Chapter 3 The Universal Context of Life Foundations Angles 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 ) 1 circle = 360 degrees (º), 1º = 60 arc minutes ( ), 1 = 60 arc seconds ( ) Angular Separation Angular and Linear Sizes Sun and Moon have same angular size (½º) but different linear sizes! 1
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 10 y 10 is called the base y is called the exponent it tells us how many times to multiply 10 by itself 10 1 = 10 10 2 = 10 x 10 = 100 10 3 = 10 x 10 x 10 = 1,000 10 4 = 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: 40000000000000000. Large # # between 1-10 x 10 y 2
Negative Exponents 10 -y 4 x 10 16 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: 0.0000000001 Small # # between 1-10 x 10 -y 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 3
Converting from Scientific Notation to Standard Notation Move decimal point in opposite direction! Fill spaces with zeros! 1.234 x 10 8 Write the following as standard numbers: 123400000 a. 1.2 x 10 4 b. 8.25 x 10-2 c. 4 x 10 6 d. 5 x 10-3 The Universe is huge! The Scale of the Universe Direct measurement virtually impossible! 4
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 10 8 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 10 8 km Sun-Mercury = 5.79 x 10 7 km = 0.39 AU Sun-Neptune = 4.5 x 10 9 km = 30 AU 5
The Stars much further! The Light Year 1 light year (ly) = distance light travels in one year at 3 x 10 8 m/s = 9.46 x 10 12 km = 63,240 AU Closest star (excluding Sun) > 270,000 AU away! Proxima Centauri the nearest star Light Travel Time Light year = how many years light takes to travel from the object Distance = 3.87 x 10 13 km = 4.22 ly 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! 6
The Milky Way Galaxy Important implications for communicating over interstellar distances! 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 The Virgo Supercluster A member of the Local Group The Local Group and its neighboring clusters Over 100 million light years across! 7
The Large-scale Structure of the Universe The most distant galaxies are billions of light years away! Hubble Ultra Deep Field Image Newton s Experiment The Nature of Radiation Light is made of different colors! A Rainbow Light behaves like a wave! Interference 8
Light has similar properties to water waves Wave-like Properties of Light Wavelength, 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 υ = 12 Hz υ = 2 Hz Visible light υ = 4-7 x 10 14 Hz Equation of Light λ = c / υ or υ = c / λ where: λ = wavelength υ = frequency c = 3.00 x 10 8 m/s = constant λ υ c = constant Light also has the properties of a particle! The Photoelectric Effect 9
Wave-Particle Duality A Wavepacket (Photon) Planck Formula Light carries energy! E = hυ where: E = energy carried υ = frequency h = Planck s constant υ E Summary The Electromagnetic Spectrum c = speed of light = constant 10
Infrared (IR) Radiation Longer wavelengths than visible visible infrared (IR) microwaves radio Microwaves Radio Waves visible infrared (IR) microwaves radio visible infrared (IR) microwaves radio Shorter wavelengths than visible Gamma rays X-rays Ultraviolet (UV) 11
X-Rays Gamma Rays Thermonuclear Explosions Radioactivity Gamma rays X-rays Ultraviolet (UV) Gamma rays X-rays Ultraviolet (UV) The Inverse Square Law All matter produces EM radiation! Variations: 1. Amount of radiation 2. Type of radiation Depends on temperature! b = 1/d 2 d b Temperature is related to atomic and molecular motion! Common Temperature Scales Make temperatures meaningful! 1. Fahrenheit Scale (ºF) 2. Celsius Scale (ºC) Not reliable! Vary with location! Temp speed 12
Cool Matter - temp speed Properties of Absolute Zero 1. The coldest possible temperature 2. Matter can never be cooled to absolute zero Absolute zero - at -273 ºC or -460 ºF atomic and molecular motion essentially stops! 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!! Continuous Spectrum Range of wavelengths with no gaps or colors missing Types of Spectra 13
Emission (bright line) Spectra Absorption (dark line) Spectra Range of wavelengths with gaps or colors missing Elements have unique patterns of lines! Kirchoff s Laws Continuous Spectrum Hot solids or high density gases Light Bulb Filament Emission Spectrum Hot, low density gas Absorption Spectrum Cooler gas in front of continuous source A Neon Sign The Sun and stars! 14
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! 15
Subatomic Particles The Nuclear Model of the Atom Particle Symbol Proton p + or p Electron e - Neutron n or n 0 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! 16
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! How do we count the number of neutrons? Z is also equal to the number of electrons! 17
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 18
Examples Hydrogen (H) Helium (He) Z = 1, A = 1 1 1 H or H-1 Lithium (Li) Z = 2, A = 4 4 2 He or He-4 19
How many protons, electrons and neutrons? 52 24 Cr Z = 3, A = 7 7 3 Li or Li-7 # 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? 56 26 Fe 3+ # protons = 26 # electrons = 26 3 = 23 # neutrons = 56 26 = 30 How many protons, electrons and neutrons? 18 8 O 2- # 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? 20
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 Quantum Mechanics n = principle quantum number Isotopes do not have equal abundances! H-1 (99.9885%), H-2 (0.0115%) H-3 (radioactive) Energy Levels n E n = 1 ground state n > 1 excited states Energy levels are like the rungs of a ladder! Photon Emission Electron jumps from a higher to a lower level 21
Photon Absorption Each line corresponds to a different downward jump. The larger the jump the shorter the wavelength of the photon produced Electron jumps from a lower to higher energy A given atom emits and absorbs at exactly the same wavelengths! Each line corresponds to a different upward jump. The larger the jump the shorter the wavelength of the absorption line Photoionization Where do the chemical elements that matter is made of come from? Electron kicked out of an atom by a high-energy photon 22
The Doppler Effect The History and Evolution of the Universe Motion of a source of radiation causes the wavelengths it emits to be shifted Also observed with sound! Doppler Shifts Radar Guns The size of the Doppler Shift is directly proportional to the object s radial velocity, v r (motion towards or away) 100 Telescope on Mt Wilson Edwin Hubble (1889-1953) 23
Hubble measured the distances and radial velocities of nearby galaxies Expected to see no correlation between the two! Hubble s Law Instead found that nearly all galaxies were receding with velocity proportional to their distance! d v slope = v / d = H 0 v = H 0 d Conclusion? The Universe is Expanding! H 0 is a measure of the current rate of expansion! 24
2D Analogy of the Expanding Universe Universe = 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! Prediction: Leftover radiation from the early Universe should still be detectable today as microwave radiation! Matter was formed from high energy radiation as the Universe expanded and cooled 25
Cosmic Microwave Background Radiation Most of the Hydrogen and Helium was formed in the Big Bang that created the Universe! Detected by Penzias and Wilson in 1965 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 26
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? Result: the protons stick together or fuse! Hydrogen Fusion This a nuclear reaction, not a chemical reaction! Heavier nuclei from lighter nuclei! Often called hydrogen burning Where does the energy come from? 27
4 1 H 4 He + energy Expect: mass 4H = mass He Find: mass 4H > mass He Mass has disappeared! Mass is converted into energy! How much energy from how much mass? E = mc 2 m = mass c = speed of light Sun s Power Output Luminosity = L Θ = 3.9 x 10 26 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 235 U 143 Cs + 90 Rb + 3n + energy Used in nuclear reactors Helium Fusion Other fusion reactions 28
During their lives, stars fuse heavy elements from lighter elements Some stars like our Sun die quietly as they eject their outer layers into space When they die, they eject their outer layers containing heavy elements into space Other stars die. violently in supernova explosions!!! 29
producing supernova remnants The heavy elements ejected collect into interstellar clouds from which new stars and planets and even life can form! Interstellar Recycling We are made of stardust! Evidence: Stellar evolution models correctly predict the relative abundances of elements found in the universe How did the Sun and the planets form? 30
The Solar System Studies 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! Order of the Planets Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune (Pluto) One mnemonic to help you remember this! My Very Erotic Mate Joyfully Satisfies Unusual Needs (Passionately) 31
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) Chemical compositions are determined from the spectroscopy of reflected sunlight from a body Main difference between stars and planets Stars generate their own light why planets reflect light from the Sun! The Spectrum of Europa 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! Europa has an icy surface! 32
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 The Terrestrial and Jovian Families Jovian Planets Jupiter-like Large, gaseous, far from Sun (> 5 AU) Low mean densities Jupiter, Saturn, Uranus, Neptune 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 33
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! 34
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 Similarly, as a cloud collapses, it spins faster forming a rotating protoplanetary disk (proplyd) around a central protostar As a rotating object gets smaller it spins faster! 35
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 Temperature Maximum temperature that a given material will stick together (condense): iron > rock > H compounds > gases high low 36
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 Protostars and Protoplanety disks are seen inside the Orion Nebula! A star formation region 1500 ly away Infrared (IR) Image 37
Disks of gas and dust are seen around other, mature solar-type stars! 38