Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 13: Measuring the Properties of Stars

Problems

1
Sirius has a parallax of 0.377 arc seconds. How far away is it?
2
The parallax of Proxima Centauri is about 0.763 arc seconds. How far away is it?
3
The parallax of the red giant Betelgeuse is just barely measurable and has a value of about 0.005 arc seconds. What is its distance? Suppose the measurement is in error by + or -0.003 arc seconds. What limits can you set on its distance?
4
Estimate the distance from where you live to a neighboring building or object using triangulation (as shown in fig. 13.1 f or a tree). Mark the location of the 90° angle with a stick. Pace off the distance along the baseline or measure it with a meterstick or tape measure. Now from the other end of the baseline, measure the angle A between the stick and the building with a protractor. Make a scale drawing (1/4 inch on the drawing to 1 foot in real life works well) to determine the distance.
5
The star Rigel radiates most strongly at about 200 nm. What is its temperature? How does this compare to the Sun?
6
The bright southern star Alpha Centauri radiates most strongly at about 500 nm. What is its temperature? How does this compare to the Sun's?
7
Arcturus is about half as hot as the Sun but is about 100 times more luminous. What is its radius compared to the Sun's?
8
A stellar companion of Sirius has a temperature of about 27,000 K and a luminosity of about 10–2 L. What is its radius compared to the Sun's? What is its radius compared to the Earth's?
9
If a star has very faint Balmer lines, what are the next steps involved in determining its spectral type?
10
A line in a star's spectrum lies at 400.0 nanometers. In the laboratory, that same line lies at 400.2 nanometers. How fast is the star moving along the line of sight? Is it moving toward or away from us?
11
Two stars in a binary system have an orbital period, P, of 5 years and an orbital separation, a, of 10 AU. What is their combined mass?
12
Two stars in a binary system have an orbital period, P, of 2 years and an orbital separation, a, of 4 AU. What is their combined mass?
13
Two stars in a binary system are determined from their position on the H-R diagram and the mass–luminosity relation to have a combined mass of 8 M.. Their orbital period, P, is 1 year. What is their orbital separation, a?
14
Estimate the luminosity and temperature of both Rigel and Barnard's Star using one of the H-R diagrams in the chapter. Calculate the radii of both stars compared to a solar radius using the Stefan-Boltzmann equation, and show the values agree with the radii in figure 13.22.
15
If a main-sequence star has a luminosity of 5000 L ., what is its mass in relation to the Sun's?
16
Use the data in table 13.6 to plot an H-R diagram. Which star is a red giant? Which is a white dwarf ? Note: Plotting will be much easier if you plot the logarithm of the luminosity; that is, express it in powers of 10 and use the power. For example, if the luminosity is 100, plot it as 2 for 102. You can use a calculator to find the power: enter the luminosity in solar units and hit the "log" key. If the luminosity is 300,000, the answer you get should be 5.477. . . .
17
The two stars τ Ceti and α Centauri B have nearly the same luminosity (and absolute magnitudes) but very different apparent magnitudes: τ Ceti is 3.5, and α Centauri B is 1.34. (A) Determine the ratio of brightness of α Centauri B to τ Ceti. (B) Use the method from section 13.8 to determine how much farther away τ Ceti is than α Centauri B.
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