II-2b. Magnitude
(Main Ref.: Lecture notes; FK Sec.17-3)
b  1 / d2
2015
Lec 2
2b-(i)
m
naked-eye
2
Therefore, six magnitudes must have ratios
= 1001/5 = 2.512
1
2.512
2.5122
2.5123 2.5124
2.5125
1
2.512
6.310
15.851
39.818
1/5
= 100
100.023
Note” the smaller the magnitude, the brighter the
star!
Table II-1
•EX 7 Modern Magnitude
•Sun : 26.7
•Full Moon:  12.6
•Venus:  4.4
•Serius (brightest star): 1.4
•Pluto: +15.1
•Largest telescope: +21
•Hubble Space Telescope: +30
(See Fig. II-5 for more details.)
3
Astronomers often use the magnitude scale
to denote brightness
• The apparent
magnitude
scale is an
alternative way
to measure a
star’s apparent
brightness
• The absolute
magnitude of a
star is the
apparent
magnitude it
would have if
viewed from a
distance of 10
parsecs
Fig. II-5: The Apparent Magnitude Scale
4
Fig. II-6: Apparent Magnitudes
5
Math Expression
m = m2 – m1 = 2.5 log ( b1 / b2 )
Eqn(6)
See examples in FK Box 17-3.
*******************************************************************
EX 8: Venus m1 =  4;
dimmest star we can see m2 = + 6.
How many times brighter is Venus than the faintest star w
can see?
Ans: 10,000 times brighter
(See class notes, also FK Box 17-3, Example 1)
6
EX 9: RR Lyrae, variable: bpeak = 2 bmin.
What is the magnitude change?
Ans: 0.75
(See class notes, also FK Box 17-3, Example 2)
EXEX
1010
(#)
2.8
7
(#) Note: If use m = 1.12, we get 2.8 times as bright.
EX 11
8
2b-(ii) Absolute Magnitude M
• Absolute Magnitude M = m a star would have
if it were located at 10 pc
9
Math Expression
m – M = 2.5 log ( bM / bm ) Eqn(7)
m – M = 5 log ( dm / dM )
Eqn(8a)
dM = 10 pc; dm = true distance
m – M = 5 log d (pc) – 5
Eqn(8b)
(See lecture notes for derivation.)
Distance Modulus DM = m – M
Eqn(9)
See FK Box 17-3 for DM(=m – M) vs d(pc) .
e.g., DM = 4
+20
d = 1.6
105
10
EX 12

Note: If we use the exact value of 1pc = 2.066 x 105 AU  get Msun = 4.8!
11
EX 13:
A Star with m = +6 (faintest we can see by
unadied eyes) at d = 20pc.
What is the absolute magnitude?
Ans: M = + 4.5
(See class notes.)
**************************************************************
EX 14:
Suppose we are at 100 pc away from Sun. Can
we still see Sun with naked eyes? What is m of
the sun then? Note: Msun = 4.8 (see Ex 12).
Ans: No, too faint to be seen.
Reason: m = 9.8 > 6
(See class notes and FK Box 17-3, Example 4.)
*********************************************************************
Study more examples in FK Box 17-3.
Luminosity Function: The Population of Stars
(See FK pp 472-473)
12
Fig. II-7: The Luminosity Function = FK Fig. 17-5
•Stars of relatively low luminosity are more common than
more luminous stars
•Our own Sun is a rather average star of intermediate
13
luminosity