by Rich Lohman
Background:
Many of the asteroids which circle the sun are
located in the region between the orbits of
Mars and Jupiter. This is known as the
Asteroid Belt. Because these objects
are relatively close to the Earth their distance
can be measured by parallax if the baseline
is long enough. In this particular activity
you will use two images taken of an asteroid
known as “Austria”. These
images were taken by the same telescope about
an hour apart. Since the Earth has rotated
and moved along its orbit during that time
the two images were actually taken from two
different positions in space. These
two different positions will define the baseline. When
you examine the two images on the computer
you will be able to observe and measure the
parallax shift of the asteroid. Knowing
the length of the baseline will allow you
to calculate the distance to the asteroid.
Goals:
- To observe
and measure the parallax shift of the asteroid “Austria”.
- To determine the factors that define
the baseline for this measurement.
- To
calculate the distance to “Austria”.
Procedure:
1. Open the Image Processing program “Hands-On
Universe”.
2. Under the FILE menu select Open Image. Locate
and open the two files entitled “AustriaV1A” and “Austria-V_2”. You
will find them in the folder “HOU Extra
Images” on the desktop.
3. Place them side by side on your screen,
with V1A on the left, and adjust their sizes
so they both fit on the screen.
4. Both of these images were taken on May 18,
2006, from a telescope in Perth, Australia. The
telescope was operated remotely through the
internet from Berkeley, California, by a group
of college students. Image V_2 was taken
51 minutes after V1A.
5. This particular asteroid is relatively easy
to locate by just spending some time comparing
the two images. You are looking for a
fairly bright object which has changed its position
from one image to the next. All other
objects in the image are distant stars which
maintain their same position over the 51 minutes,
so if you see a “star pattern” that
has changed then one of those “stars” must
be the asteroid. See if you can find it.
6. Now that you have found the asteroid you
want to determine how much it has “apparently” moved. The
HOU software has a tool, Auto Aperture,
which will help you do this. You can find
this tool under the Data Tools menu, or locate
the icon in the tool bar that looks like a small
target. Just click on that button. Bring
the cursor down onto one of the images and click
on the asteroid.
7. You will see a “Results” window
open up that gives you 3 lines of information,
including the coordinates of the asteroid. Those
coordinates are in (x,y) format and in units
of pixels. Record the coordinates of
the asteroid for image V1A. Then repeat
the process for the asteroid in image V_2 and
record its coordinates.
8. To verify that all other stars have remained
in their same position, perform the Auto Aperture
measurement on at least one other star in both
images. What do you notice about their
coordinates?
9. The parallax shift can be calculated from
your measurements above, however it can be done
more easily by “subtracting” image
V_2 from image V1A. Perform this subtraction. Then
locate the “black-white” spots which
show that those objects have shifted from one
image to the next. You can check the coordinates
of those spots if you wish to compare with your
measurements above. Then use the “slice” tool
to measure the distance between the two spots. This
is the parallax shift in units of pixels.
10. To determine the actual parallax shift
in angular units you need to know something
about the telescope and camera that took these
images. The particular piece of information
you need is called the “plate scale”. It
is a conversion factor, unique to each telescope,
that converts the pixels in the image to an
angle in arcseconds. For the telescope
in Perth the plate scale is 1.2 arcsecs/pixel
(usually written 1.2 “/px).
11. Using the given plate scale convert the “distance” in
pixels (from step #9) to arcseconds. The
result of this calculation is the parallax
shift of the asteroid.
12. Consider, for a moment, the size of this
shift. Can you picture how small that
angle is? For comparison, the Hipparcos
satellite has the capability of measuring parallax
angles as small as a few milli-arcsecs!!
13. So we come to the point of finally determining
the distance to asteroid “Austria”. From
the presentation earlier you know that you need
to know the baseline for this measurement. Even
though the two images were taken from the same
telescope, the fact that the Earth has moved
during those 51 minutes means that the telescope
was in a different location in space. In
addition, the asteroid has also moved during
this time. So the determination of this
baseline is rather complicated.
At this point you are being asked to consider
the various motions that might cause this apparent
shift in the images you are looking at. Make
a list of the possibilities, and make a drawing
to help. Consider each possibility in
turn. Which seem to be more important
than others? Make an initial assumption
to set a baseline. Calculate the distance
to “Austria” using that baseline. Check
to see if your initial assumption was justified. If
not, make an adjustment and go from there. What
is your best estimate of the Earth-“Austria” distance?
A few reference distances from the Sun: to
Earth (1 AU); to Mars (1.5 AU); to Jupiter (5.2
AU)
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