Download Absolute Magnitude - School

Absolute Magnitude
recall the definition of absolute magnitude
demonstrate an understanding of the inverse square law nature of the intensity of light
demonstrate an understanding of, and perform simple calculations involving, apparent magnitude (m), absolute magnitude (M) and distance (d in pc), using
this formula:M = m + 5 – 5 log d involving powers of 10 only (students are not required to calculate d using this equation, only M and m)
Apparent magnitude (m) is how bright a star appears to be but this obviously depends on how far away it is. The
closer the star is to us the brighter it will appear to be.
The Absolute Magnitude (M) of a star is a measure of how luminous it actually is, or rather how bright it would
appear to be from a certain distance compared with every other star at the same distance.
M is defined as how bright a star would appear to be if it were at a distance of 10 parsecs from Earth. (so if a star were
actually 10 parsecs from Earth then M and m would be equal)
If we know the apparent magnitude (m) and distance in parsecs (d) a star is away from us we can calculate its
absolute magnitude (M) using this equation;
M = m + 5 - 5 log d
10
I am not going to explain logarithms here. All you need to know is that there is a "log" button on your calculator which
you can use to find log d.
Examples:
Star
d (parsecs)
m
M
Sirius
2.64
-1.47
1.41
Vega
7.67
0.04
0.5
Betelgeuse
73.6
0.41
Polaris
132
1.99
e.g. for Sirius M = -1.47 + 5 - (5 x log 2.64) = 3.53 - 2.11 = 1.42 (near enough!)
In the exam it will be even simpler than this. Any distance involved will be a multiple of 10.
If d = 100 then log10d = 2 If d = 1,000 then log10d = 3 if d = 10,000 then log10d = 4
So you shouldn't even need a calculator.
Show that the absolute magnitude of Vega is the value shown in the table and calculate the absolute magnitudes of
Betelgeuse and Polaris yourself.
The Inverse Square Law
Imagine an object, such as a star, which emits light. As the light spreads out it becomes less intense. One can see
from the diagram below that if a certain amount of light travels twice as far then it spreads out over an area four times
as big. This means that it will be 1/4 of the intensity it was.
The intensity of the light is proportional to 1/r2 where r is the distance from the source.
If there were two stars as luminous as each other but one was twice as far away as the other then it would appear 1/4
as bright as the other.
If two stars appeared the same brightness but one was further away we know from the above that it is √ 2 x further
than the closer star.