Doppler Shift - Homework Assignment | ASTR 100 | Assignments Astronomy

Astronomy 100 Spring 2009

Homework Assignment # 3

Assigned Feb. 23, 2009

Due Date Feb. 27, 2009

To get credit for homework assignments, you must submit a Scantron showing your

multiple choice answers AND a hand-written sheet showing your solutions especially

those involving algebra. Your handwriting must be legible, and you must show how you

arrived at the answer given on the Scantron. No credit will be given for a Scantron alone.

- - - - - - - - - - - - - - - - - - - - - - -

Part I: Wien's Law & Stefan-Boltzmann Law

To solve these problems, refer to the section called "An Astronomer's Toolbox 4-1" on

page 107 of the textbook.

1. If you see a star in the sky with a very red color, this means that its maximum light

output occurs in red-to-orange wavelengths. Assume that the peak in the light output

occurs at 610 nm. Find the temperature of this star. (This will be the surface temperature

of the star.)

a. 3660o K b. 3951o K c. 4803o K d. 4917o K

2. Now do the same calculation and find the temperature for a very bluish-white star

with a maximum light output at 330 nm.

a. 4878o K b. 6468o K c. 8056o K d. 8879o K

3. The mathematical form of the Stefan-Boltzmann Law can be written as F =  T4 where

the constant  = 5.67 x 10-8 J/(m2 oK4 s). Calculate the amount of energy emitted per

square meter by a star with a surface temperature is 6400o K. All answers given below

have units of Joules per meters squared per second.

a.3.29 x 10-4 b. 8.93 x 106 c. 9.51 x 107 d. 8.77 x 1012

4. The total energy output of a star is the flux (calculated from the Stefan-Boltzmann

relation) times the surface area of the star (area = 4  r2 ). Calculate the total energy

output of the star in problem 3. Assume this star has a radius of 8.07 x 105 km. All of

the following answers are given in Joules per second.

a. 2.00 x 1015 b. 2.91 x 1024 c. 7.78 x 1026 d. 5.34 x 1040

5. A large power plant (a nuclear power plant or a coal burning power plant) can produce

10 megawatts of power. Use the definition that 1 Watt = 1 Joule/s to determine how

many power plants of the “10 megawatt” type are equivalent to the total energy output of

the Sun. The Sun’s energy output can be found on page 289 of the textbook. Notice that

the answers are all given as a range. Calculate your answer and then see which “range” it

falls in.

a. 1 to 1 million c. 1 billion to 1 trillion (where 1 trillion = 1 x 1012 )

b. 1 million to 1 billion d. more than 1 trillion

Partial preview of the text

Download Doppler Shift - Homework Assignment | ASTR 100 and more Assignments Astronomy in PDF only on Docsity!

Astronomy 100 Spring 2009 Homework Assignment # 3 Assigned Feb. 23, 2009 Due Date Feb. 27, 2009

To get credit for homework assignments, you must submit a Scantron showing your multiple choice answers AND a hand-written sheet showing your solutions especially those involving algebra. Your handwriting must be legible, and you must show how you arrived at the answer given on the Scantron. No credit will be given for a Scantron alone.

Part I: Wien's Law & Stefan-Boltzmann Law

To solve these problems, refer to the section called "An Astronomer's Toolbox 4-1" on page 107 of the textbook.

If you see a star in the sky with a very red color, this means that its maximum light output occurs in red-to-orange wavelengths. Assume that the peak in the light output occurs at 610 nm. Find the temperature of this star. (This will be the surface temperature of the star.) a. 3660o^ K b. 3951o^ K c. 4803o^ K d. 4917o^ K
1. Now do the same calculation and find the temperature for a very bluish-white star with a maximum light output at 330 nm. a. 4878o^ K b. 6468o^ K c. 8056o^ K d. 8879o^ K
The mathematical form of the Stefan-Boltzmann Law can be written as F = T^4 where the constant = 5.67 x 10-8^ J/(m^2 oK^4 s). Calculate the amount of energy emitted per square meter by a star with a surface temperature is 6400o^ K. All answers given below have units of Joules per meters squared per second. a.3.29 x 10-4^ b. 8.93 x 10^6 c. 9.51 x 10^7 d. 8.77 x 10^12
The total energy output of a star is the flux (calculated from the Stefan-Boltzmann relation) times the surface area of the star (area = 4 r^2 ). Calculate the total energy output of the star in problem 3. Assume this star has a radius of 8.07 x 10^5 km. All of the following answers are given in Joules per second. a. 2.00 x 10^15 b. 2.91 x 10^24 c. 7.78 x 10^26 d. 5.34 x 10^40
A large power plant (a nuclear power plant or a coal burning power plant) can produce 10 megawatts of power. Use the definition that 1 Watt = 1 Joule/s to determine how many power plants of the “10 megawatt” type are equivalent to the total energy output of the Sun. The Sun’s energy output can be found on page 289 of the textbook. Notice that the answers are all given as a range. Calculate your answer and then see which “range” it falls in. a. 1 to 1 million c. 1 billion to 1 trillion (where 1 trillion = 1 x 10^12 ) b. 1 million to 1 billion d. more than 1 trillion

Part II: Doppler Shift

When written in its simple algebraic form, the Doppler shift ∆λ can be expressed as follows:

∆λ / λ = v / c and this can be rearranged as v = c x ∆λ / λ where v = velocity c = speed of light = 300,000 km/s λ = rest wavelength ∆λ = wavelength shift

The rest wavelength is the wavelength of a particular spectral line (one of the lines in an atom’s “fingerprint”) as measured in a laboratory where everything is at rest. For example, during the lab demonstration in class we saw the bright red emission line of hydrogen gas at λ = 656.30 nanometers. This red line is called the H-alpha line. Note that 1 nanometer = 1 x 10-9^ m.

Let’s say that you use a telescope to record the spectrum of a star or galaxy, and you notice in the spectrum the H-alpha line of hydrogen. If the spectral line is shifted, there are two possibilities: (a.) When you measure the precise wavelength of the H-alpha line, it appears at a wavelength that is smaller than the rest wavelength (the line is shifted to smaller wavelengths, i.e. towards the blue end of the spectrum). This means that the object is approaching you, and in this case astronomers say that the velocity is negative and that the object has a “blueshift”. (b.) When you measure the precise wavelength the H-alpha line, it appears at a wavelength that is larger than the rest wavelength (the line is shifted to longer wavelengths, i.e. towards the red end of the spectrum). This means that the object is going away from you, and in this case astronomers say that the velocity is positive. In this situation, the object has a “redshift”.

Say you attach a spectrograph to a telescope, point the telescope at Proxima Centauri, the closest star to Earth, and notice that the H-alpha line is located at a wavelength λ = 656.34 nanometers. What is the velocity of Proxima Centauri? (a.) -283 km/s (b.) +283 km/s (c.) -18.3 km/s (d.) +18.3 km/s
Say you attach a spectrograph to a telescope, point the telescope at the Andromeda galaxy, and notice that the H-alpha line is located at a wavelength λ = 655. nanometers. What is the velocity of Andromeda? (a.) -283 km/s (b.) +283 km/s (c.) -18.3 km/s (d.) +18.3 km/s
A red traffic light has λ = 650.0 nanometers. A green traffic light has λ = 550. nanometers. How fast must you go toward a traffic light to make the red light look green? Give the answer as a percentage of the speed of light. (a.) 8% (b.) 15% (c.) 30% (d.) it will never look green

Doppler Shift - Homework Assignment | ASTR 100, Assignments of Astronomy

Related documents

Partial preview of the text

Download Doppler Shift - Homework Assignment | ASTR 100 and more Assignments Astronomy in PDF only on Docsity!