Download Chapter 9 “The Family of Stars “

Chapter 9 “The Family of Stars “ - Notes/Homework
Astronomy
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Chapter 9-1, 9-4, 9-5 are Reading Notes. Chapter 9-2, 9-3 are PowerPoint notes
Introduction
This chapter asks us to find out three things about stars. List them below.
1. How much energy they emit. 2. How big they are. 3. How much mass they contain.
The distance from the Earth to the Sun is _________________ miles, or ____ light minutes. The next
nearest star is ____ light years from Earth! (A light year is equal to ______________miles!)
93 million; 8; 4; 5.9 trillion
9-1 Measuring the Distance to Stars
The Surveyor’s Method
1. Summarize the surveyor’s method applying it to measuring distance to the stars. Use the sketch on
page 172 (figure 9-2) to help you.
Use trigonometry to find distance d using angles A and B (sketch in textbook.)
The Astronomer’s Method
2. What is parallax?
Apparent change in the position of an object due to change in location of an astronomer.
3. The farther away an object is, the ___________ the parallax, while the closer, the _____________
the parallax.
Smaller; larger
4. What unit is used to express parallax?
Seconds of arc
5. Write the distance/parallax formula below and identify the variables and their units.
d = 1/p where d = distance to star in parsecs, p = parallax in seconds of arc
6. What is a parsec and what are it’s equivalent units in AU and light years?
The distance to a star with a parallax of 1 second of arc; 3.26 light years; 206265 AUs
7. A piece of paper held edgewise and extended at arm’s length has about _________ seconds of arc,
while the nearest star, α Centauri, has ______________.
30; 0.76
8. Why is it so hard to measure accurately star images?
Blurring by the atmosphere smears images to 1 second of arc.
Proper Motion
9. Define “proper motion” and give its unit.
The rate at which a star moves across the sky, in seconds of arc per year
10. Why would one star have a larger proper motion than another? (Give 2 reasons)
1. A star might be moving directly toward or away from Earth. 2. A star might be very far away
from Earth
11. Stars with large proper motions are usually _________ stars while stars with small proper motions
are usually ___________ stars.
Nearby; distant
9-2 Intrinsic Brightness
Intrinsic Brightness
1. The more ___________________ a light source is, the ___________________ it appears.
Distant; fainter
2. The ____________ received from the light is proportional to its intrinsic brightness or
______________________ (L) and inversely proportional to the square of the _________________ (d)
Flux; luminosity; distance
Absolute Magnitude
3. To characterize a star’s intrinsic brightness, we define absolute magnitude, Mv. Absolute magnitude =
magnitude that a star would have at a distance of _____________.
10 parsec (pc)
4. If we know a star’s ____________________ magnitude, we can infer its distance by comparing and
absolute and __________________ magnitudes.
Absolute; apparent
9-3 The Diameter of Stars
Size of a Star and Luminosity
1. We already know: flux _____________ with surface temperature. ____________ stars are brighter.
Increases; hotter
2. Brightness increases with _________. Absolute brightness is proportional to _____________ squared
Size; radius
3. Write the formula for luminosity. Give an example of a star of similar temperature to the sun but very
different luminosity
L = 4πR2σT4
Polaris is similar temperature, but 100 times larger, therefore 10,000 times more luminous.
Organizing the Family of Stars: The Hertzsprung-Russell Diagram
4. Stars have different __________________, different _________________, and different _________.
Temperatures, luminosities; sizes.
5. In the H-R diagram, most stars are found along the _________ __________________; stars spend
most of their ______________ life on the main sequence.
Main sequence; active
6. On the next page, create a large Hertzsprung-Russell diagram labeling all axes:
H-R Diagram
9-4 The Masses of Stars
1. What are binary stars?
Pairs of stars orbiting around a common center of mass.
2. Explain why binary stars can be compared to a child’s seesaw.
Center of mass is point where two masses on seesaw must be balanced.
3. To find the mass of a binary star system, we must know the ____________ of the orbits and the
orbital _________________. The ______________ the orbits are and the ______________ the orbital
period, the ____________ the stars’ gravity must be to hold each other in orbit.
Size; period; smaller; shorter; stronger
4. Write the formula for calculating the masses of binary stars and identify each variable and the units
used to express each.
a3
p2
mA and mB are star masses; a is average distance between stars in AUs; p orbital period in years.
mA + mB =
5. What are two challenges facing scientists trying to find the mass of a binary star system?
- a.
orbits might be elliptical distorting their shapes
- b.
finding the distances to the stars to estimate the size of the orbits
6. List and describe the three types of binary star systems. Include a description of how scientists study
each type of system.
- a.
visual: separately visible in telescopes. Astronomers measure the position of the two stars directly.
- b.
spectroscopic: only by taking a spectrum can we see there are two stars. Astronomers wait to see
how long it takes for spectral lines to return to their starting positions.
- c.
eclipsing: stars eclipse one another. Astronomers study the light curves from each star.
7. More than ___________ of all stars are members of a binary star system.
50%
8. What is a light curve? What is it used for? Draw an example.
A graph of brightness vs. time to eclipsing binaries.
9. From studying binary stars, astronomers have found that the masses of stars range from roughly
__________ solar mass at the low end to somewhere between ____________________ solar masses at
the high end.
0.1; 60-100
9-5 A Survey of the Stars
1. If we label an H-R diagram with the masses of the plotted stars, we discover that the main-sequence
stars are ordered by ______________. The most massive main-sequence stars are the ___________
stars. The lowest-mass stars are the _____________, ______________ main sequence stars.
Mass; hot; coolest; faintest
2. Stars that do not lie on the main sequence are _____________ in order according to mass.
not
3. Summarize the mass-luminosity relation, and right the equation below
The more massive a star, the more luminous it is
L = M 3.5
4. ______________ and _________________ do not follow the mass-luminosity relation very closely,
and ___________________ not at all.
Giants; supergiants; white dwarfs
5. Giants and supergiants are _______________ density stars, and white dwarfs are _________ density
stars.
Low; high
Supplemental math problems for Chapter 9
Use the formula below to solve the problems, being careful with correct units for each variable.
1
a3
2
4
d=
mv − M v = –5 + 5 log10 (d)
L = 4π R σ T
MA + MB = 2
p
p
d = distance ot a star in units of parsecs (pc)
mv = apparent visual magnitude
p = parallax of a star in units of seconds of arc
M v = absolute visual magnitude
L = luminosity
M = mass
R = radius
T = temperature
L = M 3.5
1. If a star has a parallax of 0.05 seconds of arc, what is its distance in parsecs? In light years? In AU?
1
1
3.26 ly
206, 265 AU
=
= 20 parsecs ×
= 65.2 ly ×
= 4,125, 300 AU
p 0.05
1 pc
1 ly
2. If a star has a parallax of 0.16 seconds of arc and an apparent magnitude of 6, how far away is it, and
what is its absolute magnitude?
d=
1
1
=
= 6.25 parsecs
6 − Mv = –5 + 5 log10 (6.25) Mv = 7.0
p 0.16
3. Complete the following table. Use a calculator and Table 9-1 in the textbook.
d=
apparent magnitude
mv
7
11
1
4
absolute magnitude
Mv
7
1
-2
2
distance
d (parsecs)
10
1000
40
25
parallax
p (seconds of arc)
0.01
0.0001
0.025
0.040
4. If a star has an apparent magnitude equal to its absolute magnitude, how far away is it in parsecs?
10 parsecs [log10(10) = 1, so mv – Mv = 0]
5. In the table to the right, which main sequence star is:
a. Brightest in apparent magnitude? A
b. Most luminous? (use Figure 9-12 in book) C
c. Largest? (think about spectral class) C
Star
A
B
C
D
Spectral Type
G2 V
B1 V
G2 Ib
M5 III
mv
5
8
10
19
6. If a star is ten times the radius and twice the temperature of the sun, how much more luminous is it?
L = 4π R 2σ T 4 so luminosity is related to radius squared and temperature to 4th power
L = 10 2 ⋅ 2 4 Lsun = 1600Lsun
7. What is the total mass of a visual binary if its average separation is 8 AU and its period is 20 years?
a3
83
=
= 1.28 solar masses
p 2 20 2
8. What is the luminosity of a 4-solar-mass main sequence star? A 9-solar-mass main sequence star?
MA + MB =
L = M 3.5 = 4 3.5 = 128 times Lsun
L = M 3.5 = 9 3.5 = 2187 times Lsun
CHAPTER 9 REVIEW QUESTIONS, PAGE 194
RQ 2
Mars' orbit is larger than Earth's, and stars would show a larger parallax when observed from Mars as
compared to Earth. We would be able to determine the distance to nearby stars more accurately and
determine the distance to stars that are currently too far to be measured using parallax from Earth.
RQ 5
Cool stars can be more luminous than hot stars if they are larger in diameter. Examples include
Betelgeuse, which is more luminous than most stars, but yet is one of the coolest stars. Another
example is Sirius B, the white dwarf companion of Sirius. The star has a temperature of about 20,000 K
but has both a radius and a luminosity about 100 times smaller than the sun.
RQ 6
One of the best ways is to compare the temperatures and luminosities of the giant stars to those of the
sun. Stars with temperatures equal to or less than the sun and greater luminosities must have greater
surface areas, and therefore, larger diameters.
RQ 7
No, the parallax of the star is never measured. The first step in determining the distance to a star using
spectroscopic parallax is to obtain a spectrum of the star from which its spectral type and luminosity
class can be determined. The absorption lines that are present can be used to determine the spectral
type, and the widths of some of these lines can be used to determine its luminosity class. These data
allow the star to be plotted on an HR diagram, from which an estimate of the star's absolute magnitude
can be read from the vertical axis. The star's apparent magnitude must then be measured, and by using
the distance modulus, mv - Mv = -5 + 5 log10(d), the distance to the star can be determined.