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# Stars and Slopes

## Objectives

1. Students will apply the knowledge of plotting data and obtaining a slope using a log-log coordinate system.

2. Students will determine the line of best fit from a set of data obtained from X-ray astronomy satellites.

3. Students will discover the relationship between slope and the classification of stellar objects.

## Prerequisites

#### Math

Students should have learned the following algebraic concepts:

1. graphing a linear equation using slope and y-intercept

2. determining a line of best fit from a set of data

3. 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 log-log plotting and determining the slopes of such plots.

• Day 2 delves into how to use log-log plots to gain insight into certain celestial objects of interest to X-ray astronomers.

Day 2 is still under development!

## Resources

Kaufmann, William J. III, Universe, Freeman and Company, 1994, pgs. 336-340

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. 174-190

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 X-ray 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/.

•  Imagine the Universe is a service of the High Energy Astrophysics Science Archive Research Center (HEASARC), Dr. Alan Smale (Director), within the Astrophysics Science Division (ASD) at NASA's Goddard Space Flight Center. The Imagine Team Acting Project Leader: Dr. Barbara Mattson All material on this site has been created and updated between 1997-2012.