Properties
of
Stars
Finding
Distances
1
Questions:
Which stars are the brightest?
Which stars are putting out the most
watts? (luminosity = energy per
second)
NEED TO KNOW:
Distances
The most fundamental and
accurate (within a certain range)
means of finding distances is
measuring the parallaxes of stars.
2
You already know about the parallax effect:
Demonstrating parallax
Parallax of Stars
3
!Define arc second
How many degrees in a circle?
How many arc minutes in a degree?
How many arc seconds in an arc minute?
How many arc seconds in a degree?
How many arc seconds in a circle?
__?__ radians = 360 degrees
1 radian = 57.3 degrees
How many arc seconds in 1 radian?
360, 60, 60, 3600;
4
1,296,000; 2 pi; 206,265 arc sec/rad
Measured Parallax
of Stars
" Works accurately for stars within about
200 pc (Hipparchos satellite)
"
Biggest problem: measuring the miniscule
shift of a star against more distant stars
parallax = 0.75 arcseconds
1
distance =
= 1.3 pc = 4.3 ly
0.75
parallax = 0.15 arcseconds
1
6.7 pc = __?__
22 ly
distance =
= __?__
0.15
parallax = 0.0015 arcseconds
1
667 pc = __?__
2170€lyly
distance =
= __?__
0.0015
5
☛
Using SIMBAD to find the parallaxes of the stars
41 Cygni data (partial)
Parallax = 4.24 ± 0.16 mas or 0.00424 ± 0.00016 arc seconds
Distance = 1/parallax = 1/0.00424 = 236 pc or ~770 ly
6
Name ____________________________________________ Date ___________ Section_______
ACTIVITY 18
Finding Distances to Stars
Using Parallax Measurements
Learning Goals
In this activity you will determine a relationship between distance and apparent motion of a nearby
object when viewed from two vantage points. You will apply this relationship to the measuring of
distances to stars. As you work through this activity you will:
1. Demonstrate parallax of a nearby object, at different distances from your eyes, relative to a distant scale.
2. Derive the relationship between the distance of the nearby object and the sizes of its apparent
shifts relative to a distant scale.
3. Apply this knowledge to the measured parallax angles of stars.
Step 1—Measuring a Parallax Angle
You can see the parallax effect by holding your thumb out at arm’s length, looking at a distant object,
and alternately opening and closing each eye. The thumb will seem to jump back and forth relative
and alternately opening and closing each eye. The thumb will seem to jump back and forth relative
to the background. This is because the centers of our eyes are about 7 centimeters (cm) apart from
each other, so each eye has a slightly different point of view.
1. First, make a prediction about the relationship between the distance of a pencil (or other
long, thin object) and the number of fine grid marks across which it will appear to jump.
Which relationship, of those shown
in Figure 18.1, would you predict
y=x
y=1
–
x
is correct?
_______ y = x
y
y
_______ y = –x + 3
_______ y = 1/x
0
_______ y = sqrt(x)
Now let’s test how the parallax of an
object varies with distance using the
baseline measurement from our eyes.
Although using a meter stick would give
more quantitative results, we can get
respectable data by the use of an arm and
a pencil. Be sure to hold your arm straight
out toward the distant scale from which
0
x
x
y = –x + 3
y = sqrt(x)
y
y
0
0
x
x
FIGURE 18.1
79
80
ACTIVITY 18
●
Finding Distances to Stars Using Parallax Measurements
Possible unit:
Length Of Arm - nose to finger tips = 1
elbow = 0.5 LOA
middle of bicep = 0.25 LOA
middle of forearm = 0.5 LOA
choose distances in between for 6 data points
FIGURE 18.2
you will be determining the shift, and
have the pointed end of the pencil up.
Figure 18.2 illustrates what to do.
2. Your nose and eyes should be
pointing straight down your arm.
Approximate the distance from
your eyes to the end of your finger
and enter it as the first distance in
Table 1; it won’t matter if it is accurate as long as you are consistent in
your measurements. Be sure to note
the units you will be using in your
measurements.
a. Hold your arm straight and
TABLE 18.1
Data table for measurements.
DISTANCE
UNITS USED: _________
NUMBER OF GRID MARKS
your measurements. Be sure to note
the units you will be using in your
measurements.
a. Hold your arm straight and
place the pencil out as far as you
can reach with your other arm.
Alternate opening and closing
your eyes and judge the shift of
the pencil point with the distant
scale. Write the number of grid
marks that it shifted on the first
line of Table 18.1.
b. Now move the pencil to half of the original distance and alternate opening and closing
your eyes. Judge the shift of the pencil point with the distant scale and write the number
of grid marks that it shifted on the second line of Table 18.1.
c. Repeat this process for at least six more measurements, placing the pencil one-fourth the
distance to the end of your finger, then three-fourths, one-third, and so on. Enter the approximations of the distances and the number of grid marks that the pencil point shifted
on the remaining lines of Table 18.1.
3. Using Figure 18.3, graph the number of fine grid marks the pencil jumped versus the distance from your eyes. Be sure to label both axes.
Number of grid marks point shifted
4. State the relationship between the distance from the baseline of your eyes and the number of
fine grid marks the pencil jumped. Show your logic here. Was your earlier prediction correct?
Distance from eyes (units: __________)
FIGURE 18.3
Finding Distances to Stars Using Parallax Measurements
DON’T CHANGE YOUR
DATA TO MATCH YOUR
EXPECTATIONS!
CONSIDER THE SOURCES OF ERRORS AND
UNCERTAINTIES - ANALYZE YOUR METHOD STRENGTHS AND WEAKNESSES. INCLUDE IN
YOUR COMMENTS!
12
If you run out of measurements as pencil gets close to
your nose, just put down a good estimate of the shift.
Get through to the graphing part today,
for sure do it before sections tomorrow.