
# of neutrons = A - Z
Nuclear Symbols
Uniquely define each element
One way Another way
The element symbol and Z are redundant since each can be found from the other using
the Periodic Table
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Examples Hydrogen (H)
Z = 1, A = 111H or H-1
Helium (He)
Z = 2, A = 442He or He-4
Lithium (Li)
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Z = 3, A = 773Li or Li-7
How many protons, electrons and neutrons?
5224Cr
# protons = 24
# electrons = 24 (neutral atom)
# neutrons = 52 – 24 = 28
Ions
Atoms can gain or lose electrons!
X → X+ + e-
X + e- → X-
Here:
# electrons ≠ atomic number, Z
How many protons, electrons and neutrons?
5626Fe3+
# protons = 26
# electrons = 26 – 3 = 23
# neutrons = 56 – 26 = 30
How many protons, electrons and neutrons?
188O2-
# protons = 8
# electrons = 8 + 2 = 10
# neutrons = 18 – 8 = 10
If the number of protons defines the type of atom does it matter how
many neutrons there are?
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If the number of protons defines the type of atom does it matter how
many neutrons there are?
No!!!
Isotopes
Different versions of the same element
Same # protons, different # neutrons
Same Z and element symbol
Different A
Have identical chemical properties
Isotopes do not have equal abundances!
H-1 (99.9885%), H-2 (0.0115%)H-3 (radioactive)
Quantum Mechanics
Energy Levelsn ↑ E ↑
n = 1 ground staten > 1 excited states
n = principle quantum number
Energy levels are like the rungs of a ladder! Photon Emission
Electron jumps from a higher to a lower level
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Each line corresponds to a different downward jump. The larger the jump the shorter the
wavelength of the photon produced
Photon Absorption
Electron jumps from a lower to higher energy
Each line corresponds to a different upward jump. The larger the jump the shorter the wavelength of
the absorption line
A given atom emits and absorbs at exactly the same wavelengths!
Photoionization
Electron kicked out of an atom by a high-energy photon
Where do the chemical elements that matter is made
of come from?
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The History and Evolution of the Universe
The Doppler Effect
Motion of a source of radiation causes the wavelengths it emits to be shifted
Also observed with sound!
Doppler Shifts
The size of the Doppler Shift is directly proportional to the object’s radial velocity, vr (motion towards or away)
Radar Guns
Edwin Hubble(1889-1953)
100” Telescope on Mt Wilson
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Hubble measured the distances and radial velocities
of nearby galaxies
Expected to see no correlation between the two!
Instead found that nearly all galaxies were receding with velocity proportional to their
distance!
Hubble’s Law
v = H0d
∆v
∆d
slope = ∆v / ∆d = H0
Conclusion?The Universe is Expanding!
H0 is a measure of the current rate of expansion!
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2D Analogy of the Expanding UniverseUniverse = surface of expanding balloon
Galaxies = coins stuck on surface
Cosmological Expansion
Galaxy redshifts NOT caused by the motion through space, but by the
expansion of space itself!
The expansion of the Universe is a uniform expansion in all directions!
All galaxies move away from all others!
The Big Bang
Not an explosion of matter through space but the creation of space and
matter itself!
A Cosmic Fireball
The Early Universe was very hot and dense!
Matter was formed from high energy radiation as the Universe expanded and cooled
Prediction:
Leftover radiation from the early Universe should still be
detectable today as microwave radiation!
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Cosmic Microwave Background Radiation
Detected by Penzias and Wilson in 1965
Most of the Hydrogen and Helium was formed in the Big
Bang that created the Universe!
98% of the mass of all the atoms in the Universe is in the form of these two elements!
Additional helium and heavier elements are created inside
stars!
How? Example: the Sun
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Inside the Sun:
depth ↑ temp ↑
Hydrogen is ionized:
H → p+ + e-
Protons repel each other:
← p+ p+ →
At the center of the Sun temperatures reach 15 million K!
Result: the protons stick together or fuse!
Result?
This a nuclear reaction, not a chemical reaction!
Heavier nuclei from lighter nuclei!
Often called hydrogen ‘burning’
Hydrogen Fusion
Where does the energy come from?
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4 1H → 4He + energy
Expect:
mass4H = massHe
Find:
mass4H > massHe
Mass has disappeared!
Mass is converted into energy!
How much energy from how much mass?
E = mc2
m = mass
c = speed of light
Sun’s Power Output
Luminosity = LΘ = 3.9 x 1026 Watts
The Sun converts 600 million tons of matter into energy every second!
Even at this rate it has enough fuel to last 10 billion years!
Nuclear Fission
Large unstable nuclei break into smaller nuclei releasing energy
235U → 143Cs + 90Rb + 3n + energy
Used in nuclear reactors
Other fusion reactions
Helium Fusion
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During their lives, stars fuse heavy elements from lighter
elements
When they die, they eject their outer layers containing heavy
elements into space
Some stars like our Sun die quietly as they eject their outer layers into space
Other stars die…. violently in supernova explosions!!!
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producing supernova remnants
The heavy elements ejected collect into interstellar clouds
from which new stars and planets and even life can form!
We are made of stardust!
Interstellar RecyclingInterstellar Recycling
Evidence:
Stellar evolution models correctly
predict the relative
abundances of elements found in
the universe
How did the Sun and the planets form?
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The Solar SystemStudies of meteorites indicate
the solar system is approximately 4.6 billion years
old
Recent measurements of distant galaxies indicate that
the universe is about 13.7 billion years old
This is much older than the age of the solar system!
solar system = Sun + 8 planets + satellites + asteroids + comets
Pluto is no longer considered a planet!
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
(Pluto)
Order of the Planets
One mnemonic to help you remember this!
MyVery
EroticMate
JoyfullySatisfiesUnusualNeeds
(Passionately)
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Planetary Orbits
Characteristics of Planetary Orbits
Low eccentricity ellipses (except Mer, Mar)
Revolve about Sun in same direction
Revolve about Sun in same plane
Rotate in same direction as revolution (except Ven, Ura)
Main difference between stars and planets
Stars generate their own light why planets reflect light from the Sun!
Chemical compositions are determined from the spectroscopy of reflected sunlight from
a body
By comparing the spectrum of the object with the spectrum of materials in a lab we can
determine the chemical composition of surface or atmosphere of a planet or
moon!
The Spectrum of Europa
Europa has an icy surface!
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There are two kinds of planet!
Terrestrial Planets
‘Earth-like’
Small, rocky, close to the Sun (< 1.5
AU)
High mean densities
Mercury, Venus, Earth and Mars
Jovian Planets
‘Jupiter-like’
Large, gaseous, far from Sun (> 5 AU)
Low mean densities
Jupiter, Saturn, Uranus, Neptune
The Terrestrial and Jovian Families
Planetary Satellites (Moons)There are 169 currently known (Sept 2007)
All have except Mercury and Venus
Terrestrial have few (2 or less)
Jovian have many (13 or more)
7 ‘giant’ satellites (size similar to Mercury)
The Seven ‘Giant’ Satellites of the Solar System
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Asteroids – rocky debris Comets – icy debris
Location of Asteroids and Comets
The Nebular (Condensation) Theory for the Formation of
the Solar System
An interstellar cloud
Interstellar clouds are normally stable!
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is balanced by the outward force of pressure!
To form a star and planetary system we need the cloud to become unstable:
gravity > pressure
causing the cloud to collapse under gravity
size ↓ temp ↑ spin ↑
This can happen when clouds are compressed externally!
This can be caused by a nearby supernova explosion!
The Conservation of Angular Momentum
As a rotating object gets smaller it spins faster!
Similarly, as a cloud collapses, it
spins faster forming a rotating
protoplanetary disk (proplyd) around a central protostar
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Particles of gas and dust stick together within the disk
A process called accretion…..
Leading to the formation…. of a family of planets….
The Building Blocks of Planets
Condensation TemperatureMaximum temperature that a given material
will stick together (condense):
iron > rock > H compounds > gases
high low
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The type of planet formed depends on the distance from the center of the disk…
This explains why our own solar system has inner rocky Terrestrial planets and outer
gaseous Jovian planets…
Also explains the observed characteristics of Planetary
Orbits!Low eccentricity ellipses
Revolve about Sun in same direction
Revolve about Sun in same plane
Rotate in same direction as revolution
Star and planet forming has occurred throughout the Universe’s history and
continues today
The Orion Nebula
A star formation region 1500 ly away
Protostars and Protoplanety disks are seen inside the Orion Nebula!
Infrared (IR) Image
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Disks of gas and dust are seen around other, mature solar-type stars!
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