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### ASTR 3740 Relativity & Cosmology Spring 2007. Problem Set 1. Due Wed 31 Jan

1. A Scene Seen near c

From the information you can glean from the sources described below, or elsewhere, describe what a scene looks like when you pass through it at near to the speed of light. In particular, answer as precisely as possible:

(a) Aberration
In what way does the scene appear distorted?

(b) Color Changes
Are the colors changed, and if so in what way?

(c) Brightness
Is the scene changed in brightness, and if so in what way?

[Comments: This problem is a test of your powers of observation, and your ability to synthesize facts from a variety of sources into a coherent physical picture. You should reference the sites you use to draw your conclusions. Do not attempt to explain what you see mathematically - we will be discussing the problem mathematically in class later on.]

2. What's Wrong?

By comparing to simulations from other sites, determine what is wrong with John Walker's C-ship movie (http://www.fourmilab.to/cship/flythru.html).

Guide to Relativistic Flight Simulator Sites

If you can find some good sites not listed here, please let me know!

Possibly the best starting point for non-crank websites on relativity is Chris Hillman's Relativity on the World Wide Web (http://math.ucr.edu/home/baez/relativity.html).

Another site relevant to this problem is David Porthouse's Relativistic Flight Simulation Links (http://ourworld.compuserve.com/homepages/anima/rfslink.htm).

1. The best site that I know of is Ute Kraus and Corvin Zahn's Space Time Travel (http://www.spacetimetravel.org/index.html). It features several cool visualizations.

2. John Walker's C-Ship (http://www.fourmilab.to/cship/cship.html) is possibly the most clearly written and presented site, and well worth reading through for the excellent explanations. Sadly, John Walker's movies are wrong in one important way.
3. Norbert Dragon and Nicolai Mokros' View of Stonhenge (http://www.itp.uni-hannover.de/~dragon/stonehenge/stone2e.htm) has clear physical descriptions and simple pictures, although without color shifts.

4. Steve Van Devender's relativistic starflight (http://hexadecimal.uoregon.edu/relativity/index.html) site has correct if rather primitive graphics.

5. Antony Searle's BackLight movies (http://www.anu.edu.au/Physics/Searle/Movies.html) are graphically stunning and undoubtedly correct, but the presentation is confusing, and the choice of movies is not ideal. One of the better movies (if you have an mpeg player) is the Mercator (http://www.anu.edu.au/Physics/Searle/Mercator.mpg) which however mixes up the relativistic distortion with the fish-eye distortion that comes from the Mercator Projection of the sphere.

6. Sadly, one of the best movies (though rather large, at 4MB) is now a missing link, the UCLA supercomputer group's LA flyover (http://coke.physics.ucla.edu/lapd/Collaborations/Relativity/Relativity.html). If anyone can find it, let me know! Note that, as with several other movies, this one lacks color shifts.