Download Astronomy Exam #2 for the 10

Astronomy Exam #3 Summer 2015
Name Solutions
1) The mass of the Sun is closest to which of the values below?
A) 300 Earth masses
D) 300,000 Earth masses
B) 3,000 Earth masses
E) 3,000,000 Earth masses
C) 30,000 Earth masses
2) The Sun is approximately how much larger in radius than the Earth?
D) 100,000 Earth radii
A) 100 Earth radii
B) 1,000 Earth radii
E) 1,000,000 Earth radii
C) 10,000 Earth radii
3) The density of the Sun is closest to the density of ….
A) Iron, 8 g/cm3
B) Rock, 5 g/cm3
C) Water, 1 g/cm3
D) Ice, 0.9 g/cm3
E) Air, 0.001 g/cm3
4) The surface temperature of the Sun is….
A) 32,000 K
B) 15,500 K
C) 7,200 K
D) 5,800 K
E) 1,600 K
5) The core of the Sun has a temperature of…
A) Unknown
B) 15 Million K
C) 50 Million K
D) 100 Million K
E) 1.4 Billion K
6) The Sun can be functionally divided into two layers. Describe the physical characteristics of the two layers
in the space below.
The Core of the Sun
Radius range: 0 to 0.2 RSun
The Envelope of the Sun
Radius range: 0.2 to 1.0 RSun
Mass: about 1/3rd the mass of the Sun
Mass: about 2/3rd the mass of the Sun
Density: about 100 g/cm3
Density: about 1 g/cm3
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7) In a sentence or two, describe the functional difference between the core and envelope. In other words,
what purpose does the core serve in the star’s function and what purpose does the envelope serve in the
star’s function?
The function of the core is two-fold. First it produces all the energy the Sun emits. Second, it supports the
envelope through thermal pressure against further collapse.
The function of the envelope is two-fold. First it contains the core against exploding and allows the
conditions favorable for fusin in the core to continue. Second, it thermalizes core gamma rays changing
them to less harmful radiation by the time that radiation leaves the Sun.
8) A star is observed to have a stellar parallax angle of 0.037”. What is the distance to the star in light years?
Show your work.
Dpc 
 3.26 ly 
1
1
  88 ly

 27 pc  27 pc  
p 0.037
 1 pc 
9) The picture below portrays a proposed new space mission to establish a Hipparchus-like spacecraft in orbit
around Jupiter for the purpose of measuring stellar parallaxes. In a couple of sentences, explain why a
mission like this would be superior to the original Hipparchus spacecraft in orbit around the Earth during the
early
Proposed orbit of new
1990’s.
spacecraft orbiting
Jupiter
Jupiter
Nearby star
Earth
Sun
A mission like this would be superior to the original Hipparchus spacecraft in orbit around the Earth
during the early 1990’s because the larger baseline of 5.2 AU would make all the parallax angles 5.2
times larger than what they would have been if measured from the Earth at 1 AU. Thus, we could
measure stars that are 5.2 times farther away that current limits – out to 2,500 pc or about 8,000 ly.
10) What is the definition of a parsec? Answer in a few sentences.
By definition a parsec is the distance a star must have to show a parallax, as measure from Earth, of 1
arcsecond. It is equivalent to about 3.26 light years.
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On this page, write an essay that describes how the Sun produces energy by explaining the net protonproton chain reaction, define the symbols in the net reaction, stating the origin of the objects in the net
reaction, and describing the significance of thermalization of solar gamma rays.
Net proton-proton chain: 411 H 124 He  2ν  6γ
Explanation of p-p chain: The Sun produces energy by fusing 4 hydrogen atoms to create a new
helium atom, two neutrinos and six gamma rays. In the process mass is lost and converted into
energy through Einstein’s formula E  mc 2 . The Sun converts 4.3 million metric tons of mass into
energy every second to maintain its luminosity.
The hydrogen in the p-p chain is primordial having been created during the Big Bang at the
beginning of the Universe.
The helium is created by fusing the four hydrogen atoms during which two of the four protons
and two of the four electrons are combined to form two neutrons that are found in the helium
nucleus.
The two neutrinos are sub-atomic particles with almost no mass that travel near light-speed and
only weakly interact with matter. They are created with the two neutrons as a by-product of the
fusion of hydrogen into helium.
The gamma rays are very high energy photons with no mass and travel at light speed (since they
are a form of light). They interact very strongly with matter and are deadly to biologic systems.
The deadliness of the gamma rays is removed by a process called thermalization where gamma
rays gradually lose their energy through countless collisions with atoms in the Sun’s envelope on
their slow migration to the solar surface. With each collision the gamma ray loses a little energy
to the particle it collided with. By the time (50,000 years) the gamma ray reaches the surface its
energy is reduced to that of a visible or infrared photon.
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The four simulated images of a star field appear below with the year which they represent. One of the
stars is consistently changing its position relative to the other stars.
11) Identify the star that is changing its position by circling it in each of the simulated images.
12) These simulated images illustrate what type of stellar motion. Choose from the list below.
A) Spaced velocity
D) Proper motion
B) Diurnal motion
E) Annual motion
C) Radial velocity
The table below lists the properties of five stars. Answer the questions following the table based on these
parameters.
Apparent
Absolute
Spectral Type and
Distance
Designation
Magnitude, m Magnitude, M Luminosity Class
Modulus (m-M)
-0.7
-3.1
F0 II
-0.7 - (-3.1) = 2.4
α
0.0
0.5
A0 V
β
+.9
-4.5
M1 I
+0.9 – (-4.5) = 5.4
γ
0.45
-1.0
B3 V
δ
12.3
14.8
M5 V
ε
13) Which star(s) is the hottest
δ
14) Which star(s) is the brightest?
α
15) Which star(s) is the least luminous?
ε
16) Which star(s) is the largest in radius?
γ
17) Which star(s) has a temperature of about 2,500 K?
γ and ε
18) Which star is closer star α or star γ? Explain your reasoning.
Star α is closer because it has a lower distance modulus (See table above). Another way of reasoning
this out is to notice that α is the brighter of the two stars but it is the less luminous of the two. This
can only be explained it α is closer.
19) How many times more luminous is star δ compared to the Sun?
Star δ is 5.8 magnitudes more luminous than the Sun and is, therefore, 2.512 5.8  209 times more
luminous than the Sun.
20) Explain why the star γ is so luminous?
Star γ is so luminous because of its large surface indicated by its luminosity class (I) being a
supergiant. Its temperature (M spectral type) is quite cool and does not contribute to its large
luminosity.
21) In a few sentences describe, using appropriate terms, the star ε given its properties?
Star ε is a cool (about 2,500 k) main sequence dwarf star (in its adult phase of its lifetime). It is 10
magnitudes less luminous than the Sun, or equivalently, about 1/10.000’th of a solar luminosity. It is
also invisible to the naked eye. In fact, it is over 100 times dimmer (over 5 magnitudes dimmer) than
the naked-eye minimum brightness.
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22) Star α is brighter but less luminous that star β. The apparent magnitude of star α is 3 and the absolute
magnitude of star β is 0. Which of the values below could represent the absolute magnitude of star α and
the apparent magnitude of star β?
A) M = 1, m = 1
C) M = 1, m = 5
B) M = -1, m = 5
D) M = -1, m = 1
23) Star γ and star δ have equal radii and equal temperatures. Star δ is 33 ly distant from the Sun and has an
apparent magnitude of -1. What is the apparent magnitude of star γ if it is 330 ly from the Sun?
Since star δ has an apparent magnitude of -1 at a distance of 33 ly (i.e. about 1 pc), it must have an
absolute magnitude of about -1 also. Since γ is has the same radius and temperature as δ it will have
the same luminosity as δ and the same absolute magnitude as δ. However, γ is 10 times farther away
than δ, so it will appear 100 times dimmer or 5 magnitudes dimmer. So the apparent magnitude of
star γ will be m = +4.
24) The four images below represent each of the types of binary stars discussed in our text: apparent double star,
true binary star, spectroscopic binary star, and eclipsing binary star. Label each image with its appropriate
type of binary star.
A2 V, 151 ly
F2 V, 550ly
G2 IV, 37 ly
A0 V, 45 ly
F2 V, 45 ly
K8 V, 151 ly
G5 III, 550 ly
B1 V, 2,000 ly
Type: True Binary Type: Spectroscopic Binary Type: Eclipsing Binary Type: Apparent Double Star
25) A true binary star system consisting of an A5 V and a G2 V stars has an orbital separation, a, equal to 75
AU and an orbital period, P, of 375 yrs. Calculate the combined mass of the stellar system. Estimate the
mass of the A5 star using what you know about the mass of G2 V stars.
M1  M 2 
3
aAU
753

 3 Solar masses
Pyr2 375 2
Since the combined mass is three solar masses and one of the stars is a G2 V star like the Sun (assume
it is 1 solar mass) the mas of the A5 V star is about 2 solar masses.
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26) The star Vega has a luminosity of 59 L and a temperature of 9,520 K. What is its radius compared to the
Sun?
L V  4RV2  TV4
L S  4RS2  TS4
L V 4RV2  TV4

L S 4RS2  TS4
2
L V  RV   TV 
  

L S  RS   TS 
4
2
R
59   V
 RS
  9,520 k 
  

  5,800 k 
R
59   V
 RS

  7.26

RV

RS
4
2
59
 2.85
7.26
The star Vega has a radius that is about 2.85 times larger than the Sun’s radius.
27) In a randomly chosen patch of sky you can count 100 stars with the naked-eye on a very clear night. How
many of those stars are probably not solitary stars but multiple star systems?
B) 10
The HR Diagram of the 91 brightest stars in the sky
appears to the right. The Main Sequence appears as a
dotted line and the Sun appears as the gray triangle
symbol on this HR diagram.
C) 20
D) 50
The 91 Brightest Stars
-10
Absolute Magnitude
A) None
E) 80
-5
0
5
In the space below, describe the character of the
10
brightest stars in the sky as completely as you can using
15
the HR diagram at the right.
20
These brightest stars are all (almost) all more
O B
A
F
G
K
M
luminous than the Sun, shorter lived than the Sun,
Spectral Type
and are either hotter main sequence stars or cooler
giant stars (mostly).
These brightest stars are a hundreds of times more luminous if not more and will therefore have lifetimes
hundreds of times shorter than the Suns – or less than 10 million years. The giant stars have even less
time to live since they are already in the last few percent of their lifetime. The temperature of the hot
main sequence stars is above 20,000 K while the giant stars have temperatures around 3,000 K or less.
The main sequence stars are more massive than the Sun and have larger radii. We cannot say anything
definite about the mass of the giant stars.
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The Nearest Stars
Absolute
Magnitude
-10
28) HR Diagram of the 100 nearest stars in the sky appears to
the right. The Main Sequence appears as a dotted line and
-5
the he Sun appears as the gray triangle symbol on this HR
0
diagram. In several sentences contrast the properties of
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luminosity, temperature, radius, mass and lifetime of these
10
nearest stars with the Sun.
15
These nearest stars are less luminous, cooler, smaller in
radius and mass, and have much longer lifetimes than
20
O B
A
F
G
K
the Sun. These nearest stars are 100’s to 10,000’s times
Spectral Type
less luminous than the Sun. All but a few have
temperatures that are around half the temperature of the Sun (near 3,000 K). Their lifetimes are
100’s to 10,000’s longer than the Sun’s lifetime – above 1 trillion years.
Since they are mostly coller main sequence stars their radii and masses are smaller than the Sun’s
radius and mass (except for the few stars that are hotter than the Sun).
M
Use the HR diagram to the right to answer the following
questions.
HR Diagram
The bright star Deneb has a luminosity of 54,000 solar
luminosities (M=-7.0) and a temperature of 8,525 K (spectral
type A2). What is its approximate radius?
-5
7,200 K
6,000 K
5,250 K
3,800 K
1,000 R
1
17.5 M
4
100 R
5.9 M
Absolute Magnitude
The M5.5 V star’s luminosity is (M=13) about 8 magnitudes
less luminous than the Sun or about 1,585 times less
luminous than the Sun (0.000631 LSun). Its radius is about
0.1 solar radii. (2)
9,500 K
60 M
Deneb has a radius about 50 times the Sun’s radius. (1)
The star nearest the Sun is an M5.5 V star. What are its
luminosity and its radius, approximately?
30,000 K
-10
2.9 M
0
1.8 M
10 R
1.2 M
0.1 R
1.0 M
5
Sun
.67 M
1 R
0.01 R
10
.21 M
The companion star to the brightest star in the sky is designated
Sirius b. It has a spectral type of A2 and has a radius of 0.008
that of the Sun. What is its approximate luminosity?
Sirius b has a luminosity just about the same as the M5.5 V
star of the previous question - 0.000631 LSun . (3)
3
2
0.001 R
15
20
O
B
A
F
G
K
M
Spectral Type
What would be the spectral type of a main sequence star with
10 times the mass of the Sun?
A main sequence star with 10 times the mass of the Sun would have a spectral type of about B2.
Astronomy Formula and Constants Sheet for Exams
7
Conversions
Formulas
A
L

2D
360 
Main Sequence Lifetime t 
Combined mass of a binary star system:
m1  m2 
M
1010 yr
L
3
aAU
Pyr2
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