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 |
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 +8. The star is not in the solar neighborhood,
but it is nearby, and is observed to have a parallax of 0.0063
arcseconds (barely detectable). The star has a spectrum that
reveals it to be an F star, of temperature 8500 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 +5.
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
5/22/02
By James
E. Heath