2023年4月10日

1. Report task2
(Question 1) : The sun has a temperature of 5700 K and its radius is .
By using Stefan-Boltzmann’s law , please calculate the
luminosity of the sun
6.96 × 108
[m]
F = σT4
[W ⋅ m−2]
L[W]
(Question 2) : By including following keywords, please explain Hubble's law.
[keywords] spectroscopy, Doppler effect, velocity, galaxy, expansion
(Question 3) : Please choose one telescope below and explain the telescope’s scientific
achievement.
σ = 5.67 × 10−8
W ⋅ m−2 ⋅ K4
•Subaru telescope •ALMA telescope •FAST telescope

2. •Please send your report to shimabukuro@ynu.edu.cn by PDF.
Report task
Please including following information
1. The tittle of your email is “现代天⽂学作业报告”
2. Your name (姓名)
3. Your student number（学号）
Deadline of the submission: 2023/4/17 (Monday)
I accept the report written by English or Chinese, but I recommend you to write the report by
English (and it is very helpful for me!). Even if your English is wrong, it does not affect your
score.

3. Introduction to modern astronomy13
島袋隼⼠(Hayato Shimabukuro)（云南⼤学、
SWIFAR）
©GETTYIMAGES

4. 7. The stars（恒星）

5. Constellation（星座）
•When you look up sky, you can find many stars.
•Some stars consist constellation(星座)
•The stars you can see at night is similar to the
Sun. These kind of stars are called “Stellar
stars(恒星)”

6. Star in the universe
•By the way, how many stars does the Milky
Way (our galaxy) contain??
1.～10-100 million(1000万-1亿)
2. ~ 1-10 billion (10-100亿)
3. ~ 10-100 billion (100-1000亿)
4. ~ 100-1000 billion (1000亿-1兆)
5. ~ 1trilion (>1兆)

7. Star in the universe
•By the way, how many stars does the Milky
Way (our galaxy) contain??
1.～10-100 million(1000万-1亿)
2. ~ 1-10 billion (10-100亿)
3. ~ 10-100 billion (100-1000亿)
4. ~ 100-1000 billion (1000亿-1兆)
5. ~ 1trilion (>1兆)
Our galaxy is estimated to contain 200-400
billion stars(2000-4000亿)

8. What is “star”?
•（stellar) Stars（恒星）are different from planets.
≠
What is the difference between stars and planets ?
Star Planet

9. The difference between stars and planets
•Stellar stars are massive, luminous objects that generate energy
through nuclear fusion, while planets are smaller, non-luminous
objects that orbit around stars and do not generate their own
energy.

10. Distance to other stellar stars
•The closest stellar stars from the sun is Proxima Centauri
(4.25 light years)
•We often use “light year(光年)” to measure distance to
other stellar stars. It is O.K. for neighbor stars. But, for
more distant stars, we use another unit to express
distance, called “pc (parsec)”
•At first, let’s see very easy example.
•How far is it from the observer
to the tree?

11. 30°
3m
?
x × tan 30∘
= 3 → x = 3/tan 30∘
= 3m
Triangulation（三⾓测量）

12. 30°
1AU
?
Annual parallax（年度视差）
x × tan 30∘
= 1 → x = 1/tan 30∘
= 3AU

13. Annual parallax（年度视差）
•For example, when the earth is located at point A, we
can watch the star like figure A
A B
A B
•After a half year, we the earth is located at point B
and we can watch stars like figure B
•Since we know the distance between the sun and the
earth, we can estimate the distance from the sun to
the star.
•Then, we can measure parallactic angle.

14. Annual parallax（年度视差）
•For example, when the earth is located at point A, we
can watch the star like figure A
A B
A B
•After a half year, we the earth is located at point B
and we can watch stars like figure B
•Since we know the distance between the sun and the
earth, we can estimate the distance from the sun to
the star.
•Then, we can measure parallactic angle.

15. Annual parallax（年度视差）
•For example, when the earth is located at point A, we
can watch the star like figure A
A B
A B
•After a half year, we the earth is located at point B
and we can watch stars like figure B
•Since we know the distance between the sun and the
earth, we can estimate the distance from the sun to
the star.
•Then, we can measure parallactic angle.

16. Annual parallax（年度视差）
•For example, when the earth is located at point A, we
can watch the star like figure A
A B
A B
•After a half year, we the earth is located at point B
and we can watch stars like figure B
•Since we know the distance between the sun and the
earth, we can estimate the distance from the sun to
the star.
•Then, we can measure parallactic angle.

17. Annual parallax（年度视差）
•When we measure annual parallax, we often use arcsec(′′), arcmin（′）instead of degree(°)
1′

′

(
1
3600 )
∘
1′

=
(
1
60 )
∘
Parsec(pc) is defined as the distance at which 1 AU subtends an angle of 1′

′

1AU
1′

′

1pc
~3.26 light years
•If we measure the annual parallax, we can calculate the
distance to the stars.
(Ex.)
The Alpha Centauri’s annual parallax is
0.74′

′

?
tan(1′

′

) ∼ 2.78 × 10−4
tan(0.74′

′

) ∼ 2.06 × 10−4
(Hint)

18. Annual parallax（年度视差）
•When we measure annual parallax, we often use arcsec(′′), arcmin（′）instead of degree(°)
1′

′

=
(
1
3600)
∘
1′

=
(
1
60 )
∘
Parsec(pc) is defined as the distance at which 1 AU subtends an angle of 1′

′

1AU
1′

′

1pc
~3.26 light years
•If we measure the annual parallax, we can calculate the
distance to the stars.
(Ex.)
The Alpha Centauri’s annual parallax is
0.74′

′

~1.34pc

19. The map of Milky way
By using annual parallax, Gaia satellite measured ~1.8 billion
stars’ distance and made Milky way’s map.

20. Luminosity and apparent brightness
•In the astronomy, “brightness（亮度）” is also essential property similar to distance
•Imagine that you observe candles which are located at different distance to you.
•On the other hand, the candle which has larger distance to you seems darker although the
candle which has smaller distance to you seems brighter.
•The brightness which depends on distance is called “apparent brightness（视亮度）”
•The candle’s itself brightness is called “luminosity（光度）”. We often express luminosity as L
∝
L
r2
Understand the difference between luminosity and apparent brightness!

21. Apparent magnitude（视星等）
•We sometimes use apparent magnitude（视星等）to express how stars are bright. We use
as apparent magnitude.
m
•Smaller apparent magnitude is brighter.
•If apparent brightness becomes 1/100,
then apparent magnitude increases 5.
(Ex)
The difference of apparent magnitude between full moon and the sun is 14. Thus, the sun is
brighter.
100
14
5 ∼ 4.0 × 105

22. Absolute magnitude（绝对星等）
He is brighter

23. Absolute magnitude（绝对星等）

24. Absolute magnitude（绝对星等）
He is apparently brighter

25. Absolute magnitude（绝对星等）
He is apparently brighter
It’s unfair!

26. Absolute magnitude（绝对星等）
•Each star has different distance from us. Thus, we need standard brightness to compare
them fairly. We define absolute magnitude（绝对星等） for each stars.
He is apparently brighter
It’s unfair!

27. Absolute magnitude（绝对星等）
•If a star is assumed to be 10 pc away, its apparent magnitude is defined as its absolute
magnitude. We often express absolute magnitude as .
M
10pc
m − M = 5 log10 (
d[pc]
10pc )
•If a star is distance [pc] far away from us, there is a relation between distance,
apparent magnitude , and absolute magnitude .
d
m M
•We easily measure apparent magnitude of star. Thus, if we would like to know the absolute
magnitude , we need to know the distance of the star.
m
M d
M
Important point

28. Absolute magnitude（绝对星等）
•If a star is assumed to be 10 pc away, its apparent magnitude is defined as its absolute
magnitude. We often express absolute magnitude as .
M
10pc
m − M = 5 log10 (
d[pc]
10pc )
•If a star is distance [pc] far away from us, there is a relation between distance,
apparent magnitude , and absolute magnitude .
d
m M
•We easily measure apparent magnitude of star. Thus, if we would like to know the absolute
magnitude , we need to know the distance of the star.
m
M d
M
Important point
To measure distance to stars or galaxies
is very important!!

29. Stellar temperature
•Remember blackbody radiation（⿊体辐射）
•If we observe stars by electromagnetic wave with a few as two wavelength (or frequency)
and obtain fluxes, we can measure the temperature by fitting blackbody radiation.
•We know the radiation from stars is approximately
blackbody radiation.
I(ν, T) =
2hν3
c2
1
ehν/kT − 1

30. Stellar temperature
•Remember blackbody radiation（⿊体辐射）
•If we observe stars by electromagnetic wave with a few as two wavelength (or frequency)
and obtain fluxes, we can measure the temperature by fitting blackbody radiation.
•We know the radiation from stars is approximately
blackbody radiation.
I(ν, T) =
2hν3
c2
1
ehν/kT − 1

31. Stellar temperature
•Remember blackbody radiation（⿊体辐射）
•If we observe stars by electromagnetic wave with a few as two wavelength (or frequency)
and obtain fluxes, we can measure the temperature by fitting blackbody radiation.
•We know the radiation from stars is approximately
blackbody radiation.
I(ν, T) =
2hν3
c2
1
ehν/kT − 1

32. Stellar temperature
•Remember blackbody radiation（⿊体辐射）
•If we observe stars by electromagnetic wave with a few as two wavelength (or frequency)
and obtain fluxes, we can measure the temperature by fitting blackbody radiation.
•We know the radiation from stars is approximately
blackbody radiation.
I(ν, T) =
2hν3
c2
1
ehν/kT − 1

33. Stellar temperature
•Remember blackbody radiation（⿊体辐射）
•If we observe stars by electromagnetic wave with a few as two wavelength (or frequency)
and obtain fluxes, we can measure the temperature by fitting blackbody radiation.
•We know the radiation from stars is approximately
blackbody radiation.
I(ν, T) =
2hν3
c2
1
ehν/kT − 1

34. Stellar temperature
•Remember blackbody radiation（⿊体辐射）
•If we observe stars by electromagnetic wave with a few as two wavelength (or frequency)
and obtain fluxes, we can measure the temperature by fitting blackbody radiation.
•We know the radiation from stars is approximately
blackbody radiation.
I(ν, T) =
2hν3
c2
1
ehν/kT − 1

35. Color index
•In astronomical observation, we use color
band (filter) to measure flux at certain
wavelength.
(e.g.) B band : 380-480nm
V band : 490-590nm
•Fluxes measured by B and V bands are enough to specify blackbody’s curve and determine
star’s temperature.
T = 4600 K
(
1
0.92(B − V) + 1.7
+
1
0.92(B − V) + 0.62)
.
Larger : redder, low temperature
B-V
Smaller :bluer, high temperature
B-V

36. Stellar spectra（恒星光谱）
•Because stellar stars have atmosphere, the radiation from
stars are absorbed.
•Depending on the atmospheric elements, the wavelengths at
which absorption lines are appeared different.
•Stellar stars are classified according to its temperature and
spectra lines (O,B,A,F,G,K,M)
“Oh, Be A Fine Girl, Kiss Me”. *I think this way of remembering is not good in
this current era.

37. Stellar size
Red Giant（红巨星）
Surface temperature: ~5000K
Radius: 10-100 times of the sun. Some red giants have radius
which is 1000 times of the sun (super red giant)
(White) dwarf（矮星）
Radius: 0.8-2% of the sun (similar to the earth)
Mass: 0.17-1.33 times of the sun
Small radius, but mass is large > high density!
Very large star!
•The luminosity of stars usually depends on its size and
temperature

38. Stellar size
Red Giant（红巨星）
Surface temperature: ~5000K
Radius: 10-100 times of the sun. Some red giants have radius
which is 1000 times of the sun (super red giant)
(White) dwarf（矮星）
Radius: 0.8-2% of the sun (similar to the earth)
Mass: 0.17-1.33 times of the sun
Small radius, but mass is large > high density!
Very large star!
Luminosity ∝ (Radius)2
× (Temperature)4
•The luminosity of stars usually depends on its size and
temperature