Solutions PROBLEM SET #4
APAS 1200 SECTION 001
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).
Star m d (pc) T (K) M Sp Type (MGW)
Altair
.76
5.1
8100
2.22
A8
M
h Cas
A
3.45
5.9
6030
4.6
G0
M
h Cas
B
7.51
5.9
3480
8.65
M0
M
t
Ceti
3.50
3.6 5120
5.72
G8
M
UV
Ceti
12.95
2.7
2700
15.79
M6
M
e
Eridani
3.7
3.3 4600
6.11
K2
M
g Cygni
2.2
250
6250
-4.78
F8
G
40
Eridani
4.4
4.9
4700
5.95
K1
M
Sirius
A
-1.46
2.7
9600
1.38
A1
M
Sirius
B
8.7
2.7 27000
11.5
B0
W
Procyon
A
0.37
3.5
6580
2.65
F5
M
Procyon
B
10.7
3.5
7000
12.98
F3
W
YZ Canis Minoris
11.2
6.1
2950
12.27
M4
M
g Andromedae
2.1
75
4430
-2.27
K3
G
L145-141
11.4
5.0
15000
12.9
B5
W
Wolf
359
13.5
2.3
2400
16.7
M8
M
Proxima Centauri
11.0
1.3
2800
15.4
M5
M
a Centauri
A
0.0
1.3
5800
4.43
G2
M
a Centauri
B
1.33
1.3
4130
5.76
K5
M
d Pavonis
3.55
5.7
5400
4.77
G6
M
61 Cygni
A
5.2
3.4
4100
7.54
K5
M
61 Cygni
B
6.0
3.4
3850
8.34
K7
M
b Persei
2.2
32 12500
-0.32
B8
M
Antares
1.0
130 3400
-4.57
M1
G
Regulus
1.35
26
13500
-0.72
B7
M
Spica
1.0
80
25000
-3.51
B1
M
z Ophiuci
2.6
190 30000
-3.79
O9
M
z
Puppis
2.2
700 40000
-7.02
O5
M
5. Use the fact that the Sun has an absolute magnitude of 4.5 and a luminosity of 4x1026ergs/s to scale to other stars. Use the Stefan-Boltzmann Law to calculate the radius of Sirius A, Sirius B, and Antares.
A) Sirius A: M= 1.38
b) Sirius B M=11.5
c) Antares M = -4.57
