History of magnitude scales; brightness, luminosity, and Power of a star; Stefan-Boltzmann Law; Stellar Parallax; and Wien's Displacement Law of blackbody radiation.

1. Intro to Astrophysics
NIS Grade 11 Physics
By Mr. Marty
Visible Brightness = Apparent magnitude ‘m’, Absolute
Magnitude ‘M’, Luminosity and Star classification

2. Objectives:
• Understand that stars are classified by luminosity
which relates to their brightness and measured in
terms of apparent magnitude
• define apparent and absolute magnitude in terms
of “m”
• define absolute magnitude “M” of a star as the
apparent magnitude ‘m” it would have if the star
is at 10 parsecs

3. Apparent Magnitude
• Introduced by the Greek astronomer Hipparchus
– Based on naked eye observations
– Hipparchus used 6 levels of brightness that he called
magnitudes.
• Brightest stars – first magnitude
• Half as bright – second magnitude
• Dimmest stars – sixth magnitude
• Apparent magnitude decreases as
brightness increases!

4. The Apparent Magnitude Scale “m”
• The Apparent Magnitude was formalized in 1856 with
exact numerical basis of how bright a star “appears” to
a person on Earth. It is an extension of Hipparchus’
original magnitude scale.
• This magnitude scale is backwards, larger number in
magnitude means the star is dimmer.
• Our Sun has m = -26, the dimmest star seen by the
unaided eye has m = 6 and the faintest objects
observable in visible light have m = 36

5. Apparent Magnitude “m”, a measure
of brightness as seen from Earth
• The scale is logarithmic, because first magnitude stars
are 100 times brighter than sixth magnitude stars, a
magnitude difference of ‘1’ corresponds to brightness
difference factor of 2.512 = (5
100)√
• The brightness of a star is defined as the amount of
energy per second (power) striking a unit area at the
Earth’s surface.
• Also called the ‘Intensity’ of light hitting the Earth.
• Sometimes it is called the flux (flow per unit area), in
astronomy the it is the flow of radiant energy coming
to the Earth’s surface per meter squared per second.

8. Absolute Magnitude, “M”
• Absolute Magnitude “M”: the magnitude a star
would appear to have if it is placed at a distance of
10 parsecs from Earth.
• m-M = 5 log(d) – 5 where d = distance to the star in parsec
This formula does not need to be known by learners, although they should know:
stars closer than 10 pc, M is less bright and has a larger number
absolute magnitude than apparent magnitude, M > m
 stars further than 10 pc, M is more bright and has smaller
number absolute magnitude than apparent magnitude, M < m
stars at 10 parsecs have absolute magnitude equal to apparent
magnitude, M = m

9. Absolute Magnitude of our Sun
Our Sun would have a magnitude of 4.8 if it were
at 10 pc, so its absolute magnitude is 4.8!
Apparent magnitude = -26 Absolute Magnitude = 4.8
Image comparison
is estimated

10. Brightness of a Star Depends on
1. Distance and 2. Power or Luminosity of the star

11. The Inverse Square Law
The brightness of a star depends on both its luminosity and its
distance. The farther away a star is, the dimmer it will appear.
The brightness decreases as the square of the distance, the same
principal as Newton’s Law of Universal Gravitation.

12. Luminosity
• The luminosity of a star represents the Power of the
star (amount of energy a star emits per second).
• Astronomers specify luminosity using the same
magnitude scale that they use for brightness.

13. Luminosity = Power Output
The apparent brightness of a star is inversely
proportional to the square of its distance and its
Power is equal to Sigma x
Area x
Temperature4
(Kelvin).
b = L /(4πd2
) and B = σ T4
, because b=B when
d=r
L = 4πr2
σT4
→ P = σA T4
→ Stefan’s law
where: b=apparent brightness , B=absolute brightness, L=luminosity,
P=Power , d=distance to star, r=radius of star, T=temperature in
Kelvin and σ = 5.67 x 10-8
Wm-2
K-4
, is Stefan’s constant

14. Most stars have low luminosity

15. How do Astronomers measure
distances to stars and galaxies?

16. Stellar Parallax
• Stellar parallax is a direct trigonometric technique for
measuring distance by taking observations from 2
locations.
• Definition: A parallax angle is the shift, relative to
the background, caused by a shift in the observer’s
position.

19. Other Units for Stellar Distances
• One unit frequently used for stellar distances is the
light year (ly), the distance light travels in one year
(about 10 trillion kilometers).
• Astronomers use the parsec (pc), the distance from
which the size of Earth’s orbit around the Sun would
appear to be 1 arcsecond. A parsec is 3.26 light years.

20. • Parallax is denoted by ‘p’.
• Distance (d) is measured in parsec.
• d = 1 parsec = the distance at which a star has a
parallax (p) of 1 arc second.
1 parsec = 3.26 light years.
Also d = 1/p
Closest star, Proxima centauri, p = 0.772 arc
seconds. Hence distance ‘d’ in parsec is
d = 1/p = 1/0.772 = 1.3 parsec = 4.2 light years

21. The Limits for Measuring the Distance
to Stars by Parallax
• The nearest star is 4.2 ly (1.29 pc) away. Thus its
parallax is less than 1 arcsecond.
• The smallest parallax which can be accurately
measured is about 0.01 arcseconds. This corresponds
to a distance of 100 pc or 326 ly.
• Our Milky Way galaxy is about 100,000 ly across, so
stellar parallax can be accurately measured for only
the nearest stars.

22. Distances to farther away stars
Calculation techniques require the use of
• Apparent Magnitude (m)
• Absolute Magnitude (M)
• Luminosity (L)
• Inverse Square Law

23. The Surface Temperatures of Stars
•A star’s color reveals the surface temperature.
Blue stars are hotter than white stars and white stars are
hotter than red stars.
• The Wien's Displacement Law state that the wavelength
carrying the maximum energy is inversely proportional to the
absolute temperature of a black body. λmax T = b
λmax = Wavelength of maximum intensity ( meters )
T = Temperature of the blackbody ( kelvins )
b = Wien's displacement constant = 2.8977685 ± 51 × 10-3
meters·kelvins
Reference: http://www.physicshandbook.com/laws/wienlaw.htm
• A star’s spectrum reveals the surface temperature,
and additionally the chemical composition, atmospheric pressure,
and rotation rate.

24. Thermal Radiation:
Temperature and color of radiation
Hot……. Hotter…... Hottest!

25. Must Watch video for Homework:
• Our simulation Lab on Mon/Tue will give you
an experience with Wien’s Displacement Law
which relates the Wavelength emitted by a
blackbody to its temperature.
• The temperature and composition of stars:
• http://www.youtube.com/watch?v=01U7ZUKVW8o

26. Black Body Radiation and Wien’s Law
http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html

27. Black Body Radiation and Wien’s Law
http://hyperphysics.phy-astr.gsu.edu/hbase/wien.html#c2

29. Surface Temperature and Apparent Color of
Stars

30. Vocabulary Terms of Astrophysics
Astronomy Term Definition Russian Kazakh
Absolute Magnitude
“M”
The apparent magnitude a star would have
at 10 parsecs (32.6 light years)
Абсолютная величина
"М"
Apparent Magnitude
brightness “m”
Each division is 2.51 times brighter than
the next magnitude, sun has m= -26
Кажущаяся яркость
Магнитуда "м"
Apparent Magnitude
scale
A modern version of Hipparchus scale Полная шкала
Магнитуда
Intensity Power per unit area at the observer:
I=P/4πr2
интенсивность
Luminosity Total power radiated by a star
(joules/sec=watts), depends on the
temperature and distance between the
star and the observer. L≈ d2
T4
светимость
Parallax Angle The shift, relative to the background,
caused by a shift in the observer’s position.
Параллакс Угол
Parsec The distance at which one AU subtends an
angle of one arc second (1/3600th
of a
degree), 1 pc = 3.26 light years
парсек
Relative Brightness
scale
A scale created by in 120 BC where 1 is the
brightest star and 6 is the dimmest star
Относительная шкала
Яркость
Spectral Class A classification of a star based on
features of its spectrum which also indicate
its surface temperature and chemical
composition
Спектральный класс
Wein’s Displacement
Law
Defines a relationship between the peak
radiation emitted by a star and its
temperature.
Объем Закон Wein в

31. References:
• Wien’s Law from Physics Handbook:
• http://www.physicshandbook.com/laws/wienlaw.htm
• Astronomy General Topics Page with links to specific topics:
http://www.astro.cornell.edu/academics/courses/astro201/topi
cs.html
• Windows to the Universe from National Association of Earth
Science Teachers:
• http://www.windows2universe.org/the_universe/Stars/magnit
ude_scale.html
• Spectral Classes of Stars:
• http://hyperphysics.phy-astr.gsu.edu/hbase/starlog/staspe.html
• Wien’s and Stefan-Boltzman Laws explained:
• http://csep10.phys.utk.edu/astr162/lect/light/radiation.html

32. References 2:
• Brightness, Luminosity and Radius:
• http://science.howstuffworks.com/star3.htm
• Luminosity and how far away things are:
• http://zebu.uoregon.edu/~soper/Light/lumin
osity.html
• Properties and Classification of Stars:
• http://www2.astro.psu.edu/~mce/A001/lect
13.html