Part 1: Finding the
Distance to Stars Using the Parallax Angle
Instructions:
Read Chapter 15 and Appendix D
(pp. 543-545) in the textbook and the background information below.
Answer the three questions at the
bottom directly in this lab worksheet.
This NASA web page provides
additional explanation and allows you to check your answer:
http://imagine.gsfc.nasa.gov/features/yba/HTCas-size/parallax3.html
Background:
Stellar Parallax is the apparent
shift in the location of a star due to the orbit of the Earth. In other words, the star will appear
to be in a different place depending on the line of sight from the Earth. By
knowing the diameter of Earth’s orbit and by measuring the angle of apparent
shift (the parallax angle), astronomers can calculate the distance to the
nearby stars using trigonometry. This method has been used for centuries. The
ancient Greeks were able to measure some of the closest stars this way. Today,
sophisticated telescopes have greatly enhanced this method. Figure 1 is a
graphic from your textbook showing how this works:
Assignment:
For this assignment, you will
determine the distance to a star, “HT Cas”, using the method of stellar
parallax. Figure 2 and 3 below are photos of HT Case, taken six months apart:
|
Fig 2. Image of HT Cas taken 06/96 |
Fig. 3. Image of HT Cas taken 12/96 |
When we super-impose these
photos, we get the following image (figure 4):
You can see that the position of
the star appears to have changed over the six-month time period. However,
it is actually the angle from which the photos were taken that has
changed. During that
6-month period, the Earth moved from one side of the sun to the other.
Using a stellar astrometric
catalog, we find that the two stars closest to HT Cas are a distance of 0.01
arcseconds apart. Based on this information, we can estimate that the angle of
shift of HT Cas (the parallax angle) to be approximately 0.015 arcseconds
apart.
We also know that the radius of
the Earth’s orbit is 1.0 A.U. (astronomical units).
Using these two measurements, we
can then determine the approximate distance to HT Cas using the following
equation:
d= distance to HT Cas
a=radius of the Earth’s orbit
p=parallax angle
1. (10
points) Given the above equation and information provided, about how far away
is HT Cas?
a. 133
parsecs
b. 67
parsecs
c. 33
parsecs
d.
0.015 parsecs
2. (10
points) Your answer was calculated in parsecs. Given that 1 parsec = 3.2616light
years, about what is the distance to HT Cas in light years? (Your answer in parsecs X 3.2616 light years = The
Distance to HT Cas in light years).
a. 0.025
light years
b. 217 light
years
c. 434 light
years
d. 219 light
years
3. (30
points) Based on your answer, do you think this is a star that we might be able
to send a space probe to? Why
or why not? Support your
answer.
Part 2: Using a
Hertzsprung-Russell Diagram
Instructions:After reading the Unit VIII lesson, clickhereto access the NASA web page “Stars” and answer
the questions below using Figure 5. You can also copy and paste the web address
into your browser:
http://science.nasa.gov/astrophysics/focus-areas/how-do-stars-form-and-evolve/
Background:
Notice that the stars in Figure 5
are not uniformly distributed. Rather, about 90 percent of all stars fall along
a band that runs from the upper-left corner to the lower-right corner of the
H-R diagram. These “ordinary” stars are called main-sequence stars. As you can
see in Figure 5, the hottest main-sequence stars are intrinsically the
brightest, and, conversely, the coolest are the dimmest. The absolute magnitude
of main-sequence stars is also related to their mass. The hottest (blue) stars
are about 50 times more massive than the Sun, whereas the coolest (red) stars
are only 1/ 10 as massive. Therefore, on the H-R diagram, the main-sequence
stars appear in decreasing order, from hotter, more massive blue stars to
cooler, less massive red stars (Lutgens, Tarbuck, & Tasa, 2014).
Assignment:Use Figure 5 to answer the questions. Once
all questions have been answered for both part 1 and part 2, save this
worksheet with your last name and student number and upload to Blackboard for
grading.
1. (10 points) Main Sequence
stars can be classified according to which characteristics? What are the
characteristics of our Sun?
|
Main sequence stars can be |
2. (10 points) Which main
sequence stars can be found with a surface temperature of between 3000K-4000K?
Which stars have a luminosity about 100 times less than that of the Sun?
|
The red dwarf |
3. (30 points) Briefly describe
the solar evolution time-line of a common star like our own from formation
through collapse.
