

Stars and Slopes 
Objectives
 Students will apply the knowledge of plotting data and obtaining a slope
using a loglog coordinate system.
 Students will determine the line of best fit from a set of data
obtained from Xray astronomy satellites.
 Students will discover the relationship between slope and the
classification of stellar objects.
Grade Level
10th to 12th + grades
Prerequisites
Math
Students should have learned the following algebraic concepts:
 graphing a linear equation using slope and yintercept
 determining a line of best fit from a set of data
 using logarithms
Science
Students should have had an introduction to the concepts of physics
and space astronomy.
Time Requirements
For each class of students, you will probably need at least
2 periods.
Introduction
Many problems in physics, mathematics, engineering, and other fields are
fundamentally the study of the relationship between two variables. For
example, how the velocity of a falling object varies with time; the angular
distribution of radiant energy transmitted from a small hole; the pressure
response frequency characteristic of a crystal telephone receiver. Such
everyday applications involve an independent variable (i.e., one that
progressively changes such as time or frequency) and a dependent variable
which is mathematically determined from the change in the independent variable
in some way (e.g., velocity or intensity).
By displaying the data in a graphic, the relationship of the dependent
variable on the independent variable can be seen. The most powerful form of
display is when the result is a straight line  which can always be
converted quickly into a mathematical equation. However, obtaining a
straight line curve may require the selection of very special types of graph
paper or axis values.
There are different types of graph paper which can be used for the
presentation of data. They each have their own advantages and disadvantages.
The most common three types are "rectangular" (or "Cartesian") coordinates,
polar coordinates, and logarithmic (or log) coordinates. This lesson will looks
at two of the three  rectangular and logarithmic.
Day 1 focuses on loglog plotting and determining the slopes of such
plots.
Day 2 delves into how to use loglog plots to gain insight into
certain celestial objects of interest to Xray astronomers.
Day 2 is still under development!
Resources
Kaufmann, William J. III, Universe, Freeman and Company, 1994, pgs. 336340
Kerrod, Robin, Encyclopedia of Science: The Heavens Stars, Galaxies, and
the Solar System, Macmillan Publishing Company, 1991
Kondo, Herbert, The New Book of Popular Science Vol. 1, Grolier
Incorporated, 1982, pgs. 174190
Overbeck, C.J., Palmer, R.R., Stephenson, R.J., and White, M.W., 1963,
Graphs and Equations, Selective Experiments on Physics, Central Scientific
Company
Seward, Frederick D. and Charles, Philip A., Exploring the Xray Universe,
Cambridge University Press, 1995
The graphics and other information found within this
lesson can also be found on Imagine the Universe!
which is located on the World Wide Web. The URL for this
site is
http://imagine.gsfc.nasa.gov/.
The data were retrieved within The HEASARC Data
Archive using W3Browse which is located on the World
Wide Web. The URL for this site is
http://heasarc.gsfc.nasa.gov/.
