Calculating Distances from Parallax Angles
The parallax angle is given in units of arcseconds. The distance
to the star is given by the formula
d = 1/p,
where p is the parallax angle in arcseconds and d is the distance to the
star in parsecs, abbreviated pc (1 pc = 3.26 light-years).
Now, practice finding the distances to a few stars from their parallax angles.
Exercise 4. Look at the following table (this table
is formatted similarly to the tables you will get from the NVO tools). The first column
of table lists star names (some you may be familiar with, some not). The next two columns
show each star's celestial coordinates, right ascension (RA) and declination (dec).
RA is like longitude on Earth, dec is like latitude.
The fourth column shows each star's parallax angle in milli-arcseconds (mas). One
thousand milli-arcsecond equal one arcsecond. Be sure to convert the parallaxes into
arcseconds before calculating the distances.
The final two columns are left blank for you to find. Use the parallax angle to
calculate the distance to each star in parsecs. Then calculate the distance
to each star in light-years (remember 1 pc = 3.26 light-years).
Name |
RA |
Dec |
Parallax angle
(mas) |
Distance
(pc) |
Distance
(light-years) |
Alpha Centauri A |
219.90 |
-60.84 |
742.12 |
|
|
Sirius |
101.29 |
-16.72 |
379.21 |
|
|
Pollux |
116.329 |
28.026 |
50.09 |
|
|
Gliese 7 |
1.62 |
-27.40 |
29 |
|
|
Wolf 9003 |
1.24 |
24.10 |
26 |
|
|
|
Now that you know the distances to these stars, you can calculate their
absolute magnitudes for yourself. All you need to know is the stars' apparent
magnitudes (how bright they appear from Earth).
Remember that absolute magnitude is defined as the magnitude a star would appear
to have if it were 10 parsecs away from us. Our Sun's absolute magnitude is
4.84 (compared to its visible magnitude of -26.2!).
The relationship between a star's apparent magnitude and absolute
magnitude is given by the expression
M = m - 5 log d + 5,
where m is the star's apparent magnitude, M is the star's absolute
magnitude, and d is the distance to the star in parsecs.
As an example. let's take the nearest star, Proxima Centauri. It has a
visual magnitude of 11.05 and it is 1.29 parsecs away. Therefore, its absolute
magnitude is
M = 11.05 - 5 log (1.29) + 5 = 15.50.
Exercise 5.
Use the visual magnitudes and distances you found earlier to find the
absolute magnitudes of these stars. Fill in the distances you found in Exercise
3, then calculate the absolute magnitudes.
Name |
Distance
(pc) |
Apparent
Magnitude |
Absolute
Magnitude |
b-v |
Alpha Centauri A |
|
-0.01 |
|
0.71 |
Sirius |
|
-1.46 |
|
0.0 |
Pollux |
|
1.14 |
|
1.0 |
Gliese 7 |
|
11.22 |
|
1.5 |
Wolf 9003 |
|
8.7 |
|
0.8 |
Now that you have absolute magnitudes and b-v colors, make an H-R diagram
for these five stars.
|
Question 10.
Look at the H-R diagram you made at the end of Exercise 4. Can
you identify the star groupings you learned in the last section? Which of
the five stars is a giant?
Notice that you had only five stars on this diagram, but you could still
identify which stars belonged to which groups. You would have never been able
to group these stars if you hadn't made a thorough H-R diagram in Exercises 1,
2, and 3. You can make an even more thorough H-R diagram once you understand
how to use NVO tools.
|
Now that you know how to make an H-R diagram, and how to calculate distances
and apparent magnitudes yourself, you are ready to make a new, bigger H-R diagram
using NVO tools. Click Next to learn how to use the tools.
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