Download Apparent Magnitude

Ch 28 Apparent Magnitudes
In 125 B.C., a famous astronomer of that time, named Hipparchus, was making a star
map of the “celestial sphere”. Hipparchus not only wanted to locate each star’s position on his
map, but also to indicate the brightness of each star. To do this Hipparchus invented the concept
of stellar magnitude. Hipparchus designated the brightest stars as stars of the first magnitude.
The dimmest stars visible he designated sixth magnitude stars. The other stars were given
magnitudes from second through fifth. Notice the brighter the star, the lower the actual number
of the magnitude. The symbol for apparent magnitude is a lower case m.
Hipparchus’ system was used until the late 1700’s when it became possible to more
accurately measure stellar magnitudes. William Herschel modified the system into essentially the
system we use today. Herschel determined the difference in brightness between each magnitude
is equal to 5√100 or 2.512. For the purpose of our calculations, we will use the approximation of
2.5. We can therefore produce the following table.
Table 1
Difference in Magnitudes
1
=
2
=
3
=
4
=
5
=
(2.5)1
(2.5)2
(2.5)3
(2.5)4
(2.5)5
Difference in Brightness
= 2.5
= 6.25
= 16
= 40
= 100
Example 1 If one star is a first magnitude star and the other is a third magnitude star, what is the
difference in brightness?
Answer We first find the difference in magnitude between the two stars (3-1=2). Then we look
for the number 2 in the left hand column in Table 1. Now read horizontally across to the right
hand column. The answer is 6.25 times difference in brightness.
Problems
1a. Star A has a magnitude (m) of 1; Star B has a magnitude (m) of 4. Using Table 1, what is the
difference in brightness between the two stars?
1b. Which is the brighter star?
2a. Star A has a magnitude (m) of 2, star B has a magnitude (m) of 6. What is the difference in
brightness between the two stars?
2b. Which is the brighter star?
Remember that the brighter the star, the lower the magnitude, and that the average of the
20 brightest stars is magnitude 1. Since some of these stars are brighter than the average of their
group, a few stars have magnitude lower than 1, and in fact, lower than zero (ex. Negative #’s)
Example What is the difference in brightness between a m +2 star and a m or –1 star?
Answer The difference in magnitude is three (+2-(-1)=3). Therefore, the difference in
brightness (using Table 1) is 16. Also, the star with m= -1 is the brighter star.
Problems
3a. Star A has a m of 4, star B has a m= -1. What is the difference in brightness between the
two stars?
3b. Which star is the brighter star?