Download Practice Exam for 3 rd Astronomy Exam

Practice Astronomy Exam #3
I have left the original study guide points in italicized font to better enable you to see the connection between the study guide and the
practice exam questions/exercises.
The successful student will be able to…
1.
The Sun
a. List or identify the vital statistics of the Sun
Radius of the Sun in Earth radii = 109 Earth Radii
Mass of the Sun in Earth masses = 330,000 Earth Masses
Density of the Sun in g/cm3 = 1.4 g/cm3
Temperature of the Sun in K = 5,800 K
Core temperature of the Sun in K = 15 Million K
b.
Describe the Sun in terms of a 2-layer model
What function does the core of the Sun perform? 1. Produces all the energy
2. Supports the envelope against collapse
What function does the envelope of the Sun perform?
1. Contains the core to allow energy production to continue
2. Thermalizes core gamma rays
List the radius, mass, temperature and density of the core of the Sun.
Radius= 1/5 RSun
Mass = 1/3 MSun
Temperature =15 Million K
Density = 100 g/cm3
List the radius, mass, temperature and density of the envelope of the Sun.
Radius= between 1/5 RSun and 1RSun
Mass = 2/3 MSun
Temperature =5 Million K
Density = 1 g/cm3
2.
The Sun’s Source of Power
a. Describe, in an essay, how the Sun produces energy by
i. Describing the Net proton-proton chain reaction,
ii. Defining the symbols in the reaction,
iii. Stating the origin of the symbols in the reaction,
In a brief essay describe the net proton-proton chain defining all symbols and the origin of the elements of the p-p chain.
What is the origin of energy from stars? Answer in a sentence.
b.
Describe the process of thermalization of gamma rays in the Sun and state its significance.
Why do γ-rays produced in the p-p chain not extinguish life on Earth?
Gamma rays produced in the proton-proton chain do not extinguish life on Earth because they are changed
Stellar Nomenclature
c. Properly decode the stellar nomenclature terms apparent magnitude, absolute magnitude, spectral type and luminosity class to
answer questions about a list of stars.
Stars in the Constellation Bootes
α
β
γ
Apparent
Magnitude,
m
-0.06
3.48
3.05
Absolute
Magnitude,
M
-0.3
+0.3
+0.2
δ
3.47
ε
η
Designation
K2 III
G8 III
A7 III
Solitary
or
Multiple
Solitary
Solitary
Binary
+0.3
G8 III
Binary
Intentionally
blank
2.37
Intentionally
blank
K0 II
Binary
203
2.69
+2.7
G0 IV
Spec.
Binary
32
Spectral Type and
Luminosity Class
Distance,
ly
Distance
Modulus
(m-M)
37
140
120
3.48-.3=3.18
3.47-.3 = 3.17
Which of the listed stars in the table above is the …
Brightest?
α
Dimmest?
β
Most Luminous?
α
Least Luminous?
η
Hottest?
γ
Coolest?
α
Largest in radius? ε
Which star is closer β or δ? Justify your answer. δ, δ has a lower distance modulus compared to β. Thus, δ is closer. –or- Both
δ and β have the same luminosity (because their absolute magnitudes are equal), but δ is just a bit brighter (as judged by
comparing apparent magnitudes). Thus, δ is closer.
Which star is more luminous ε or η? Justify your answer. ε, ε is a bit brighter than η (as judged by comparing the apparent
magnitudes) but ε is much farther away compared to η. The only way a more distant star can be brighter that a closer star is if it
is more luminous. Thus ε is more luminous.
Construct an HR diagram for the stars of Bootes listed in the table above on the blank HR diagram attached. Be certain to label
the axes correctly. Note the Sun is indicated with the ☼ symbol.
d.
e.
f.
In a paragraph contrast the stars of Bootes listed in the table above to the Sun. Are the stars in Bootes like the Sun?

66% of stars in Bootes are in multiple star orbital geometries compared to the solitary Sun

All the stars in Bootes are giant stars very near the end of their evolution unlike the Sun that is an adult main sequence
star.

Average absolute magnitude of stars in Bootes is 1.54 which means that the average luminosity of the stars in Bootes is
about 20 or 25 times the luminosity of the Sun.

4 of the 6 stars in Bootes are cooler than the Sun, 1 is the same temperature and 1 as hotter than the Sun.
Using the stellar nomenclature terms compare a set of stars to the Sun.
Construct and analyze an HR diagram for a set of stars.
Characterize the bright stars in the sky and the stars nearest to the Sun in the sky.
Write a paragraph describing in detail the character of the brightest stars in the sky. AN HR diagram is provided below to assist
you.
Write a paragraph describing in detail the character of the most common stars in the galaxy. AN HR diagram is provided below
to assist you.
The 300 Brightest Stars
-10
108 Nearest Stars
-10
-5
-5
Absolute Magnitude
Absolute Magnitude
0
0
5
5
Main Sequence
Sun
10
Bright Stars
15
10
Sun
Main Sequence
20
O
15
B
A
F
G
K
M
Spectral Type
20
3.
0
O
1
B
2A
3
F
4G
5K
M6
7
Spectral Type
Star Formation
a. Describe the physical characteristics of a giant molecular cloud
List the characteristics of a typical giant molecular cloud.
b.
Composition
H2 and He gas with trace amount of other gases and dust
Diameter
~ 300 ly
Mass
~ 300,000 solar masses
Temperature
~ 10 K
Internal structure
Clumpy with dense cores
Identify the source of heating (energy production) in protostars.
Proto-stars have a surface temperature typically around 1,000 K. However, they are not yet stars and have not yet initiated fusion
in their cores. If fusion is not creating heat in proto-stars, then what is the source of their heat? Answer in a sentence.
The source of heat in proto-stars is the conversion of gravitational potential energy into thermal energy as the proto-star
collapses. Recall that all gasses heat up when they are compressed. The self-gravity of the proto-stars (i.e. the weight of its
envelope) compresses the inner layers of the proto-star causing them to heat and radiate away energy mosty in the IR part of the
spectrum.
c.
Explain why more low-mass K & M main sequence stars form rather than the high-mass O & B stars.
Describe the Birth Function (a.k.a. Initial Mass Function) and how it helps explain why the most common star in the galaxy is a
low mass M & K main sequence star.
The Birth Function (a.k.a. The Initial Mass Function) is an empirical Monte Carlo model that predicts the number of fragments a
Giant Molecular Cloud (GMC) will break into as it collapses as a function of cloud fragment mass. It reveals that a GMC will
fragment into hundreds of times more abundant smaller fragments of mass about 0.2 to 0.1 solar masses that larger 100 to 10
fragments. These very more numerous smaller cloud fragments evolve to form low-mass K and M main sequence stars. Thus, K
and M main sequence stars are the most common stars in the galaxy because they form hundreds of times more often than higher
mass O and B main sequence stars.
d.
List the mass limits of stars and explain why these limits apply.
What is the mass of the smallest cloud fragment that will form a star? Why is this the smallest mass cloud fragment that will
form a star?
The mass of the smallest cloud fragment that will form a star is about 0.1solar masses. This is the smallest mass fragment that
will form a star because if the fragment were any less massive the pressures, densities and temperatures in the interior of these
clouds fragments would never reach the threshold for fusion to begin. No fusion…no star.
What is the mass of the largest cloud fragment that will form a star? Why is this the largest mass cloud fragment that will form a
star?
The mass of the largest cloud fragment that will form a star is about 100 solar masses. This is the largest mass fragment that will
form a star because if the fragment were any more massive the temperatures and pressures developed as these large fragments
collapse are sufficient to further fragment the cloud fragment into smaller pieces. It essentially blows itself apart if the cloud
fragment has mass greater than about 100 solar masses.
e.
Describe the processes and stages of star formation from a giant molecular cloud to an open cluster.
Write a paragraph using the word list below correctly to describe the process of star formation.
Bok Globules
Dense Cores
Giant Molecular Cloud
HII Region
Open Cluster
Birth Function
OB Association
In the Milky Way Galaxy there are very many Giant Molecular Clouds (GMC). A typical GMC contains most hydrogen and
helium gas and microscopic solid particles of ice and rocky material known collectively as “dust”. The typical GMC may be 300
ly in diameter and encompass 300,000 solar masses of gas and dust. So large are these clouds that they are inhomogeneous being
peppered with dense cores that are the seed points for future stars. If the GMC is very cold, about 10 K, then it can collapse
under the gravity of its own mass and the process of star formation begins.
The GMC will collapse and fragment around the very many dense cores in its interior. An empirical Monte Carlo simulation of
this process of collapse predicts the size distribution of cloud fragments called the Birth Function. The Birth Function states that
there will be hundreds of mall fragments for every large fragment in a collapsing GMC. The largest fragment that forms a star
has a mass of about 100 solar masses. If the fragment were any more massive it would further fragment into smaller pieces as it
continued to collapse from the large energy it releases during further collapse. The smallest fragment that forms a star has a mass
of about 0.1 solar masses. If the fragment were any less massive it would not attain conditions in its center to initiate fusion and
who fail to become a star. These GMC fragments are known as Bok Globules.
These Bok Globules collapse a rates dependent upon their mass with the numerically few high mass fragments collapsing in
about 200,000 years to collapse to a star while the much more numerous smallest fragments require about 200 million years to
collapse to a star. A 2 solar mass Bok Globule takes about 50 million years to collapse to a one solar mass star like the Sun.
Thus the first stars to form from a collapsing GMC are the high mass fragments that develop higher pressures and temperatures in
their cores. These extreme conditions drive high fusion rates and, thus, create groups of high luminosity stars – so called OB
Associations. OB Associations are relatively small groups of stars (dozens to hundreds) of newly formed O and B main sequence
stars that represent the leading wave of newly formed stars. Many more lower mass, less luminous stars will be forming from the
smaller less massive Bok Globules that are continuing to collapse but at a slower rate.
The OB Association has a profound effect on the remnant hydrogen gas of the GMC. The O and B stars in the OB Association
are of such a high temperature (20,000 K to 50,000 K) that the radiation (i.e. light) they emit is most intense in the hard-UV
portion of the electromagnetic spectrum. These hard-UV photons are energetic enough to ionize the remnant GMC hydrogen gas
and cause the hydrogen to glow red – the characteristic color of excited hydrogen. These large regions of glowing red excited
hydrogen are known as HII regions and they are the signature of a star forming region – meaning that the presence of an HII
region signifies to astronomers that stars are forming there. The reason is HII regions signify a star forming region is that the OB
Association, which are composed of the first stars to actually form from the GMC, creates the HII region with their high energy
photons. Thus an HII region is powered by an OB Association and the OB Association represents the leading edge of a wave of
new forming stars.
After all the Bok Globules have collapsed and formed stars, the resulting group of new stars that was once a GMC is called and
Open Cluster. Open Clusters are groups of a few thousands of new stars arranged in irregularly shaped star clusters that are
typically about 15 light years in diameter. The appearance of these Open Clusters is dominated by their high luminosity B and A
stars (No O stars since the lifetime of main sequence O stars is so short they perish before the Open Cluster forms) even though
these high luminosity stars represent only a small fraction of the total number of stars in the Open Cluster. The Open Cluster’s
most numerous stars are the smaller, low mass, low luminosity, virtually invisible at the distances typical of Open Clusters, K and
M main sequence stars.
f.
Identify in a photograph the following objects: a GMC, Bok Globule, OB Association, HII region, Open Cluster
Go to the Astronomy Picture of the Day web site and use the search button to display examples of the following objects: a giant
molecular cloud, a Bok Globule, an OB Association, an HII region, an Open Cluster. Learn to recognize the identifying
characteristics of each.
g.
Describe the t-Tauri wind.
h.
Interpret the physical changes of a forming star on an HR diagram.
Describe how the temperature, luminosity and radius are changing for the evolutionary track
of a forming star shown on the right between the indicated points on the evolutionary track.
Between point A and point B:
A
C
B
Temperature is increasing slightly
Luminosity is decreasing by a factor of 100
Radius is decreasing by a factor of 100
Between point B and point C:
B
Temperature is decreasing
Luminosity is constant
Radius is decreasing
i.
Identify and define the ZAMS line on an HR diagram.
On the HR diagram to the right, sketch in the approximate location of the ZAMS line.
ZAMS is an acronym that stands for “Zero Age Main Sequence” and represents the position on the HR diagram where conditions
will be sufficient in the interior of a collapsing cloud fragment to initiate core H-burning. When the evolutionary track (Hayashi
Track) of a collapsing GMC cloud fragment reaches the ZAMS line, the cloud fragment begins the p-p chain in its core and
becomes a main sequence star.
ZAMS Line
j.
Describe the relationship between OB associations and HII regions.
(The bottom left side of
the Main Sequence)
In a sentence or two describe the relationship between an OB Association and its HII Region.
An OB Association is a small group of very hot O and B main sequence stars that are the first to form from a collapsing Giant
Molecular Cloud. (These stars form first because the higher mass cloud fragments collapse faster due to their higher selfgravity.) These O and B stars are so hot they emit most of their radiation at UV wavelengths (this follows from Wien’s Law).
The UV radiation emitted by these very hot O and B stars is energetic enough to ionize the hydrogen gas that surrounds these
newly formed stars. Ionized hydrogen will glow a characteristic red color as the freed electrons recombine with the hydrogen
ions. This large cloud of glowing red hydrogen is called and HII region. Thus the OB Association provides the power to ionize
the Hydrogen gas in the GMC and causes the Hydrogen to glow red. The OB Association is to the HII region as a light switch on
a wall is to the overhead lights.
What is an HII region? What does HII symbolize?
The Roman numeral in HII means that one electron has been removed from the hydrogen atom. Thus HII is hydrogen with its
only electron removed creating a positive hydrogen ion. HI is regular neutral hydrogen with no electrons removed. You cannot
have HIII because that would mean that 2 electrons have been removed from hydrogen and hydrogen only has one electron.
HII regions are the signature of a star forming region, almost all the time. This is because most HII regions are created by OB
Associations that represent the first stars to form in a star forming collapsing GMC. Thus, where ever a large HII region is seen,
astronomers infer that star formation is occurring there.
4.
Main Sequence Stars
a. List or identify the luminosity, mass, radius, temperature, and lifetime of an O main sequence star, the Sun and an M main
sequence star.
Complete the following table by filling in approximate values for the missing numerical quantities
Main Sequence O star
Main Sequence M star
b.
c.
Mass in solar masses = ~60 Solar Masses
Mass in solar masses = ~ 0.1 Solar Masses
Temperature = ~50,000 K
Temperature = ~ 2,500 k
Luminosity in solar units = ~ 30,000 LSun
Luminosity in solar units = ~0.0003 LSun
Lifetime in years = ~ few million years
Lifetime in years = ~ few trillion years
State the impact of convection in the envelope of very low mass stars on the stars main sequence lifetime.
Describe or identify changes in a star during its main sequence lifetime.
List the changes in luminosity, temperature and radius that a main sequence star like the Sun experiences during its main
sequence lifetime.
As shown in the portion of the HR diagram at the right, the Sun (1 MSolar ) increases its
luminosity (and radius) with little change in its temperature as it evolves from the ZAMS
line to the end of core H-burning across the Main Sequence.
Summary of Main Sequence Life from http://cseligman.com/text/stars/sunms.htm

The Main Sequence represents a long, stable stage of stellar life in which the
thermonuclear fusion of hydrogen to helium in the core replaces the heat escaping
at the surface.

To a good first approximation a star like the Sun remains the same throughout its
Main Sequence lifetime, but it does change as it ages, just a little bit at first, but
more and more the older it gets.

The Sun is now about 25% larger and 50% more luminous than when first formed, and is growing about 5% larger and
10% more luminous every billion years.

But if the Sun is now larger and more luminous than it was when it reached the Main Sequence, that means that it was
once only 70% as luminous as now; and if it continues to get larger and more luminous, it will eventually be much
more luminous than now. In other words, stars like the Sun do not maintain constant luminosity while on the Main
Sequence, but gradually increase in luminosity. And by the time the Sun is nearly finished with its Main Sequence life,
it will be about half again as large and twice as luminous as when it became a Main Sequence star.
5.
Giant Stars
a. Describe how shell fusion in a star causes the star to become giants.
Why do stars that generate energy by shell fusion become giants?
When energy production in a star shifts from the core to a shell around the core, the shell γ-rays enter the envelope immediately
and can deposit more of their energy in the envelope of the star. This increased energy deposited causes the envelope to swell
and the star becomes a giant star. Recall that the core of a star may encompass about one third of the star’s mass and γ-rays
produced in the core have to thermalize their way out of the core before they enter the envelope. So a substantial fraction of a
core γ=ray’s energy is deposited in the core itself and less is available to heat the envelope. Shell γ-rays are not depleted in
energy by having to thermalize out of the core. Whenever energy production in a star shifts from the core to a shell around the
core, the star swells into the giant region of the HR diagram.
b.
Identify the “ashes” of H-burning and He-burning
At the end of its main sequence lifetime, what is the core of a star composed of?
At the end of its main sequence lifetime the core of a star is composed of helium…the ashes of H-burning.
At the end of core He-burning, what is the core of a star composed of?
At the end of core He-burning the core of a star is composed of carbon…the ashes of He-burning.
6.
Mass loss and Death of Low-Mass Stars
a. Match the stage of the Sun’s future evolution with the mechanism of energy production in that stage.
Complete the following table
Phase of Stellar Evolution
Proto-star
Method of energy production
Gravitational Collapse with heating
Main Sequence Star
Red Giant Star
Horizontal Branch Star
Red Super Giant Star
Planetary Nebula
White Dwarf Stellar Remnant
b.
Core H-burning
Shell H-burning
Core He-burning
Shell He-burning
none
none
Identify on an HR diagram the stage of the Sun’s evolution and its mechanism of energy
production.
Identify on an HR diagram to the right the name of the stage of the Sun’s evolution and
its mechanism of energy production for the points numbered 7, 8, 10, 11 and 13.
Point
numbered
7
c.
8
Red Giant
Shell H-burning
10
Horizontal Branch
Core He-burning
11
Red Supergiant
Shell He-burning
13
White Dwarf
none
Conversion of Gravitational Potential energy into thermal energy.
Core H-burning – p-p chain in the core creating an “ash” of helium.
Shell H-burning – p-p chain in a shell around a core creating an “ash” of helium..
Core He-burning – triple α process in the core creating an “ash” of carbon.
Shell He-burning– triple α process a shell around the core creating an “ash” of carbon.
List in chronological order the stages of evolution in Sun-like stars.
1.
2.
3.
4.
5.
6.
7.
8.
9.
e.
Main Sequence
Method of Energy
Production
Core H-burning
List in chronological order the mechanisms of energy production in Sun-like stars.
1.
2.
3.
4.
5.
d.
Phase name
GMC………………………………..No energy production
Bok Globule………………………..No energy production
Proto-Star…………………………..Conversion of gravitational potential energy into thermal energy
Main Sequence Star………………..Core H-burning
Red Giant…………………………..Shell H-burning
Horizontal Branch Star……………..Core He-burning
Red Super Giant……………………Shell He-burning in helium flashes
Planetary Nebula…………………...The last helium flash in the shell
White Dwarf Stellar Remnant……...No energy production
Describe the relation between the Helium Flash and the creation of a planetary nebula.
In as few sentences, describe how the phenomenon of the Helium Flash is related to the creation of a planetary nebula.
f.
Describe the components and characteristics of a planetary nebula.
What is a planetary nebula and what are its characteristics dimensions and lifetime?
From Wikipedia, the free encyclopedia with additions
A planetary nebula, often abbreviated as PN is a kind of emission nebula consisting of an expanding glowing shell of ionized
gas ejected from old red supergiant stars late in their lives. The word "nebula" is Latin for mist or cloud and the term "planetary
nebula" is a misnomer that originated in the 1780s with astronomer William Herschel because when viewed through his
telescope, these objects appeared to him to resemble the rounded shapes of planets. Herschel's name for these objects was
popularly adopted and has not been changed. They are a relatively short-lived phenomenon, lasting a few tens of thousands of
years, compared to a typical stellar lifetime of several billion years. They tend to be around 1 light year in diameter.
A mechanism for formation of most planetary nebulae is thought to be the following: at the end of the star's life, during the red
supergiant phase, the outer layers of the star are expelled by strong stellar winds driven by the high luminosity due to Shell He-
burning. Eventually, after most of the red supergiant's atmosphere is dissipated, the exposed hot, luminous core emits ultraviolet
radiation to ionize the ejected outer layers of the star. Absorbed ultraviolet light energizes the shell of nebulous gas around the
central star, appearing as a bright colored HII region.
Planetary nebulae may play a crucial role in the chemical evolution of the Milky Way, returning material to the interstellar
medium from stars where elements, the products of nucleosynthesis (such as carbon, nitrogen, oxygen and neon), have been
created. Planetary nebulae are also observed in more distant galaxies, yielding useful information about their chemical
abundances.
In recent years, Hubble Space Telescope images have revealed many planetary nebulae to have extremely complex and varied
morphologies. About one-fifth are roughly spherical, but the majority are not spherically symmetric. The mechanisms which
produce such a wide variety of shapes and features are not yet well understood, but binary central stars, stellar winds and
magnetic fields may play a role.
g.
Identify the characteristics of white dwarf stellar remnants.
What is a white dwarf stellar remnant and what are its characteristics dimensions and lifetime?
From Wikipedia, the free encyclopedia with additions
A white dwarf is a stellar remnant composed mostly of Carbon nuclei. They are very dense; a white dwarf's mass is comparable
to that of the Sun, and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored
thermal energy. The nearest known white dwarf is Sirius B, 8.6 light years away, the smaller component of the Sirius binary star.
There are currently thought to be eight white dwarfs among the hundred star systems nearest the Sun.
White dwarfs are thought to be the final evolutionary state of all stars whose mass is below about 9 solar masses (including our
Sun)—over 97% of the stars in the Milky Way. After the hydrogen–fusing lifetime of a main-sequence star of low or medium
mass ends, it will expand to a red giant which fuses helium to carbon and oxygen in its core by the triple-alpha process. If a red
giant has insufficient mass to generate the core temperatures required to fuse carbon, around 1 billion K, an inert mass of carbon
and oxygen will build up at its center. After shedding its outer layers to form a planetary nebula, it will leave behind this core,
which forms the remnant white dwarf. Usually, therefore, white dwarfs are composed of carbon and oxygen.
The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy, nor is it supported by the
heat generated by fusion against gravitational collapse. It is supported only by electron degeneracy pressure, causing it to be
extremely dense. The physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit—
approximately 1.4 M☉—beyond which it cannot be supported by electron degeneracy pressure. A carbon-oxygen white dwarf
that approaches this mass limit, typically by mass transfer from a companion star, may explode as a Type Ia supernova via a
process known as carbon detonation. (SN 1006 is thought to be a famous example.)
A white dwarf is very hot when it is formed, but since it has no source of energy, it will gradually radiate away its energy and
cool. This means that its radiation will lessen and redden with time. Over a very long time, a white dwarf will cool to
temperatures at which it will no longer emit significant heat or light, and it will become a cold black dwarf. However, the length
of time it takes for a white dwarf to reach this state is calculated to be longer than the current age of the universe (approximately
13.8 billion years), and since no white dwarf can be older than the age of the universe, it is thought that no black dwarfs yet exist.
The oldest white dwarfs still radiate at temperatures of a few thousand kelvins.
7.
Old age and Death of Massive Stars
a. List the differences in energy production between low-mass stars and high-mass stars.
How does the sequence on energy production methods differ between low-mass and high-mass stars? Answer in a sentence or
two.
b.
Describe the interior structure of a high-mass star near the end of its lifetime.
What does the interior of a high-mass star just before it is about to supernova look like.
c.
Identify the types of stars that will experience a core-collapse (Type II) supernova.
What spectral types of main sequence stars will experience a Type II supernova?
d.
Identify the composition of the core of a star about to experience a core-collapse (Type II) supernova.
What element is the core of star that is just about to supernova composed of? Where did this element come from?
e.
Describe two reasons why type II supernova a very useful standard candles.
What is a standard candle in astronomy?
List two reasons that Type II supernovas are very good standard candles.
1.
2.
f.
Describe the impact of supernovas on the chemical evolution of the universe.
How do supernova’s impact the chemical evolution of the universe?
8.
Why do we owe our very existence to supernovas?
Problems
a. Apply Wien’s Law to find the temperature of a star or its wavelength of maximum emission.
From the spectrum of a star an astronomer determines that the star emits the peak of its radiation at λMax = 100 nm. Use Wien’s
Law to estimate the temperature of this star and identify its spectral type.
Wien’s Law
T
2.9  106 K  nm
Max
2.9  106 K  nm

 29,000 K
100 nm
The star has a temperature about 29,000 K.
b.
Use the Stefan-Boltzmann Law to determine the luminosity, radius or temperature of a star compared to the Sun.
A star is observed to have 4 times the temperature of the Sun and a luminosity of 10,000 solar luminosities. What is the radius of
this star compared to the Sun’s radius?
Stefan Boltzmann Law:
L  4R 2  T 4
2
2
4
2
4
2
4
 RStar
  TStar
  RStar   TStar 
LStar 4RStar
 TStar
RStar
 TStar




 





2
4
2
4
2
4 



LSun
4RSun  TSun
RSun  TSun  RSun   TSun   RSun   TSun 
2
 R  T 
L
 Star   Star    Star 
LSun  RSun   TSun 
4
4
Now, that we have a simple expression with ratios, we’ll fill in the known ratios and find the unknown ratio
2
R 
4
10,000   Star   4 
 RSun 
2
 R  10,000
  Star  
256
 RSun 
RStar
 39.06  6.25
RSun
The star has a radius 6.25 times that of the Sun.
c.
Calculate the density of a star or other spherical object.
A typical B5 main sequence star has a mass of about 6.5 M Sun and a radius of about 3.8 RSun. What is the density of this typical
B5 star compared to the Sun?
Density is given by


 6.5   M Sun 
M Star
6.5M Sun
Mass
  0.12  Sun





Volume 4  R 3 4  3.8R 3  3.83   4  R 3 


Star
Sun
Sun
3
3
3

The stars has a mass of 12% the density of the Sun.
d.
Calculate the main sequence lifetime of a star.
The following properties apply to a main sequence K5 star:
Stellar
Class
K0
Radius
Mass
Luminosity Temperature
R/R☉ M/M☉
L/L☉
K
0.85
0.40
5,240
0.78
Calculate the approximate main sequence lifetime of this K0 star.
The approximate main sequence lifetime of the star is given by
the star is
Mass of Star
Luminosity of Star
0.78
 1.95 solar lifetimes or about 19.5 Billion years.
0.40
in solar lifetimes. Thus the lifetime of
HR Diagram
Main…
Absolute Magnitude
-10
-5
0
☼
+5
+10
Spectral Type
+15
+20
O
B
A
F
G
K
M