Todd TimberlakeThe Scale of the Universe

The Scale of the Universe

A set of computer simulations and curricular materials for teaching the history of galactic astronomy from Ancient Greece to the discovery of the cosmic microwave background.

DiffRotation Shapley1 SpiralNebulaRotation
[Overview]  [Syllabus]  [Simulations]  [Activities]  [Textbook]  [Credits]  [Terms of Use]  [Presentations]


This page contains curricular materials that I have developed for a course on the history of galactic astronomy. The course is intended to satisfy a science requirement for non-science majors. The course explores the historical development of ideas about our place among the stars from the Ancient Greeks to Big Bang cosmology. The main purpose of the course is to use galactic astronomy as an example for illustrating how scientific theories are developed and tested and how scientific knowledge changes over time.

I teach the course using interactive methods. Students work in small groups to complete worksheet-based activities. Most of the activities involve using computer simulations. Some of the activities make use of free planetarium software (Stellarium). The remaining activities use computer simulations that I have created using the Easy Java Simulations (EJS) package. These simulations are part of the Open-Source Physics (OSP) project and are available for free using the links below, along with all of the worksheets for the activities. Interested faculty may also be able to get a pre-publication version of a textbook for this course.


The syllabus for the course, which provides a list of topics as well as some details about how I run the course, is available below.

Computer Simulations

The computer simulations come in the form of Java executable files (JAR files). The programs should run on any computer with Java 1.5 (or newer) installed. All of the simulations were created using Easy Java Simulations (EJS) and are open-source, so you are free to alter and redistribute them (but please see the Terms of Use before doing so). You are free to use the simulations any way you wish, but I have developed a series of worksheet-based activities that use the simulations (as well as some other software and some physical equipment) to guide students through an exploration of this material. The worksheets are available below.

I am continuing to refine the simulations and the activities.  I will update the simulation package and the activities after each time I teach the course.  Therefore, the simulations and activities that you download should work together, but may not work with older versions of the simulations/activities.  In any case, I make no promises that there are not flaws in the simulations or errors in the activities.  Try them yourself before you try them on your students!

Download a Launcher package containing all of the simulations using the link below.  Just double click the JAR file (after extracting it from the zip archive) to run the Launcher package.  Use the tabs to select a section and the menu of simulations on the left side to launch a particular model.  In addition, there is one extra simulation (UniformUniverse) that you will need to download separately because it didn’t make it into the Launcher package.

Activities and Labs

The worksheets for the activities and labs are available in two formats: PDF and LaTeX source. You can use the links below to download zip archives containing the entire set in either format. You are free to use (and even change) the worksheets, but please see the Terms of Use before doing so. To edit the worksheets you need to know how to use LaTeX (or be willing to learn).

The table below contains a list of topics that students explore in my Scale of the Universe course. Each topic corresponds to an activity or lab worksheet.  For each topic I provide a link for the simulations used for that worksheet, and a list of any other materials needed to complete the activity. The worksheets designated with “(A)” are activities designed to be used in a single 75 minute class period. The worksheets designated with “(L)” are laboratory exercises designed to be used in a single 120 minute laboratory period. Ideally these materials should be used in the order in which they are listed, but there is some flexibility.

Please watch out for typos and other errors in these handouts. I cannot guarantee that they are without flaws – but the handouts posted here are all materials that I have used in my own class. Please work carefully through the exercises yourself before you give them to your students!

Topic Simulations Other Materials
The Night Sky I (L) Stellarium none
The Night Sky II (A) Stellarium, CelestialGlobe none
Distance and Parallax (A) Eratosthenes, Parallax2D none
Cosmos: Greece to Copernicus (L) SuperiorPtolemaic none
Copernicus’ Revolutions (A) DailyRotation, EarthOrbit, CopernicanSystem, VenusPhases none
Universe: Finite or Infinite (A) AngularDiameter, Parallax2D none
Photometric Distances (L) none none
Uniformity of the Stars (A) UniformUniverse none
Stellar Motions (A) Parallax3D, StellarAberration2D, StellarAberration3D none
Dark Sky Riddle (L) none none
Models of the Universe (A) StarSystemModels none
Motion of the Sun (A) ParallacticMotion none
The Construction of the Heavens (A) StarSystemModels, HerschelStarGages none
The Nebulae in the 19th Century (A) none none
Spectroscopy (A) none excitation lamps, spectrum tubes, incandescent lamp, spectrometer
Olber’s Paradox (A) DarkSkyFiniteAge none
Photometry and Photography (L) none none
Radial Velocities and Binary Stars (A) RadialVelocityMeasurement none
Spectral Classification (L) VIREO (CLEA program), StellarBlackbodySpectrum none
The H-R Diagram (A) none none
Stellar Evolution (A) none none
Statistical Astronomy (L) KapteynProperMotion none
Spirals: Dark Lanes and Novae (A) none none
Spirals: Spectra and Motions (A) SpiralNebulaRotation none
Cepheid Variables and Distance (L) none none
The Big Galaxy (A) ShapleyGlobularClusters none
The Great Debate (A) none none
Cepheids in Spirals (A) none none
Galactic Rotation (A) DifferentialGalacticRotation none
Absorption and Galactic Size (L) ShapleyGlobularClusters none
Relativity (A) none none
Relativistic Cosmology (A) EinsteinUniverse, DeSitterUniverse, LemaitreUniverse none
Expanding Universe (L) MilneUniverse ruler
Stellar Populations (A) none none
Radio Astronomy (A) JanskyAntenna, GalacticHydrogenMapping none
Relics of the Big Bang (A) none none


I have written a textbook for the Scale of the Universe course. Although the textbook is not yet ready for publication, interested college faculty or high school teachers may be able to obtain a pre-publication version of the text for review and possible use in a college or high school astronomy course. Please contact Todd Timberlake ( if you are interested in receiving an electronic copy of the textbook for review.


  • All of the simulations were developed using the Easy Java Simluations authoring tool by Francisco Esquembre (see the EJS Wiki page for more information).
  • EJS is part of the Open Source Physics project by Wolfgang Christian and collaborators (see the OSP page on ComPADRE for more details).
  • Wolfgang Christian and Mario Belloni provided much helpful advice on improving the simulations.
  • Todd Timberlake developed all of the EJS simulations and activity handouts associated with this course.
  • A couple figures in the handouts have been borrowed from sources that I now can’t remember. (If they are yours, please let me know so I can either cite you or remove the figures if you wish.)

Terms of Use

All of the materials on this page are available free of charge. Feel free to download the materials and explore them with no obligation whatsoever. However, if you use any of these materials in a class please contact me ( to let me know. I would like to receive feedback on the simulations and the worksheets (especially if you find an error!) and I would like to keep track of where they are being used. If you make any modifications of the simulations or worksheets I would like to know about it (if you made it better then I want to use your improved version!).

The Java programs linked above are Open Source Physics (OSP) programs that were created using Easy Java Simulations (EJS) and are freely distributable under the GNU GPL license. For more information about the Open Source Physics project visit

Creative Commons License
All of the curricular materials (including the narratives in the Launcher package) are copyrighted by Todd Timberlake and/or Paul Wallace and are licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License. You may modify and redistribute these materials for non-commercial use as long as you clearly cite the original author (Todd Timberlake for all simulations materials and the activity handouts, Paul Wallace and Todd Timberlake for the lab handouts) and release the materials under the same license.

Presentations Of This Material

I have published and presented some of this material and the links below provide access to my articles and presentation materials.

  • “Seeing Earth’s Orbit in the Stars: Parallax and Aberration,” The Physics Teacher 51, 478-481 (2013). Reprint: ParallaxAberration
  • “Mapping the Galaxy: Herschel’s Star Gages” The Physics Teacher 51, 48-51 (2013). Reprint: HerschelStarGages
  • “Engaging with the History of Astronomy” invited talk at the 2012 Gordon Research Conference on Physics Research and Education, Waterville, ME, June 2012. Slides: EngagingHistoryAstronomy
  • “Astronomy, History, and Computer Simulations: An Approach to Teaching the Nature of Science” talk given at the 2011 Summer Meeting of the American Association of Physics Teachers, Omaha, NE, August 2011.  Slides: TimberlakeAAPTSum11Astro
  • “Astronomy, History, and Computer Simulations: An Approach to Teaching the Nature of Science” talk given at the Tenth Biennial History of Astronomy Workshop, South Bend, IN, July 2011.  Slides: TimberlakeNDX