This document provides an overview of astronomy concepts including: 1. It describes the distances and locations of nearby stars like Proxima Centauri, Alpha Centauri, and Sirius. 2. It explains how stellar parallax can be used to measure the distances to stars, where a star with a parallax of 1 arcsecond is 1 parsec away. 3. It discusses how the brightness of stars decreases with the inverse square of their distance due to light spreading out over a greater area, known as the inverse square law.

1. Astonishing Astronomy 101
With Doctor Bones (Don R. Mueller, Ph.D.)
Educator
Entertainer
J
U
G
G
L
E
R
Scientist
Science
Explorer

2. Chapter 17 – The Stars

3. Nearby Stars
Proxima-Centauri
(4.23 ly)
Alpha-Centauri A,
B
(4.32 ly)
Barnard’s Star
(5.9 ly)
Sirius A, B
(8.60 ly)
Ross 128
(10.9 ly)
The Sun’s stellar
neighborhood
Sun

4. Measuring the distances to the stars: Parallax to Stellar Parallax
• As an observer’s
viewing location
changes, foreground
objects appear to
shift relative to
background objects.
• This effect is called
parallax and it can be
used to measure the
distance to closer
astronomical objects.

5. A star's apparent motion against a stellar background of more distant
stars (as the Earth revolves around the Sun) is known as stellar parallax.
A star with a parallax of 1 arc-second
has a distance of 1 Parsec.
Parallax decreases with Distance.
Example of Parallax Distance:
Alpha Centauri has a parallax of
p = 0.742 arc-seconds
d = 1/p = 1/0.742 = 1.35 parsecs

6. Earth
(December)
Earth
(June)
Sun
Distance d is in parsecs:
( 1 parsec ≈ 3.26 light-years)
d = 1/p
p
d
1 AU
The distance d to the star is inversely
proportional to the parallax p:
Parallax angle p:
Measured in arc-seconds

7. Some Trigonometry
d = 1 parsec (pc) = 3.3 ly
Circumference = 2p x 1 pc = 2p d
p = 1 arc-second


360
arcsecond1AU1
nceCircumfere


360
arcsecond1
2
AU1
dp
1,296,000
1
arcseconds1,296,000
arcsecond1
2
AU1

dp
d = 206,265 AU = 3.09 x 1013 kmπ2
AU1,296,000
d 

8. The Effect of Distance on Light
• Light from distant objects
appears to be very dim:
• Why? Because light spreads
out as it travels from source
to destination.
• The further you are from the
source, the dimmer the light.
• The object’s brightness or
amount of light received
from a source, is decreasing.
• The amount of light reaching
us is a star’s brightness.
2
d4
OutputLightTotal
Brightness
p

This is an inverse-square law :
The brightness decreases with the
square of the distance (d) from
the source.

9. The Inverse-Square Law

10. Inverse-Square Law
• Stars, like light bulbs, emits light in all
directions: called isotropic radiation.
We see the photons that are heading
in our direction.
• As you move away from the star,
fewer and fewer photons are headed
toward you, thus the star appears to
dim.
• The total amount of energy a star
emits into space is its luminosity
(power) and is measured in Watts.
• Some types of stars have a known
luminosity and we can use the
standard candle to calculate the
distance to the stars.
• The brightness decreases with the
square of the distance from the
star.
• When you move twice as far from
the star, its brightness decreases
by a factor of 22 = 4.
• If we know the total energy
output of a star (luminosity L) and
we can count the number of
photons we receive from the star
(brightness b), we can calculate
its distance d:
b4
L
d
p


11. The Hipparchus Star Magnitude Scale
• We can quantify the brightness of a
star by assigning it an apparent
magnitude or number in this case:
• Brighter stars have lower numbers.
• Dimmer stars have higher numbers.
• Differences in magnitudes correspond
to ratios in brightness.
• Hipparchus classified the naked-eye
stars into 6 star classes: the brightest
being 1st-class (magnitude) stars and
the faintest being 6th class stars.
• The “brightness” numbers in the star
ranking system of Hipparchus are
called apparent magnitudes.

12. Absolute Magnitude
• It’s easier to compare the respective luminosities of two
stars if they are at the same distance from the Sun.
• We can calculate how bright the stars would appear if they
were all the same distance from us. Solely as a matter of
convenience we choose 10 parsecs (pc).
• The magnitude of a star “moved” to 10 pc from us is
referred to as its absolute magnitude.
• For example, when a star that is actually closer to 100 pc
from us is placed at the 10 pc standard, its distance d has
decreased by 10 times. In turn, the star’s apparent
brightness would increase by a factor of d2 = 102 =100 (the
inverse square law). The star’s apparent magnitude has
decreased by a factor of 5.
• Years ago, astronomers in their refinement of the star
magnitude scale of Hipparchus, established that a difference
of 5 orders in magnitude corresponded to a factor of 100
times in brightness (intensity).

13. Relating Magnitude to Brightness Ratio
Magnitude Difference Ratio of Brightness
0 2.5120 = 1:1
0.1 2.5120.1 = 1.10:1
0.5 2.5120.5 = 1.58:1
1 2.5121 = 2.512:1
2 2.5122 = 6.31:1
3 2.5123 = 15.85:1
4 2.5124 = 39.81:1
5 2.5125 = 100:1
10 2.51210 = 104:1
20 2.51220 = 108:1

14. Photons in Stellar Atmospheres:
Absorption spectra provides, a “fingerprint” for the star’s composition.
The strength of this spectra is determined by the star’s temperature.

15. Stellar Surface Temperatures
• The peak wavelength emitted by a star shifts with the star’s
surface temperature:
– Hotter stars look blue
– Cooler stars look red
• We can use the star’s color to estimate its surface temperature:
– If a star emits stronger at a particular wavelength  (nm),
then its surface temperature (T) is often given by Wien’s Law:
λ
nmK102.9
T
6


Wien’s Law: Hotter bodies emit more strongly at shorter
wavelengths. When  decreases, T increases.

16. Measuring the Temperatures of Astronomical Objects
Wien’s Law:
To estimate the temperature T in
degrees Kelvin (K) of stars:
• We just need to measure the
wavelength (max) at which the
star emits the most photons.
• Solving for T:
If the wavelength of maximum emission
(max) for the spectral distribution of the
blackbody curve is plotted versus 1/T, a
straight line is obtained.
maxλ
nmK109.2
T
6



17. Measuring Temperature T using Wien’s Law
λ
nmK6109.2
T


Measure a star’s brightness
at several wavelengths ()
and then plot the brightness
versus wavelength.

18. The total emitted radiant energy is
proportional to the 4th power of
the temperature T (K): K4
• If we know an object’s
temperature (T), then we can
calculate how much energy is
being emitted by the object,
using the Stefan-Boltzmann law:
• The power P is in Watts, area A
is in square meters and the
Stefan-Boltzmann constant:
 = 5.6710-8 Watts/m2K4
4
σT
A
P

Stefan-Boltzmann Law
Luminosity increases rapidly with temperature

19. The Stefan-Boltzmann Law
A star’s luminosity is related to both a star’s size and temperature:
(a) Hotter stars emit more. (b) Larger stars emit more.
Each square meter
of the star’s surface
emits T4 watts.
The total energy radiated per
second is the Luminosity L:
A spherical star of radius R, has a surface area S = 4pR2
42
σTRπ4L 

20. Spectral Classification
• Spectral classification
system: By temperature
Hotter stars are O type
Cooler stars are M type
• New Types: L and T
– Cooler than M
• From hottest to coldest, they are:
O-B-A-F-G-K-M
– Mnemonics: “Oh, Be A Fine
Girl/Guy, Kiss Me
– Or: Only Bad Astronomers Forget
Generally Known Mnemonics

21. Spectral Classification
• Application of Wien’s law and theoretical calculations show
that temperatures range from more than 30,000 K for O stars
to less than 3500 K for M stars.
• Because a star’s spectral type is set by its temperature, its
type also indicates its color; ranging from violet-blue colors
for O and B stars, to reddish colors for K and M stars.
• To distinguish still smaller gradations in temperature,
astronomers subdivide each type by adding a numerical
suffix—for example, B0, B1, B2,..., B9—with the smaller
numbers indicating progressively higher temperatures.

22. Summary of Spectral Types
Spectral Type Temperature Range (K) Features
O Hotter than 30,000 Ionized helium, weak hydrogen.
B 10,000-30,000 Neutral helium, hydrogen stronger.
A 7500-10,000 Hydrogen very strong.
F 6000-7500 Hydrogen weaker, metals—especially
ionized Ca—moderate.
G 5000-6000 Ionized Ca strong, hydrogen weak.
K 3500-5000 Metals strong, CH and CN molecules
appearing.
M 2000-3500 Molecules strong: especially TiO and
water.
L 1300-2000 TiO disappears. Strong lines of metal
hydrides, water and reactive metals
such as potassium and cesium.
T 900?-1300? Strong lines of water and methane.

23. 23
O-B-A-F-G-K-M SchemeStellar Spectral Classes

24. A convenient tool for organizing stars
• A star’s luminosity depends on its temperature and diameter.
A Hertzsprung-Russell diagram is used to find trends in this relationship.
Constructing
Hertzsprung-Russell
(H-R) Diagrams

25. The H-R Diagram• A star’s location on the H-R
diagram is given by:
temperature (x-axis) and
luminosity (y-axis).
• Many stars are located on a
diagonal line running from
cool, dim stars to hot bright
stars: The Main Sequence
• Other stars are cooler and
more luminous than main
sequence stars:
Have large diameters
(Red and Blue) Giant stars
• Some stars are hotter, yet
less luminous than main
sequence stars:
Have small diameters
White Dwarf stars

26. H-R Diagram
• Most stars are
found on the
main sequence.
• Giants
• Supergiants
• White dwarfs
Main Sequence
White Dwarfs
Giants
Super Giants
Temperature (K)
Luminosity Spectral Type

27. 27
Lines of constant Radius in the H-R diagram
 Main sequence
• B stars: R ~ 10 RSun
• M stars: R ~ 0.1 RSun
 Betelgeuse:
R ~ 1,000 Rsun
(Larger than 1 AU)
 White dwarfs:
R ~ 0.01 Rsun
(A few Earth radii)
l

28. A Family of Stars

29. Stars of all sizes

30. The Mass-Luminosity Relation• When we look for trends in
stellar masses, we notice
something interesting:
Low mass main sequence stars
tend to be cooler and dimmer.
High mass main sequence stars
tend to be hotter and brighter.
• Mass-Luminosity Relation:
Massive stars burn brighter.
5.3
ML 

31. 31
Mass-Luminosity Plot
L = M3.5

32. Stellar Luminosity Classes
Class Description Example
Ia Bright
supergiants
Betelgeuse, Rigel (brightest stars in Orion)
Ib Supergiants Antares (brightest star in Scorpius)
II Bright giants Polaris (the North Star)
III Ordinary giants Arcturus (brightest star in northern
constellation Boötes)
IV Subgiants Procyon A (brightest star in Canis Minor)
V Main sequence The Sun, Sirius A (brightest star in sky, in
Canis Majoris)

33. Luminosity Classes
Ia Bright supergiant
Ib Supergiant
II Bright giant
III Giant
IV Subgiant
V Main sequence
Sun: G2 V
Rigel: B8 Ia
Betelgeuse: M2 Iab

34. Measuring Star Diameters
by employing
Interferometric Techniques
• Stars are simply too far away to easily
measure their diameters.
• Atmospheric blurring and telescope
effects smear out the light.
• Interestingly, we can combine the light
from multiple telescopes in a process
called astronomical interferometry:
Two telescopes separated by a distance of
300 meters have nearly the same
resolution as a single telescope with a
diameter of 300 meters.
The diameter of the red giant Betelgeuse
was determined using this technique.
Speckle interferometry, which
employs Fourier analysis, uses
multiple images from the same
telescope to increase resolution.

35. Using eclipsing binary systems to measure stellar diameters

36. Types of Binary Stars• Stars found orbiting other stars
are called binary stars.
Three types are known:
1. Visual Binary - If we can see from
photos taken over time that the stars
are orbiting each other, the system is
a visual binary.
2. Spectroscopic Binary - If the stars
are so close together that their
spectra blur together, the system is
called a spectroscopic binary.
3. Eclipsing Binary - If the stars are
oriented edge-on to the Sun, one
star will periodically eclipse the
other star in the system. These are
known as eclipsing binaries.

37. Using the Doppler Shift to detect binary systems
• As a star in a binary system moves away from us, its spectrum is
shifted towards red wavelengths. As it moves toward us again, the
spectrum is shifted toward blue wavelengths.
• This Doppler Shifting allows us to detect some binaries.

38. Measuring Stellar Masses with Binary Stars
This technique gives us the combined mass of the two stars.

39. The Center of Mass COM: (1) calculate the combined mass,
(2) using the distance from the center of mass COM, we can
calculate each star’s mass.
• In a binary system, the two
stars orbit a common COM.
• The masses and distances
from the COM are related
through:
MA × aA = MB × aB
• If the stars are of equal
mass, the COM is directly
between them.
• If the stars are of unequal
mass, the COM is closer to
the more massive star.