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Stellar Magnitudes and
Exponentials
Exponents

52 = 5x5= 25

63 = 6x6x6 = 216

74 = 7x7x7x7 = 2401
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4-2 = 1/42 = 1/16 =0.0625
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52.3 = 40.52
Stellar Magnitudes

Based on the brightness of stars

Used in comparing the brightness of two stars
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An arbitrary scale not an absolute scale

In science and math “arbitrary” just means
your making a scale for comparison. There is
no in natural absolute for what you are doing.
What is an Arbitrary Scale?

It’s a scale that is made up.
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Example- the Celsius Temperature Scale
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Freezing point of water 0o
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Boiling point of water 100o
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Divide the distance on thermometer with 100
marks
Kelvin Scale an Absolute Scale


Based on absolute zero- all molecular
motion stops
0 Kelvin = -273o Celsius
Number Line
Stellar Magnitude
Magnitude
Example
-25
The Sun -26.7
-20
-15
-10
The Moon -12.6
-5
Venus -4.4
Stellar Magnitude
Magnitude
Example
0
Sirius -1.4 Brightest star
+5
+6 Naked Eye Limit
+10
+10 Binocular Limit
+15
Pluto +15.1
+20
Largest Telescope (visual limit)
Stellar Magnitude
Magnitude
Example
+25
+30
Hubble Space Telescope and large
Earth Based Telescopes Photo
Graphic Limit +30
Stellar Magnitude Based on an
Arbitrary Scale

Base is 2.512

2.5125 = 100

The stellar magnitude Scale is an exponential scale


A magnitude difference of 5 equal a brightness
difference of 100
Greek Astronomer Hipparchus
Sample Problem

Proxima Centauri apparent magnitude +11.09
Alpha Centauri A apparent magnitude
-0.01

Distance on the number line 11.1
Which star is brighter?
Could you see Proxima Centauri without a telescope?
Could you see Alpha Centauri A without a telescope?
Sample Problem




How much brighter is Alpha Centauri A than
Proxima Centauri?
2.51211.1 = 27,556.11
The apparent brightness of Alpha Centauri A
is 27,556.11 times as bright as Proxima
Centauri
Notice this is a method for comparing it is not
an absolute scale.