Summary

Students will use a spreadsheet program (such as MS Excel) to study the properties of the 27 nearest stars and the 25 brightest stars (as seen from Earth).  Students are given two tables of stars' colors and magnitudes, use Excel or create an H-R diagram by hand, and analyze trends observed. 

This lesson can be taught as a classroom activity or as a lab.  

Suggested Time

2 hours; more if you need to establish background material.  

Prerequisites

Magnitude, color, graphing, H-R diagram, computer skills (optional).

This lesson works best if students are already familiar with the H-R diagram.  It can be preceded with a similar lesson using stars from a globular cluster rather than local stars.  

Learning Outcomes

Process/Skills

Upon successful completion of this lesson, students will

• know how to enter data into a spreadsheet
• know how to graph in a spreadsheet (or by hand)
• relate graphical data to physical quantities
• be able to observe trends in data
• be able to draw conclusions from graphs

Content

Upon successful completion of this lesson, students will understand the science and astronomy concepts of

• the HR diagram, main sequence, magnitude, color
• a representative sample

High School Frameworks

Massachusetts

• Earth & Space 1.1, 1.3, 1.8
• HS Physics 4.1, 4.2, 6.2
• SIS 1, 2, 3, 4
• Math skills (various)

NSES A, B, D, F, G

Materials

1. List of 27 closest stars' B and V values (.pdf, webpage, MS Excel) 
2. List of 25 brightest stars' B and V values (.pdf, webpage, MS Excel) 
3. Student Handout (.pdf, webpage, text, MS Word) 
4. Computer-based: 
   1. Spreadsheet/graphing program (such as MS Excel, OpenOffice) 
   2. Printer 
5. Paper-based: 
   1. Graph paper 
   2. Colored pencils 

Background

What Mendeleev's Periodic Table of the Elements did for Chemistry, the Hertzsprung-Russel Diagram did for Astronomy.  Building upon the stellar classification systems of Williamina Fleming, Cecilia Payne-Gaposchkin, and Annie Jump Cannon, and the knowledge of temperatures from Wien's Law, the H-R Diagram makes sense of star colors/temperatures and luminosities.  A good example of it can be found here, and a simpler version is below.

There are two equivalent versions of the H-R Diagram.  Using physical quantities, we measure temperature in Kelvins on the horizontal axis (shown across the top of the above graph, measured logarithmically increasing to the left) and luminosity in solar units on the vertical axis (shown on the right, also a logarithmic scale).  

However, these are not the most convenient units for astronomers.  Luminosity is measured more conveniently in the magnitude system.  The magnitude system is believed to have been created by the ancient Greek Hipparchus.  Picture him saying "That's the brightest star so I'll call it number 1; that's the second brightest so I'll call it number 2," and so on down to 6th magnitude as the faintest the human eye could see (without modern day light pollution).  This had the inadvertent effect that the values run backwards of what you might expect: small numbers are bright objects, while large numbers are faint objects.  The scale is also logarithmic, though what precisely that means is beyond the scope of this lesson.  The system was later formalized, with decimal magnitudes being introduced between, larger numbers for fainter objects, and negative numbers for brighter ones.  The apparent magnitude system describes how bright objects appear from Earth, while absolute magnitudes describe the inherent brightness of objects.  When a set of objects are all the same distance from Earth, as in a globular cluster, then apparent magnitudes may be substituted for absolute magnitudes.  Magnitude in "visible" (green) wavelength is on the vertical axis of an H-R diagram (on the left of the graph above) since magnitude is equivalent to luminosity.  

Similarly, temperature cannot be directly measured by astronomers.  However, Wien's Law mathematically describes how the color of an object relates to its physical temperature - when the burner on a hot plate is cool, it does not glow.  As it heats up it becomes red, and orange as it gets hotter.  If you could make it even hotter yet it would become yellow and white.  The way astronomers measure this is they use filters on their cameras to compare the brightness of the star at two particular wavelengths, blue and "visible" (green).  This is similar to how the human eye has three different types of color sensing (cone) cells to determine the overall color of objects.  In a mathematical form, astronomers define color as the blue magnitude minus the visible magnitude, or B-V.  Color is on the horizontal axis of an H-R diagram (at the bottom of the above graph) since it is equivalent to temperature.  On some H-R diagrams the spectral class is displayed, as it is also dependent upon the temperature of the star.  

When an H-R diagram is created of all stars, most seem to fall along a single diagonal line, called the Main Sequence.  Stars in the upper left (O and B) are hot, bright, blue, massive, short-lived, and are less common; stars in the lower left (K and M) are cooler, dimmer, red, less massive, long-lived, and are more common.  As stars age, they move rightwards on the graph, so that if the stars are from an older group (such as a globular cluster) only the small red dwarfs will remain on the main sequence while the O and B giants will have become red giants.  Where the stars are just starting to leave the Main Sequence is called the Turn-Off Point and can be used to determine the age of the cluster.  

This lesson seeks to reinforce the above material, presumably already conveyed through lecture or other lessons.  In addition, students investigate the H-R diagrams for not only the nearest stars but also the brightest stars.  Examining the brightest stars introduces the bias of selecting only stars with a high luminosity, so the resulting H-R diagram will be inaccurate in that it does not include the majority of stars that actually exist.  

Lesson

Intro

Remind students of background info, above (15 minutes).  If students are unfamiliar with the H-R diagram, it is suggested that an intermediary lesson be taught using a globular cluster instead.  

Activity

Break students into pairs on computers.  If no computers are available or students have poor computer skills, they may graph by hand instead.  Each student should get a printed handout and printed or file version of the data, linked above in the materials section.  

Students complete handout with teacher direction.  Should you bring in external data such as luminosities or temperatures, note that MS Excel can do logarithmic axes and can graph an axis backwards, but neither are needed for the above magnitude data.  

Encourage students to swap roles when they reach Phase 2. 1:30+

Assessment

Formative

• During the activity, the teacher can observe how students are working together,  whether they are "getting" the goals, and if they are staying on task.  

Summative

• Collect groups' answers to questions, and printouts of graphs.  
• Teacher can have a wrap-up discussion to assess student knowledge.  
• Students can perform further research about the H-R diagram, magnitude, color, or other related topics.  

Accommodations

Students with visual disabilities are most readily accommodated with computers with enlarged font or screen readers.  

• Give the data file already typed rather than making them type the data in by hand.  
• Provide computers with screen readers, Braille output, or adjust font or magnification size for students with some visual ability.  
• If other accommodations are not available, pair with students of typical visual ability.  

Students with ADD/ADHD can be assigned to help pass out materials or perform the data entry.  Students who finish early can be given additional tasks, such as using the definition of apparent magnitude to calculate the distance to the objects, or researching the different filters and other related topics online.  

References

• SDSS lesson
• 30 closest stars
• 25 brightest stars
• CDS
• SIMBAD