Download Distance Measurement in Astronomy

Distance Measurement in Astronomy
Being able to measure the distances of astronomical objects is very important in our understanding of the
scale of the Universe.
Radar
The distance from the Earth of objects in the Solar System can be measured using radar. A pulse is sent
out and the time taken for the reflected pulse to be received is recorded. Knowing the speed of radar in free
space and the time between transmission and reception the radar pulse enables us to find the distance of
the object.
For example the time between the radar pulse being sent out and the reflected pulse being received would
be 2.5 s for the Moon and up to 50 minutes for Jupiter and around five and a half hours for Pluto. (The last
two numbers depend on the relative positions of the Earth, Jupiter and Pluto in their orbits)
For objects outside the solar system other methods have to be found.
Parallax
You can find the distances of stars that are ‘relatively close’ to the Earth using parallax.
A very simple example of parallax is to hold one forefinger upright about 30 cm in front of your nose and
close your right eye. Using just your left eye line up your forefinger with an object on the other side of the
room. Now open your right eye and close your left eye. Your finger appears to move against the
background.
To understand exactly what is meant by parallax go and stand at one end of the lab, you will be the
observer. Now get one member of your class to stand at A in the middle of the lab (they represent a star
that is close to the Earth and we will call them the 'nearby star’) and some others to stand at the far end
(they represent distant stars). Look the ‘nearby star’ and see which of the ‘distant stars’ lie in line with it
(See Figure 1).
Now walk across the lab to Position 2 and check again which of the ‘distant stars’ is in line with the ‘nearby
star ’, you will see that the apparent position of the ‘nearby star’ compared with the distance stars has
changed.
Position 2
Nearby stars
2P
‘Distant stars’
2Q
A
B
Figure 1
Position 1
The angle between the two directions in positions 1 and 2 is 2P, and half that angle is called the
PARALLAX (P) of the ‘nearby star’.
Now look at the ‘nearby star’ when it is in position B. The parallax here is Q and you can see two things
about the ‘nearby star’ now:
(a) it is further away from the observer
(b) the parallax of the star is smaller than that of the ‘star’ at A
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Figure 2 shows the use of parallax to measure the distance of an actual star – say  Centauri. This time the
‘base line’ is the diameter of the Earth’s orbit – in other words a line joining the position of the Earth at two
points six months apart.
Earth
Distant stars
P1
Parallax (A)
R
Centauri
Sun
2A
D
Parallax (A)
P2
Earth
Distant stars
Figure 2
The direction of  Centauri is measured against the background of the distant stars at the two points P1 and
P2. The angle 2A is measured and so the parallax (angle A) can be found.
If you know the angle A and the radius of the Earth’s orbit (R) you can find the distance of the star (D).
Stars that are close to the Earth clearly have a larger parallax than ones far away.
Even nearby Stars are so far away that their direction changes only slightly against the background of the
distant stars when seen from points on the Earth’s orbit six months apart.
Nearby stars have a parallax of only a fraction of a second of arc (one second of arc is 1/3600 of a degree).
In the example shown  Centauri (distance 4.3 light years) has a parallax of 0.75 “ of arc.
A more distant star such as Spica in the constellation of Virgo, which is 220 light years away, has a parallax
of only 0.023”.
The parallax of a number of stars is shown in the following table.
Star
Parallax Distance (l.y)
(" of arc)
0.750
4.3
 Centauri
Barnard's Star
0.545
6.0
Sirius
0.377
8.6
Procyon
0.285
11.4
Star
Parallax Distance (l.y)
(" of arc)
Vega
0.133
25
Arcturus
0.097
34
Aldebaran
0.054
60
Adhara
0.067
570
At distances much greater than this the parallax method becomes impossibly difficult to measure.
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Parallax Lab
How Do Astronomers Measure Distances To Stars?
Hold up a pencil about 15 cm in front of your nose. Close one eye and observe a distant object.
Now close the other eye and observe the same object. The pencil appears to jump back and forth.
This is known as the parallax effect. Now you are going to learn how the parallax effect can be
used to measure star distances.
Materials:
Back ground screen
Premeasured paper
T-pins
Pencil
Card-board base mat
Metric ruler
Tape
Procedure:
Part A — Parallax Nearby
1. Fold the background screen in half the long way a screen that will stand.
2. Make sure the premeasured paper is on top of the card board base mat
3. Place the paper and the screen on the table as shown in the illustration. The edge of the paper
should be even with the edge of the table. Tape the paper and the screen in place. (See the
illustration.)
4. Place a T-pin in the premeasured paper 5 cm from the screen.
5. Stoop down so that your eyes are level with the T-pin. The T-pin should be level with your eyes.
Close your right eye and look at the T-pin with your left eye. Note the apparent position of the Tpin on the scale on the screen. Record your position under the heading Position A in the chart on
the following page.
6. Now close your left eye and look at the T-pin. Note its apparent position. Record this in
the chart under Position B.
7. Determine how many centimeters the pin appears to shift. To do this, subtract the number
in Position B from the number in Position A. Record this in the last column of the chart.
8. Repeat steps 4-7 with the pin placed at 10 cm, 15 cm, and 20 cm from the screen. Record
the data in the chart.
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Data
Parallax Observations Chart
Distance of T-pin
Position A:
from screen
Pin Viewed with
Left Eye
Position B:
Pin Viewed with
Right Eye
Distance Pin
Appears to
Shift
5 cm
10 cm
15 cm
20 cm
Part B — Parallax at a Great distance
1. Place the T-pin at the 20-cm position. Back off about 3 meters.
2. Look at the T-pin first with one eye, then the other. Observe the apparent shift, write an
observation.______________________________________________________________
Conclusion:
1. In Part A, at which distance did the T-pin appear to shift most? ________ shift least? _______
2. In Part B, you were far away from the pin. Was the parallax shift as great as when you were
close? _____________________________________________________________________
3. When was the parallax shift great—when the T-pin was close to you or far away from you?
__________________________________________________________________________
4. Suppose there were two pins in front of the screen. How could you determine which was
closer to you? ______________________________________________________________
5. Astronomers use the parallax effect to measure distances to nearby stars. The background of
far distant stars serve as a screen. Astronomers don’t close one eye, then the other. Instead,
they look at the stars from two widely separated locations. Suppose they observe stars A and
B from two telescopes on opposite sides of Earth. When viewed against the background of
distant stars, star A appears to shift very little. Star B shows a large parallax shift.
Which star is farther away from Earth? __________________________________________
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