1. The table below provides the spectral class and absolute magnitude data for 14 Main Sequence stars. The first step will be to convert the absolute magnitude into luminosity in solar units for each of these stars. Step 2 gives an explanation on how to use the formula L = 85.51 x 1O~"'
2. We will calculate the star's luminosity in three steps:
Step I: If the star's absolute magnitude M = +3, (-0.4M) = (-O.4)x(+3) = -1.2
Step ii: Calculate 1O~' , by punching into your calculator, 10, then press the yX
key or the A key, then enter —1.2. The answer should be 0.063.
Step iii: Multiply 85.51 with 0.063. Answer is 5.4.
3. Let's try another example. Suppose a star has an absolute magnitude of -2.0.
Therefore, M = -2.0
Step i: (-0.4) x (-2.0) = 0.8
Step ii: 10-04M= 100J=6.31
Step iii: L= 85.51 x 6.31 = 539.5
4. Use the procedure outlined above to fill in the following table:
| Star Name | Spectral Type | Absolute Magnitude (M) |
| Spica | B1 | -3.6 |
| Achernar | B5 | -1.0 |
| Regulus | B7 | -0.6 |
| Vega | A0 | +.05 |
| Sirius | A1 | +1.4 |
| Fomalhaut | A3 | +2.0 |
| Procyon A | F5 | +2.6 |
| Zeta-Cancer | F8 | +3.9 |
| Eta-Cassiopeia | G0 | +4.5 |
| Alpha Centauri | G2 | +4.4 |
| Mu-Cassiopeia | G5 | +5.7 |
| Tau-Ceti | G8 | +5.7 |
| Epsilon-Eridani | K2 | +6.1 |
| Erdani Lacaille | M0 | +8.7 |
| Stars Name | -0.4M | 10^-0.4M | L=85.51X10^-.04M |
| Spica | 1.44 | 27.5 | 2350 |
| Achernar | ___________ | ___________ | ___________ |
| Regulus | ___________ | ___________ | ___________ |
| Vega | -.02 | 0.63 | 53.9 |
| Sirius | ___________ | ___________ | ___________ |
| Fomalhaut | ___________ | ___________ | ___________ |
| Procyon A | ___________ | ___________ | ___________ |
| Zeta-Cancer | ___________ | ___________ | ___________ |
| Eta-Cassiopeia | ___________ | ___________ | ___________ |
| Alpha Centauri | ___________ | ___________ | ___________ |
| Mu-Cassiopeia | ___________ | ___________ | ___________ |
| Tau-Ceti | ___________ | ___________ | ___________ |
| Epsilon-Eridani | ___________ | ___________ | ___________ |
| Lacaille | ___________ | ___________ | ___________ |
B. DRAWING THE H-R DIAGRAM
5. The semi-log graph paper is at the end of this exercise. The spectral class will be marked along the horizontal (x) axis and the luminosity scale along the (y) axis must be chosen as shown. Notice that the luminosity values in the table, range from 2350 for Spica to about 0.028 for Lacaille. To enable us to plot this large range of numbers, we allow each large square to increase by a factor of 10. Notice that the lines on the graph paper along the vertical axis are not evenly spaced. This scale is called "logarithmic." Since the numbers increase evenly along the x-axis, the graph paper is called "semi-logarithmic." Choose the numbers along the y-axis as shown.
6. Plot the luminosity versus spectral class for the 14 stars given above. These are all main sequence stars. Draw a smooth curve through the middle of the points. You do NOT have to join all the dots, but draw a line (use a high lighter pen if you prefer) that represents the "average" position. This is the main sequence line.
C. USING THE H-R DIAGRAM
7. Let us use all the information we have accumulated to calculate the physical properties of Denebola, (beta Leo). Its spectral classification is A3.
8. From the H-R diagram x-axis, you can estimate that Denebola's temperature is between 9,000 and 9,500 K, let's choose it to be 9,400K. But 9400/5800 = 1.6 solar temperature.
9. If you draw a line from A3 up to the main sequence line you plotted, and then read the corresponding luminosity, it turns out to be about 20 times that of the Sun.
10. From the mass-luminosity graph, a luminosity of 20 corresponds to 2 solar masses. See fIg 1 for how this is estimated.
11. Radius = [L]"2 / T2 = [20]1/2 / El .6]2 = 1.75 (solar radius) = (1.75) (7 x 1 ~8 in) = 1.23 x 109m
Relative Volume = R3 = [1 .75]3 = 5.4 (solar volume) = (5.4) (1.4 x 1 ~27 in3) = 7.56 x 1027 in3
12. Relative density = Mass /volume = 2/5.4 = 0.37 (solar density) = (0.37) (1400 kg/m3) = 518 kg/m3
13. Lifetime = T = Mass/Luminosity 2/20 = 0.1 solar lifetime = (0.1)(10 billion years) = 1 billion year.
14. Do the calculations for 61-Cygni which has a spectral classification of KS.
Temperature T =
Luminosity L =
Mass M =
Radius R =L½/T2
Volume V =R3
Density p =M/V
Lifetirne T =M/L
15. Do the calculations for Sterope, which is B8 and is one of the stars in Pleaiades.
Temperature T =
Luminosity L =
Mass M =
Radius R = L^(1/2)/T^2
Volume V = R^3
Density p = M/V
Lifetime T = M/L
16.Do the calculations for P1-3-Orion , with spectral classification F6.
Temperature T =
Luminosity L =
Mass M =
RadiusR =L½/T2
Volume V =
Density p =M/V
Lifetime T M I L
17. Sumtiarize what you have learned from this lab.