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Deciphering the Secrets of Celestial Bodies

By Yongfeng Huang, 7th Jun 2023
Translated by Yifan Wang, 7th Jun 2023

In the darkness of night, both bright and dim stars shine fabulously against the dark backdrop of the sky. It is easy to notice the various shining bodies in the sky, such as Venus or more obviously the moon. However, have you ever wondered how bright these celestial bodies actually are, and how we exactly we are able to record their brightness?  

PART.1
How do we measure the brightness of celestial bodies?

The question regarding the brightness of stars first dates itself back all the way to the ancient Greeks 2200 years ago, who, with their limited understanding of the cosmos, had decided to develop an intuitive set of measurements based off the stars they are able to see in the sky. With the brightest star being a first-magnitude star and the dimmest being a sixth-magnitude star, with this scale, they were then able to compare the brightness of stars with one another. Although such a system now may appear far too primitive and not rigorous enough, the system was still adopted and passed down the annals of time.  

Using the system of the ancient Greeks, modern scientists created a new measurement for the magnitude of stars. To make it easier to understand, try to think of the number axis we were taught in high school. A number axis has three key characteristics: its origin, the positive direction, and unit length; our scale will be defined by these characteristics. Using the brightness of the star Vega, we define the brightness of magnitude 0, and from this origin, any star with a magnitude larger than 0 will be dinner than Vega whilst any star with a magnitude smaller than 0 will be brighter. The scale follows a logarithmic coordinate system, which simply put, means that a star with a magnitude of 0 is 2.512 times brighter than a star with a magnitude of 1, -1 is to 0, 1 to 2, 2 to 3, which all follow a common ratio of 1/2.512.

But you may be wondering, why specifically 2.512? Well, as mentioned earlier, with the ancient Greek system, there had been a difference of five magnitudes between the brightest and dimmest stars. With modern measurements, scientists have found that the brightest and dimmest stars differ approximately 100 times in brightness, and as

We decided to use the figure 2.512. Coincidentally, the ability of the human eye to evaluate brightness accurately also follows a logarithmic scale, giving another reason for this method of measurement. As such, that is how an ancient Greek system has been passed down and transformed into the modern standard for measurement.

So, if we use this system on the brightest stars in the night sky, what would the ranking look like?

PART.2
Data tables & Evaluation

Table 1: Stars

Apparent Magnitude
Scientific name
English name
-26.74
-
Sun
-1.46
Alpha Canis Major
Sirius
-0.74
Carinae Alpha
Canopus
-0.27
Alpha Centauri
Rigil Centaurus
-0.05
Alpha Bootes
Arcturus
0.03
Alpha Lyrae
Vega
0.08
Alpha Auriga
Capella
0.13
Beta Orion
Rigel
0.34
Alpha Canis Minor
Procyon
0.42
Alpha Orion
Achernar
0.46
Alpha Eridani
Betelgeuse
0.61
Beta Centauri
Hadar
0.76
Alpha Aquila
Altair
0.77
Alpha Southern Cross
Acrux
0.86
Alpha Taurus
Aldebaran
0.96
Alpha Scorpio
Antares
0.97
Alpha Virgo
Spica
1.14
Beta Gemini
Pollux
1.16
Alpha Pisces
Fomalhaut
1.25
Alpha Cygnus
Deneb
1.25
Beta Southern Cross
Mimosa
1.39
Alpha Leo
Regulus
1.5
Epsilon Canis Major
Adhara
1.58
Gemini alpha
Shaula
1.62
Lambda Scorpio
Castor

Table 2: Celestial Objects in the Solar System

English name
Magnitude
Moon
-12.7
 Venus
  -4.6
 Jupiter
  -2.7
 Mars
  -2.3
 Mercury
  -2.2
 Saturn
  -0.4
 Ganymede (J3)
  4.6
 Io (J1)
  5.0
  4 Vesta 
  5.2
 Europa (J2)
  5.3
 Uranus
  5.7
 Callisto (J4)
  5.7
 Neptune
  7.9

After seeing the two tables, you may have two questions: 1. How are the decimal places of the magnitude calculated? 2. What are absolute magnitudes?

Regarding the first question, it is actually very simple, as it only requires bringing decimals into the calculation.

Imagine two stars with the brightness b1 and b2 , with the relative magnitudes m1 and m2

Then their relationship would then subsequently be:

Or:

As such even if the magnitudes are decimal, the relationship between the brightness can still be obtained.

PART.3
Observing the stars
图片2.png

When we peer into the night sky, how faint are the dimmest stars we can see, and how many of them can we see.

Again, as mentioned earlier, the ancient Greeks had defined as the dimmest stars to have a six-magnitude level of brightness, but this doesn’t necessarily mean they can be seen everywhere. This is due to the effects of light pollution, which, as the name suggests, is light emitted by human activities that constantly refracts and reflects within the atmosphere, lighting up the night skies. As stars and other bodies are easier to see in dark skies, light pollution and brighter skies subsequently makes stars less obvious and thus more difficult to see.

Fist, lets look at the distribution and quantity of stars for a specific magnitude:

Magnitude
Range
Number of stars in this range
Cumulative sum of the number of stars
Increase in the number of visible stars
-1
-1.50 to -0.51
2
2
-
0
-0.50 to +0.49
6
8
400%
1
+0.50 to +1.49
14
22
275%
2
+1.50 to +2.49
71
93
423%
3
+2.50 to +3.49
190
283
304%
4
+3.50 to +4.49
610
893
316%
5
+4.50 to +5.49
1,929
2,822
316%
6
+5.50 to +6.49
5,946
8,768
311%
7
+6.50 to +7.49
17,765
26,533
303%
8
+7.50 to +8.49
51,094
77,627
293%
9
+8.50 to +9.49
140,062
217,689
280%

Amateur astronomer Portel had also developed a scale for the levels of light pollution. With levels 1-9 corresponding to different “limiting magnitudes” (that is, the dimmest brightness that can be seen with the naked eye in a certain light condition. But for ordinary people with average eyesight, the limiting magnitude will often still need to be lowered by 1 magnitude)

图片3.png

Using the limiting magnitude, we can then correspond the total number of stars in different magnitude ranges as detailed above. Note that we can also only see half of the sky, so the number of stars we can see will also need to be divided by 2. For example, in downtown Shanghai, even under the best weather conditions, the limiting magnitude at midnight is still only about 3.5, and only about 283/2=14 stars are visible to the naked eye. Whilst on the high mountains in Sichuan, Tibet and other regions, at least more than 10,000 stars can be seen. (You can find light pollution information for their location from https://www.lightpollutionmap.info/ )

图片4.png
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