Writing Assignment 1: Cosmological Distance Ladder

Due Thursday, January 29, 4 pm

Reading:

Attached Section 2.2 from Michael Berry, Principles of cosmology and gravitation (Cambridge University Press, New York, 1976).

Writing

This writing assignment is based on the second paragraph in Berry's introductory passage to section 2.2, on the ``parable of the city.'' The parable serves as a qualitative summary of the entire section, in a way that you will flesh out in this assignment.

Summary

In his parable, Berry proposes several methods for the Martian to measure distances, each having limited range. List three of the proposed methods, stating for each (1) the quantities measured by the Martian and how (mathematically) they determine the distance; (2) the method's range of validity; and (3) an analogous method used by humans to measure astrophysical distances (if no analog exists, say why). For both (2) and (3), give enough information to uniquely specify what an observer measures and when his method has broken down.

Extension

Imagine that the Martian has in fact landed on a skyscraper in downtown Atlanta, and has the following sensory/observational skills: he can

• emit no light signals himself.
• resolve rooftop parallax angles out to a distance of 5 city blocks.
• resolve individual stoplights out as far as Emory.
• see light in our visible spectrum out past the perimeter (with individual sources unresolved past Emory).
• design a ``standard candle'' device in his native part of the light spectrum, which has no earth-based sources. He can resolve such devices to distances well past the perimeter, and is able to plant them on cars parked in the skyscraper's parking garage, which then diffuse over the metropolitan area.

The Martian attempts three tasks, all under night lighting and heavy traffic conditions: He must

1. map his local 10-block radius grid of streets.
2. extend his grid out to the distance of Emory.
3. determine average traffic speeds on the perimeter.

The Martian sends regular progress reports to his superiors, which detail his methods and results at the level of a scientific lab report. Write his method reports for each of the above tasks. Each should include the quantities to be measured and any experimental setup; necessary theory, justifications or calibrations for the method; as well as one worked example data point, to show how the Martian applies the method to his observational data. (Make up whatever Martian units you desire.)

Martians are terse; you should keep the method report for each task shorter than 1 to 2 pages maximum.