ASTR 3730 Problem Set #4 Reading: Chapters 10 and 13 Note. Please feel free to use Excel or other computer programs to complete this assignment. 1. Page 2 carries a list of stars together with their apparent magnitudes, distances, and temperatures. For each one calculate the absolute magnitude and enter it in the blank column labeled M. Use the formula:              where d is the distance in parsecs.  Example, Altair -- m=0.76, d=5.1pc M=.76+5.-5.log(5.1) M=5.76-5.x.707 M=2.2  2. Use interpolation from the following table to estimate the spectral type of each star. Enter type in column Sp of page 2. (If you don't know what interpolation means, look it up!) Spectral Type                  Temperature (K) O5                                    40,000 B0                                     28,000 B5                                     15,500 A0                                      9,900 A5                                      8,500 F0                                       7,400 F5                                       6,580 G0                                       6,030 G5                                       5,520 K0                                       4,900 K5                                       4,130 M0                                       3,480 M5                                       2,800 M8                                       2,400   3. Plot each star on the blank HR diagram provided on page 3. Using a pencil sketch in the main sequence.   4. Return to the table on page 2 and fill in the last column. Classify each star as main sequence (M), giant (G), or white dwarf (W). 5. Use the fact that the Sun has an absolute magnitude of 4.5 and a luminosity of 4x1033ergs/s to scale to other stars. Use the Stefan-Boltzmann Law to calculate the radius of Sirius A, Sirius B, and Antares. Star                              m          d (pc)          T (K)                  M                    Sp Type                   (MGW) Altair                          .76          5.1            8100 h Cas A                    3.45          5.9           6030 h Cas B                    7.51          5.9            3480 t Ceti                        3.50          3.6           5120 UV Ceti                   12.95         2.7           2700 e Eridani                    3.7            3.3           4600 g Cygni                      2.2          250           6250 40 Eridani                  4.4           4.9            4700 Sirius A                   -1.46          2.7            9600 Sirius B                      8.7           2.7          27000 Procyon A                  0.37        3.5            6580 Procyon B                 10.7         3.5             7000 YZ Canis Minoris     11.2         6.1             2950 g Andromedae          2.1            75             4430 L145-141                 11.4         5.0           15000 Wolf 359                  13.5         2.3             2400 Proxima Centauri      11.0         1.3            2800 a Centauri A              0.0          1.3            5800 a Centauri B              1.33         1.3           4130 d Pavonis                    3.55         5.7           5400 61 Cygni A                 5.2           3.4           4100 61 Cygni B                 6.0           3.4           3850 b Persei                      2.2           32          12500 Antares                      1.0            130          3400 Regulus                      1.35          26          13500 Spica                         1.0            80          25000 z Ophiuci                   2.6           190         30000 z Puppis                    2.2            700        40000