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1.
a. Which is brighter, a third magnitude star
or a sixth magnitude star? By how many times?
b. Which is brighter, a fourth magnitude
star or a thirteenth magnitude star? By now many times?
c. A star has an apparent magnitude of
+4.45 and an absolute magnitude of +4.44. Approximately how far away
from us is this star? Justify your answer in words, not with
calculations.
HINT: Use the definition of Absolute Magnitude.
2.
Consider two stars with the statistics below:
|
Name
|
Temperature
|
Apparent Magnitude
|
Absolute Magnitude
|
|
Antares A
|
2650 K
|
+0.92
|
-4.5
|
|
Ross 128
|
2650 K
|
+11.1
|
+13.5
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a. Which of these stars looks brighter in
the sky? Why do you say this?
b. Which of these stars is the most
luminous? Justify your answer without calculations.
c. One of these stars is closer to us than
10 parsecs, one is farther away. Which is which? Justify your
answer with words instead of calculations.
HINT: Use the definition of Absolute Magnitude.
d. Calculate the ratio between the
luminosities of the two stars using the absolute magnitude figures.
HINT: We discussed in class how to turn a difference in
absolute magnitude into a ratio of luminosities.
e. Since the two stars have identical
temperatures, they must have vastly different sizes. Which star has the
larger radius, and how many times larger is it?
HINT: You can use the Luminosity
formula to find how the radius of one star compare to that of the other,
since you know how their luminosities relate.
3. Consider Murray's Star, a very nondescript star of
apparent magnitude +9.2. The star is not in the solar neighborhood, but
it is nearby, and is observed to have a parallax of 0.0075 arcseconds (barely detectable). The star has a
spectrum that reveals it to be an K star, of
temperature 4500 Kelvin.
a. What is the distance of Murray's
Star? Express your answer in parsecs, light years, and kilometers.
HINT: This is a straightforward application of the parallax
formula given in class. You can find the conversion factors for parsecs to
light-years and kilometers in the appendices of the book.
b. Use the distance and apparent magnitude
information to determine the absolute magnitude of Murray's Star.
HINT: Consult the web page on Distance
Modulus for a model of how to do a problem like this.
c. How does the luminosity of Murray's Star
compare to the luminosity of the Sun? Consider the Sun's absolute
magnitude to be +4.83.
HINT: We reviewed in class how to turn an absolute magnitude
into a luminosity.
d. How does the radius of Murray's Star
compare to the radius of the Sun? Consider the Sun's temperature to be
5800 K. What is that radius, in kilometers?
HINT: You can use the Luminosity
formula to find the radius, since you know the luminosity and temperature.
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Updated 1/10/20