Being a Good Astronomer:
The Unknown
Use science we learn on Earth to understand things we
can’t experiment on…
.
What is “normal” in astronomy?
 how do stars work?
 when is a star abnormal?
…use the Sun for comparison
Surprises are usually interesting…
Measuring Star Characteristics
How different are other stars?
• Distance (parallax)
• Luminosity
• Surface Temperature
• Size
• Mass
• Chemical Composition
• Speeds (radial and
transverse velocities)
How Far are Stars?
 ONLY method for directly measuring distances in astronomy!
Which of the stars in the picture below shows a
measurable parallax?
G
E
A
K
C
F
B
I
D
H
J
Distance (d)
Parallax: use geometry:
d
1 AU
p
1 AU
sin p =
d
æ p ö æ 1 pc ö
ç ÷=ç
÷
è 1" ø è d ø
•p: parallax angle
•d: distance between Earth and star
Typical distances between stars in Milky Way: about 1 “parsec”
1 parsec (pc) = 3.26 light-years = 206,265 AU !!!
A Scale Model
How far away is the nearest star?
to Proxima Centauri --near Balboa Park (almost 7 km)…
260,000x Earth-Sun distance
Earth’s orbit
(3 cm)
6800x Sun-Pluto distance
Pluto’s orbit
(1 meter)
SPACE IS VERY EMPTY!!
Thought Question:
The brightest star in the sky (Sirius) has a parallax of
about 0.4”. What is its distance in parsecs and in
light-years?
(Enter your answer in light-years, rounded to the nearest whole number.)
Thought Question:
On Earth, the parallax angle measured for the star
Procyon is 0.29 arcseconds. If you were to
measure Procyon’s parallax angle from Venus,
what would the parallax angle be? (Note: Venus’
orbit is smaller than Earth’s orbit.)
A. More than 0.29 arcseconds
B. 0.29 arcseconds
C. Less than 0.29 arcseconds
D. Zero arcseconds (no parallax)
Other Stars…
Proxima Centauri (nearest star)
0.0008 Sun’s luminosity
3000 K temperature
Sirius (brightest star in sky)
23 Sun’s luminosity
9940 K temperature
Flux vs. Luminosity
• flux (F): energy reaching each square meter of collecting
surface per time
light collector
also called apparent brightness
units: J / (m2·s)=W / m2
(what our eyes measure)
SURFACE AREA OF A SPHERE
• luminosity (L): total amount of
energy released per time
units: Watt (W): 1 W = 1 J / s
 property of star: its “power”
Flux vs. Luminosity
• luminosity (L): rate of energy release
If L is constant, equal amounts of energy flow through
each sphere each second…
BUT:
flux (F): rate of energy
reaching each square meter
of surface
…energy spreads out over a
larger area
SURFACE AREA OF A SPHERE
Thought Question:
How much brighter does the Sun appear to us on Earth
compared to what you would see standing on the dwarf
planet Eris (67.7 AU from the Sun on average)?
(Enter your answer rounded to the nearest whole number.)
Brightness
Earth’s orbit
1 AU = 1.5´1011 m
W
FSun = 1370 2
m
Sun
W
L = 4p d × FSun = 4p (1.5´10 m) ×1370 2
m
W
L = 12.5(2.25´10 22 m 2 )×1370 2
m
L = 3.9 ´10 26 W
2
11
2
Thought Question:
Imagine you are comparing the brightness of two
stars. Star A’s luminosity is 5 times higher than star
B’s, and star A is 3 times farther away from you than
star B. What is the ratio of the brightness of star A to
the brightness of star B?
(Enter the ratio as a two digit number: if the ratio is 2/3,
enter “23”)
FA
=?
FB
Luminosity (L)
maximum for stars
106 L
Sun
minimum for stars
1 L
10-4 L
centi-firefly?
How to calculate L for stars:
1) measure brightness (flux) at Earth
2) measure distance
3) use inverse-square law:
O
Surface Temperature
B
• star colors change as
temperature changes
A
F
G (Sun)
K
M
Compared to Sun:
 hotter stars look
blue-white
 cooler stars look red
 Sun is actually
white
Surface Temperature (T)
maximum
Sun
minimum
105 K
5800 K
2800 K
How to measure:
• overall color or most intense wavelength
lpeak
• spectral lines
(2.9 ´106 nm × K )
»
T
Spectral Types
• pattern of
absorption lines
reveals star
temperature
hottest
 reads like a
barcode or a
fingerprint
coolest
Radius
R = 7  105 km

measured by knowing
distance from Earth and
its angular size
Sun:
Jupiter
0.1 R
.
Earth
0.01 R
0.5º
1 AU
Betelgeuse
Approximate size of
Sun:
.
Temperature, Size, Luminosity
Two things can increase LUMINOSITY of a star:
REMEMBER THERMAL RADIATION!
A HOTTER OBJECT RELEASES
MORE LIGHT PER SECOND
FROM EACH BIT OF SURFACE
HOT
A LARGER AREA RELEASES MORE
LIGHT PER SECOND:
COOL
SAME AREA
SAME TEMPERATURE
Star Sizes
Stars release THERMAL RADIATION:
 brightness of each piece of surface
only depends on temperature
average flux
from star’s
surface
flux due to thermal radiation
(Stefan-Boltzmann Law)
We can calculate the size of the star!
The HR
Diagram
…a “snapshot” of
star properties
Star properties
change very
slowly, so we
can’t see them
change…
Thought Question
Luminosity
In the graph below, which star (each represented by a dot)
must have the smallest size?
A
B
C
D
E
F
H
I
G
Temperature
Thought Question:
The stars Antares and Mimosa have about the
same luminosity, but Mimosa is 8 times
hotter than Antares. What is the ratio of the
radii?
RAnt
=?
RMim
L = 4pR sT
2
4
Dwarfs and Giants
If a star is LUMINOUS but COOL:
LUMINOSITY of a star
depends on:
• surface temperature
• size
L = 4pR sT
2
4
If a star is HOT but LOW LUMINOSITY
it must be small (small surface area)
 WHITE DWARF
it must be big (large surface area)
 GIANT
Luminosity
The HR
Diagram
…a “snapshot” of
star properties
Star properties
change very
slowly, so we
can’t see them
change…
Temperature
Thought Question:
If you took a star that was the same mass as
the Sun and made it 10 times smaller (in
diameter), how would its density compare
to the Sun’s?
Dstar
=?
DSun
VOLUME = LENGTH 
WIDTH  HEIGHT
4
VOLUME = pr 3
3
Sirius B
• temperature: 25000 K!
• 1/40th Sun’s luminosity!
• 1/100th the size of the Sun
(Earth size!)
• 106x as dense
…like crushing an elephant
into a teaspoon
SIRIUS B (Hubble Space Telescope image)
Radius (R)
main sequence
stars:
maximum
Sun
minimum
.
20 R
1 R
0.1 R
(Jupiter-size)
How to calculate:
• blackbodies:  brightness of thermal
radiation at star’s surface:
 average brightness released by surface:
So:
L
R=
4psT 4
or
R
L
=
RSun
LSun
æ T ö
/ç
÷
T
è Sun ø
4
Luminosity
Main Sequence Stars
highest mass
SPICA:
11x Sun’s mass,
20000x Sun’s luminosity
lowest mass
SUN
Temperature
PROXIMA CENTAURI
.
0.1x Sun’s mass,
0.0006x Sun’s luminosity
Measuring Ages with Stars
Outside the solar system, the
objects that can be age-dated
most accurately are stars…
HIGH-MASS
(SPICA)
SUN
VERY LOW-MASS
(PROXIMA CENTAURI)
.
Messier 9 A globular star
cluster
 About 300,000
stars
 About 12
billion yrs old
25 light-yrs across
Rules for Stars
To survive, stars must be in balance, or EQUILIBRIUM:
Forces are balanced:
• gravity is always
trying to crush a star
 another force
MUST oppose gravity
OR ELSE the star
would collapse
quickly
Energy flows are
balanced:
• stars are
continuously losing
energy by radiation
 stars MUST have
an energy source
OR ELSE their
temperatures
would drop rapidly
Pressure
units: force per area (N / m2)
COLLISIONS OF PARTICLES CREATE PRESSURE:
DENSITY (number per volume):
N
n=
V
crowded particles  more collisions per sec.  more pressure
TEMPERATURE:
faster particles  more frequent,
more violent collisions
 more pressure
P = nkT
k = 1.38 ´10
Pressure animation
- 23
J/K
Pressure
Gas must have enough pressure to
support weight of everything above it



Pressure at center must
be largest because it
supports the rest of the
star…
… so gas becomes DENSE
(150 g/cm3… 15 lead)
and HOT (1.5  107 K)!
Thought Question:
ClassAction question
The Sun’s Lifetime
Stored Energy
Lifetime =
Luminosity
SOURCE OF
ENERGY
FUEL
ENERGY LOST FROM SUN
(LUMINOSITY)
• Sun’s luminosity: 4  1026 J/s
• Sun’s age: about 4.6  109 yr
• What source can provide energy for Sun for this long?
Candy Sun
If the Sun’s mass was all “Milky Way”
candy bars (58.1 g, 280 Calories), how
much energy could be released by
burning the whole thing?
(Enter the scientific notation exponent of the energy in J.)
If the Sun was powered by these candy bars, how long
could it maintain its current luminosity?
(Enter the scientific notation exponent of the time in yr.)
Hydrogen Fusion
STARS NEED:
• hydrogen gas
• high temperature for high-speed collisions between nuclei
After several reactions, 4 hydrogen nuclei
fuse together into 1 helium nucleus
Nuclear Energy and E=mc2
• Hydrogen nucleus:
1 proton:
• Helium nucleus parts:
2 protons:
2 neutrons:
• Actual helium nucleus
mass:
mass of a proton
1.0000 m p
2.0000 m p
+ 2.0028 m p
4.0028 m p
3.9711 m p
HELIUM ATOM HAS LESS MASS (0.8%) THAN ITS PARTS!!
 “LOST MASS” IS CONVERTED TO ENERGY!
Thought Question:
In nuclear fission, a massive nucleus (like
uranium) breaks into several smaller nuclei. If
a power plant generates energy using nuclear
fission, which of the following must be true?
A.
B.
C.
The mass of the uranium nucleus is more than the sum of the
masses of the smaller nuclei.
The mass of the uranium nucleus is less than the sum of the
masses of the smaller nuclei.
The mass of the uranium nucleus has to equal the sum of the
masses of the smaller nuclei.
+
Star Lifetime
• Star’s stored nuclear energy comes from
mass that will be converted (E=mc2):
Thought Question:
The bright star Vega has about 3 times the Sun’s mass
and 60 times the Sun’s luminosity. How will Vega’s
lifetime compare to the Sun’s?
The Importance of Nuclear Reactions
NUCLEAR REACTIONS
heat
GAS
which exerts
PRESSURE
that opposes
GRAVITY
convert
HYDROGEN
into
HEAVIER
ELEMENTS
that lead to
STAR’S DEATH