Useful information:
Astronomers measure the brightness of a star in magnitudes. This is a very old system used by the Greeks who called the brightest stars magnitude 1 and the faintest that they could see (without a telescope, of course) magnitude 5. It is a logarithmic system in which a difference of five magnitudes corresponds to a factor of 100 in brightness. Thus, if two stars have the luminosities l₁ ans l₂, respectively, their magnitudes are related by the formula
log₁₀(l₁/l₂) = 0.4*(m₂-m₁)  or  l₁/l₂ = 10^[0.48(m₂^-m₁^)]
Absolute magnitude is the apparent brightness of the sun at a distance of 32.6 light years. The absolute magnitude can be found from the equation
M = m + 5 - 5*log(plx) where M=absolute magnitude, m=apparent magnitude, and plx is the parallax.
The distance of a star in light years is 3.26 times the reciprocal of the parallax in arcseconds.
The sun's absolute magnitude is about +5; its color, B-V is about 0.54.
The magnitude difference between a star's brightness in the blue (on old films) and that as seen by the eye, B-V, is a measure of the color of a star; the redder (cooler) a star, the larger is its B-V.
Radial velocity is usually measured in kilometers/second. (To express it in miles/second, divide by 1.6.) It is positive if the star is moving away (receding) and negative if the star is approaching the observer.
Number of kilometers in a light year = 0.95 * 10¹³ (9,500,000,000,000)         kilometers         
Number of seconds in a year = 3.16 * 10⁷ (31,600,000) seconds

Collect the data
Select the catalog 5070A, Gliese's catalog of Nearby Stars. (Gliese is a German astronomer who spent many years collecting data on the stars closest to the sun. For the brighter stars, much of his data on stellar positions and distances has been superseded by data from the Hipparcos satellite.)

In the table showing the types of data, click on RA, DE, pm, RV, Vmag, B-V, plx, and Mv,. In the line for plx, change the smaller value to 217. This will limit the list to stars closer than 15 light years and limit the number of records you receive to a reasonable number to work with. Note the column that explains each type of data. Also, note the units for each type of data. (A milliarcsecond (mas) is the diameter of a dime in Seattle, Washington when seen from Columbus, Ohio.) You can use the list on-line, download it to your computer, or print it.

You now have the information you need for the following:

Projects:

Make a model of the stars within 15 light years (lty) of the solar system.

Plot the absolute magnitude of each star against its color (B-V). What percentage of the stars are redder than the sun? Are the redder stars brighter or fainter than the sun. (See the notes for more information.)
Now do the same exercise for the apparently very bright stars. Use the Bright Star Catalog, 5050. Click on HR number, Right Ascension, Declination, visual magnitude, B-V, and parallax. Set the maximum apparent magnitude at 2.2 and the minimum declination at -30. This will give you the stars that can be seen from Washington, even in a bright sky. As before, remove the arrows that fill the cell if no datum is present.  Note that in this table, the parallax is in arcseconds, not milliarcseconds. Also note that you cannot compute the absolute magnitudes for stars with negative parallaxes as a negative parallax is physically impossible. In fact, parallaxes less than 0.01 arcsec are uncertain.

Assume that the radiation per square centimeter of the surface of a star at V is independent of the color (not true; hotter stars radiate more for the same area). Compute the size of a sample of stars compared to the sun. Your sample should include a range of absolute magnitudes.

Which is the hottest star in this region? Which is the coolest? Which is the largest? Which is the smallest?

How many stars are double? You can learn more about these and other multiple stars in the Washington Double Star Catalog (1237) and the catalog of spectroscopic binaries (5064).

Which five stars are moving most rapidly angularly? (This motion is called proper motion. In French, "proper" means "its own")

Which of these stars is moving most rapidly in kilometers/second perpendicular to the direction to the sun. (This is called tangential velocity). If the proper motion and the parallax are in the same units, the velocity in kilometers/second is 4.7 times the proper motion divided by the parallax. (For miles/second, use 3 instead of 4.7.)

Which five stars are moving most rapidly in radial velocity toward the sun?

Which of the stars approaching the sun will come closest to the sun? When? At what distance?

List the stars observed by Hipparcos (1239) that are nearer than 15 light years to the sun. These will be stars whose parallaxes are greater than 217 mas (milliarcseconds) as in Gliese's catalog. The Hipparcos catalog has many files. Choose the one labeled "hip_main.dat". In this file, select (by clicking on the entries) RAhms, DEdms, Vmag, Plx, pmRA, pmDE, B-V, and SpType. The total proper motion, pm must be computed from pmRA and pmDE. THe formula is pm² = pmRA² + pmDE². The Hipparcos satellite did not observe very faint stars. Compare the data from the Hipparcos catalog with those in the Gliese catalog. The positions in the Gliese catalog are for the year 1950 while those in the Hipparcos catalog are for 2000.  (The change in star positions with time results from the precession of the pole of the earth's rotation that, in turn is the basis of the celestial coordinate system used in these catalogs.) The right ascensions (RA) of the stars in Hipparcos will be about three minutes of time larger. The declinations (DE) will also differ a little but not by as much as a degree. Aside from this difference in position, what differences do you notice between the two catalogs? Why do you think they have occurred?