Chapter 1: How Science Works

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Chapter 1
How Science Works

  • The Scientific Method
  • Evidence
  • Measurements
  • Units and the Metric System
  • Measurement Errors
  • Estimation
  • Dimensions
  • Mass, Length, and Time
  • Observations and Uncertainty
  • Precision and Significant Figures
  • Errors and Statistics
  • Scientific Notation
  • Ways of Representing Data
  • Logic
  • Mathematics
  • Geometry
  • Algebra
  • Logarithms
  • Testing a Hypothesis
  • Case Study of Life on Mars
  • Theories
  • Systems of Knowledge
  • The Culture of Science
  • Computer Simulations
  • Modern Scientific Research
  • The Scope of Astronomy
  • Astronomy as a Science
  • A Scale Model of Space
  • A Scale Model of Time
  • Questions

Chapter 2
Early Astronomy

  • The Night Sky
  • Motions in the Sky
  • Navigation
  • Constellations and Seasons
  • Cause of the Seasons
  • The Magnitude System
  • Angular Size and Linear Size
  • Phases of the Moon
  • Eclipses
  • Auroras
  • Dividing Time
  • Solar and Lunar Calendars
  • History of Astronomy
  • Stonehenge
  • Ancient Observatories
  • Counting and Measurement
  • Astrology
  • Greek Astronomy
  • Aristotle and Geocentric Cosmology
  • Aristarchus and Heliocentric Cosmology
  • The Dark Ages
  • Arab Astronomy
  • Indian Astronomy
  • Chinese Astronomy
  • Mayan Astronomy
  • Questions

Chapter 3
The Copernican Revolution

  • Ptolemy and the Geocentric Model
  • The Renaissance
  • Copernicus and the Heliocentric Model
  • Tycho Brahe
  • Johannes Kepler
  • Elliptical Orbits
  • Kepler's Laws
  • Galileo Galilei
  • The Trial of Galileo
  • Isaac Newton
  • Newton's Law of Gravity
  • The Plurality of Worlds
  • The Birth of Modern Science
  • Layout of the Solar System
  • Scale of the Solar System
  • The Idea of Space Exploration
  • Orbits
  • History of Space Exploration
  • Moon Landings
  • International Space Station
  • Manned versus Robotic Missions
  • Commercial Space Flight
  • Future of Space Exploration
  • Living in Space
  • Moon, Mars, and Beyond
  • Societies in Space
  • Questions

Chapter 4
Matter and Energy in the Universe

  • Matter and Energy
  • Rutherford and Atomic Structure
  • Early Greek Physics
  • Dalton and Atoms
  • The Periodic Table
  • Structure of the Atom
  • Energy
  • Heat and Temperature
  • Potential and Kinetic Energy
  • Conservation of Energy
  • Velocity of Gas Particles
  • States of Matter
  • Thermodynamics
  • Entropy
  • Laws of Thermodynamics
  • Heat Transfer
  • Thermal Radiation
  • Wien's Law
  • Radiation from Planets and Stars
  • Internal Heat in Planets and Stars
  • Periodic Processes
  • Random Processes
  • Questions

Chapter 5
The Earth-Moon System

  • Earth and Moon
  • Early Estimates of Earth's Age
  • How the Earth Cooled
  • Ages Using Radioactivity
  • Radioactive Half-Life
  • Ages of the Earth and Moon
  • Geological Activity
  • Internal Structure of the Earth and Moon
  • Basic Rock Types
  • Layers of the Earth and Moon
  • Origin of Water on Earth
  • The Evolving Earth
  • Plate Tectonics
  • Volcanoes
  • Geological Processes
  • Impact Craters
  • The Geological Timescale
  • Mass Extinctions
  • Evolution and the Cosmic Environment
  • Earth's Atmosphere and Oceans
  • Weather Circulation
  • Environmental Change on Earth
  • The Earth-Moon System
  • Geological History of the Moon
  • Tidal Forces
  • Effects of Tidal Forces
  • Historical Studies of the Moon
  • Lunar Surface
  • Ice on the Moon
  • Origin of the Moon
  • Humans on the Moon
  • Questions

Chapter 6
The Terrestrial Planets

  • Studying Other Planets
  • The Planets
  • The Terrestrial Planets
  • Mercury
  • Mercury's Orbit
  • Mercury's Surface
  • Venus
  • Volcanism on Venus
  • Venus and the Greenhouse Effect
  • Tectonics on Venus
  • Exploring Venus
  • Mars in Myth and Legend
  • Early Studies of Mars
  • Mars Close-Up
  • Modern Views of Mars
  • Missions to Mars
  • Geology of Mars
  • Water on Mars
  • Polar Caps of Mars
  • Climate Change on Mars
  • Terraforming Mars
  • Life on Mars
  • The Moons of Mars
  • Martian Meteorites
  • Comparative Planetology
  • Incidence of Craters
  • Counting Craters
  • Counting Statistics
  • Internal Heat and Geological Activity
  • Magnetic Fields of the Terrestrial Planets
  • Mountains and Rifts
  • Radar Studies of Planetary Surfaces
  • Laser Ranging and Altimetry
  • Gravity and Atmospheres
  • Normal Atmospheric Composition
  • The Significance of Oxygen
  • Questions

Chapter 7
The Giant Planets and Their Moons

  • The Gas Giant Planets
  • Atmospheres of the Gas Giant Planets
  • Clouds and Weather on Gas Giant Planets
  • Internal Structure of the Gas Giant Planets
  • Thermal Radiation from Gas Giant Planets
  • Life on Gas Giant Planets?
  • Why Giant Planets are Giant
  • Gas Laws
  • Ring Systems of the Giant Planets
  • Structure Within Ring Systems
  • The Origin of Ring Particles
  • The Roche Limit
  • Resonance and Harmonics
  • Tidal Forces in the Solar System
  • Moons of Gas Giant Planets
  • Geology of Large Moons
  • The Voyager Missions
  • Jupiter
  • Jupiter's Galilean Moons
  • Jupiter's Ganymede
  • Jupiter's Europa
  • Jupiter's Callisto
  • Jupiter's Io
  • Volcanoes on Io
  • Saturn
  • Cassini Mission to Saturn
  • Saturn's Titan
  • Saturn's Enceladus
  • Discovery of Uranus and Neptune
  • Uranus
  • Uranus' Miranda
  • Neptune
  • Neptune's Triton
  • Pluto
  • The Discovery of Pluto
  • Pluto as a Dwarf Planet
  • Dwarf Planets
  • Questions

Chapter 8
Interplanetary Bodies

  • Interplanetary Bodies
  • Comets
  • Early Observations of Comets
  • Structure of the Comet Nucleus
  • Comet Chemistry
  • Oort Cloud and Kuiper Belt
  • Kuiper Belt
  • Comet Orbits
  • Life Story of Comets
  • The Largest Kuiper Belt Objects
  • Meteors and Meteor Showers
  • Gravitational Perturbations
  • Asteroids
  • Surveys for Earth Crossing Asteroids
  • Asteroid Shapes
  • Composition of Asteroids
  • Introduction to Meteorites
  • Origin of Meteorites
  • Types of Meteorites
  • The Tunguska Event
  • The Threat from Space
  • Probability and Impacts
  • Impact on Jupiter
  • Interplanetary Opportunity
  • Questions

Chapter 9
Planet Formation and Exoplanets

  • Formation of the Solar System
  • Early History of the Solar System
  • Conservation of Angular Momentum
  • Angular Momentum in a Collapsing Cloud
  • Helmholtz Contraction
  • Safronov and Planet Formation
  • Collapse of the Solar Nebula
  • Why the Solar System Collapsed
  • From Planetesimals to Planets
  • Accretion and Solar System Bodies
  • Differentiation
  • Planetary Magnetic Fields
  • The Origin of Satellites
  • Solar System Debris and Formation
  • Gradual Evolution and a Few Catastrophies
  • Chaos and Determinism
  • Extrasolar Planets
  • Discoveries of Exoplanets
  • Doppler Detection of Exoplanets
  • Transit Detection of Exoplanets
  • The Kepler Mission
  • Direct Detection of Exoplanets
  • Properties of Exoplanets
  • Implications of Exoplanet Surveys
  • Future Detection of Exoplanets
  • Questions

Chapter 10
Detecting Radiation from Space

  • Observing the Universe
  • Radiation and the Universe
  • The Nature of Light
  • The Electromagnetic Spectrum
  • Properties of Waves
  • Waves and Particles
  • How Radiation Travels
  • Properties of Electromagnetic Radiation
  • The Doppler Effect
  • Invisible Radiation
  • Thermal Spectra
  • The Quantum Theory
  • The Uncertainty Principle
  • Spectral Lines
  • Emission Lines and Bands
  • Absorption and Emission Spectra
  • Kirchoff's Laws
  • Astronomical Detection of Radiation
  • The Telescope
  • Optical Telescopes
  • Optical Detectors
  • Adaptive Optics
  • Image Processing
  • Digital Information
  • Radio Telescopes
  • Telescopes in Space
  • Hubble Space Telescope
  • Interferometry
  • Collecting Area and Resolution
  • Frontier Observatories
  • Questions

Chapter 11
Our Sun: The Nearest Star

  • The Sun
  • The Nearest Star
  • Properties of the Sun
  • Kelvin and the Sun's Age
  • The Sun's Composition
  • Energy From Atomic Nuclei
  • Mass-Energy Conversion
  • Examples of Mass-Energy Conversion
  • Energy From Nuclear Fission
  • Energy From Nuclear Fusion
  • Nuclear Reactions in the Sun
  • The Sun's Interior
  • Energy Flow in the Sun
  • Collisions and Opacity
  • Solar Neutrinos
  • Solar Oscillations
  • The Sun's Atmosphere
  • Solar Chromosphere and Corona
  • Sunspots
  • The Solar Cycle
  • The Solar Wind
  • Effects of the Sun on the Earth
  • Cosmic Energy Sources
  • Questions

Chapter 12
Properties of Stars

  • Stars
  • Star Names
  • Star Properties
  • The Distance to Stars
  • Apparent Brightness
  • Absolute Brightness
  • Measuring Star Distances
  • Stellar Parallax
  • Spectra of Stars
  • Spectral Classification
  • Temperature and Spectral Class
  • Stellar Composition
  • Stellar Motion
  • Stellar Luminosity
  • The Size of Stars
  • Stefan-Boltzmann Law
  • Stellar Mass
  • Hydrostatic Equilibrium
  • Stellar Classification
  • The Hertzsprung-Russell Diagram
  • Volume and Brightness Selected Samples
  • Stars of Different Sizes
  • Understanding the Main Sequence
  • Stellar Structure
  • Stellar Evolution
  • Questions

Chapter 13
Star Birth and Death

  • Star Birth and Death
  • Understanding Star Birth and Death
  • Cosmic Abundance of Elements
  • Star Formation
  • Molecular Clouds
  • Young Stars
  • T Tauri Stars
  • Mass Limits for Stars
  • Brown Dwarfs
  • Young Star Clusters
  • Cauldron of the Elements
  • Main Sequence Stars
  • Nuclear Reactions in Main Sequence Stars
  • Main Sequence Lifetimes
  • Evolved Stars
  • Cycles of Star Life and Death
  • The Creation of Heavy Elements
  • Red Giants
  • Horizontal Branch and Asymptotic Giant Branch Stars
  • Variable Stars
  • Magnetic Stars
  • Stellar Mass Loss
  • White Dwarfs
  • Supernovae
  • Seeing the Death of a Star
  • Supernova 1987A
  • Neutron Stars and Pulsars
  • Special Theory of Relativity
  • General Theory of Relativity
  • Black Holes
  • Properties of Black Holes
  • Questions

Chapter 14
The Milky Way

  • The Distribution of Stars in Space
  • Stellar Companions
  • Binary Star Systems
  • Binary and Multiple Stars
  • Mass Transfer in Binaries
  • Binaries and Stellar Mass
  • Nova and Supernova
  • Exotic Binary Systems
  • Gamma Ray Bursts
  • How Multiple Stars Form
  • Environments of Stars
  • The Interstellar Medium
  • Effects of Interstellar Material on Starlight
  • Structure of the Interstellar Medium
  • Dust Extinction and Reddening
  • Groups of Stars
  • Open Star Clusters
  • Globular Star Clusters
  • Distances to Groups of Stars
  • Ages of Groups of Stars
  • Layout of the Milky Way
  • William Herschel
  • Isotropy and Anisotropy
  • Mapping the Milky Way
  • Questions

Chapter 15
Galaxies

  • The Milky Way Galaxy
  • Mapping the Galaxy Disk
  • Spiral Structure in Galaxies
  • Mass of the Milky Way
  • Dark Matter in the Milky Way
  • Galaxy Mass
  • The Galactic Center
  • Black Hole in the Galactic Center
  • Stellar Populations
  • Formation of the Milky Way
  • Galaxies
  • The Shapley-Curtis Debate
  • Edwin Hubble
  • Distances to Galaxies
  • Classifying Galaxies
  • Spiral Galaxies
  • Elliptical Galaxies
  • Lenticular Galaxies
  • Dwarf and Irregular Galaxies
  • Overview of Galaxy Structures
  • The Local Group
  • Light Travel Time
  • Galaxy Size and Luminosity
  • Mass to Light Ratios
  • Dark Matter in Galaxies
  • Gravity of Many Bodies
  • Galaxy Evolution
  • Galaxy Interactions
  • Galaxy Formation
  • Questions

Chapter 16
The Expanding Universe

  • Galaxy Redshifts
  • The Expanding Universe
  • Cosmological Redshifts
  • The Hubble Relation
  • Relating Redshift and Distance
  • Galaxy Distance Indicators
  • Size and Age of the Universe
  • The Hubble Constant
  • Large Scale Structure
  • Galaxy Clustering
  • Clusters of Galaxies
  • Overview of Large Scale Structure
  • Dark Matter on the Largest Scales
  • The Most Distant Galaxies
  • Black Holes in Nearby Galaxies
  • Active Galaxies
  • Radio Galaxies
  • The Discovery of Quasars
  • Quasars
  • Types of Gravitational Lensing
  • Properties of Quasars
  • The Quasar Power Source
  • Quasars as Probes of the Universe
  • Star Formation History of the Universe
  • Expansion History of the Universe
  • Questions

Chapter 17
Cosmology

  • Cosmology
  • Early Cosmologies
  • Relativity and Cosmology
  • The Big Bang Model
  • The Cosmological Principle
  • Universal Expansion
  • Cosmic Nucleosynthesis
  • Cosmic Microwave Background Radiation
  • Discovery of the Microwave Background Radiation
  • Measuring Space Curvature
  • Cosmic Evolution
  • Evolution of Structure
  • Mean Cosmic Density
  • Critical Density
  • Dark Matter and Dark Energy
  • Age of the Universe
  • Precision Cosmology
  • The Future of the Contents of the Universe
  • Fate of the Universe
  • Alternatives to the Big Bang Model
  • Space-Time
  • Particles and Radiation
  • The Very Early Universe
  • Mass and Energy in the Early Universe
  • Matter and Antimatter
  • The Forces of Nature
  • Fine-Tuning in Cosmology
  • The Anthropic Principle in Cosmology
  • String Theory and Cosmology
  • The Multiverse
  • The Limits of Knowledge
  • Questions

Chapter 18
Life On Earth

  • Nature of Life
  • Chemistry of Life
  • Molecules of Life
  • The Origin of Life on Earth
  • Origin of Complex Molecules
  • Miller-Urey Experiment
  • Pre-RNA World
  • RNA World
  • From Molecules to Cells
  • Metabolism
  • Anaerobes
  • Extremophiles
  • Thermophiles
  • Psychrophiles
  • Xerophiles
  • Halophiles
  • Barophiles
  • Acidophiles
  • Alkaliphiles
  • Radiation Resistant Biology
  • Importance of Water for Life
  • Hydrothermal Systems
  • Silicon Versus Carbon
  • DNA and Heredity
  • Life as Digital Information
  • Synthetic Biology
  • Life in a Computer
  • Natural Selection
  • Tree Of Life
  • Evolution and Intelligence
  • Culture and Technology
  • The Gaia Hypothesis
  • Life and the Cosmic Environment

Chapter 19
Life in the Universe

  • Life in the Universe
  • Astrobiology
  • Life Beyond Earth
  • Sites for Life
  • Complex Molecules in Space
  • Life in the Solar System
  • Lowell and Canals on Mars
  • Implications of Life on Mars
  • Extreme Environments in the Solar System
  • Rare Earth Hypothesis
  • Are We Alone?
  • Unidentified Flying Objects or UFOs
  • The Search for Extraterrestrial Intelligence
  • The Drake Equation
  • The History of SETI
  • Recent SETI Projects
  • Recognizing a Message
  • The Best Way to Communicate
  • The Fermi Question
  • The Anthropic Principle
  • Where Are They?

Precision and Significant Figures


Population density (people per km^2) map of the world in 1994. Red and pink areas denote regions of highest population density.

Scientists record information according to the accuracy of the measurement. The number of digits used to write a measurement indicates the precision of the measurement — it is also called the number of significant figures. Suppose we quote the population of the Earth as 6,300,000,000 people. This estimate has only two non-zero digits or significant figures and implies a measurement of low precision. Alternatively, we might quote the population of the Earth as 6,356,908,417 people. This estimate has ten significant figures and implies that we counted every person!

Clearly, the way scientists write a measurement carries an implication of the degree of certainty about the measurement. The non-zero digit that is farthest to the left is the least significant digit. The non-zero digit that is farthest to the right is the most significant digit — it indicates the precision of the measurement. In our population example, the most significant digit of the number 6,300,000,000 is 3, so we infer that the uncertainty in the estimate is one unit in the most significant digit, or 100,000,000. With two significant figures, we see that the accuracy of the estimate is 1 part in 63 or about 1 to 2%. The most significant digit in the number 6,356,908,417 is 7, so the implied accuracy of the number is 1 part in 6 billion or about 0.00000001%. Since someone is born and dies on the Earth every second or so, this highly accurate estimate is very implausible! A better estimate of the Earth's population might be 6,356,910,000 — a precision of six significant figures.


The amount this bill is worth is $100. We know each unit precisely, so it has three significant figures.

Here are a few more examples of measurements and their precision. Remember to count a zero just like any other digit. For example, 9004 has four significant digits. There are two types of exception where 0 is not counted as a significant digit. The first is in a decimal fraction, where the leading zeros are just placeholders behind the decimal point. The second is the fact that some numbers just happen to be round numbers. For example, a hundred-dollar-bill represents exactly $100 and has three significant figures.

• 65,400 K has 3 significant figures

• 0.00002 g/cm3 has 1 significant figure

• 980,014 km has 6 significant figures

• 7.5 × 105 pc has 2 significant figures

• 1.007 × 10-8 kg has 4 significant figures

• 3.3206 × 106 W has 5 significant figures

The precision of a number relates to the implied accuracy of the measurement. We will use the diameter of the Earth — measured to be 12,756 km — as an example. Notice that it is always possible to quote a measurement with lower precision by rounding the number. Here is how to round off a number: if the most significant digit is 4 or less, you set it to 0, and if the most significant digit is 5 or higher, you set it to 0 and increase the next less significant digit by 1.


Explication of the equation E=mc²

Consider the speed of light, which is one of the most accurately determined constants in nature. It is a good example of a physical constant that just happens to be nearly a round number in the metric system. Its measurement is 299792.458 km/s, with a precision of 9 significant figures and an error of 0.001 km/s, so accurate to 1 part in 108 (a 10-6% error).

The precision of a number — how many significant figures we quote — has an implication about the accuracy of the measurement. Accuracy reflects how far the measurement deviates from the true value. Therefore, precision has little meaning if we know nothing about the amount of observational error. To return to our first example, it is meaningless to quote the population of the Earth with a precision of 9 or 10 significant figures, since no one could possibly count people that accurately. Scientists talk about observational error, but a better term is uncertainty. Measurements are not usually wrong or in error, but they are uncertain due to unavoidable limitations in the measuring apparatus.

Author: Chris Impey