by Rich Lohman
Introduction: On March 4, 2005,
telescopes from two different observatories
in the United States took simultaneous images
of an asteroid called “1998wt”. The
two observatories were Gettysburg College Observatory
in Pennsylvania and Yerkes Observatory (24” telescope)
in southern Wisconsin. They are approximately
970 km apart as the crow flies. This was
not a new discovery of an asteroid, but the
images were taken to demonstrate the use of
parallax to determine the distance to a relatively
nearby object in the sky. When you view
these images you will discover a noticeable
difference in the location of the asteroid against
the background stars as you compare one set
of images to the other set. A measurement
of this “parallax shift” and the
knowledge of the distance between the telescopes
will allow you to calculate the distance to “1998wt”.
Images: FITS files 1998wt-050304-0245g,
1998wt-050304-0250g, 1998wt-050304-0255g,
1998wt-050304-0245y, 1998wt-050304-0250y,
1998wt-050304-0255y. (Don’t use
those labeled “zoom”.) The
three images ending in “g” are
from the Gettysburg scope. Those ending
in “y” are
from the Yerkes scope. The “050304” indicates
the date, March 4, 2005. The “0245”,
etc. indicates the time the images were taken
in Universal Time (UT). As you can see
the images were taken simultaneously and with
5 minute intervals. There are two ways to
get thses images: on the GSS CD-ROM or download
the compressed archive file in the right column
on this page.
Procedure:
1. Using the HOU-IP software open the
three Yerkes images. The Yerkes images
have a smaller field of view, so it’s
a bit easier to analyze these images. If
you choose, try to locate the asteroid moving
through this field by comparing the 0245 and
0250 images. Often an asteroid will have
something of an elongated, sausage-like look. Once
you have found the asteroid then see if you
can find it in the 0255 image. If you’re
unsuccessful, or as a confirmation, use the
procedure in step #2 below to locate the asteroid.
2. Use the “subtract” tool
in the software to subtract 0250y from 0245y. Make
sure you “Display result in a new window”. Now
you should be able to locate the asteroid’s
tell-tale trace with the white and black spots. Go
back to the two original images to see if you
can now see the asteroid. You will want
to do that with image 0255y as well.
3. At this point it’s a good idea
to identify the x-y coordinates of the asteroid
in the three images so you can locate it later
in your procedure. 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. 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 that information.
4. For the moment minimize the three
Yerkes images. Open the three Gettysburg
images, and go through the same analysis as
you have done with the Yerkes images. You
will notice the obvious difference that these
images have a much larger field of view, so
finding the asteroid by sight is quite difficult. You
might bring up one of the Yerkes images to compare. Keep
in mind, these telescopes were looking at the
same star fields at the same time. You
will also notice that the “stars” in
the Yerkes images are farther apart, indicating
a different Plate Scale.
5. At this point you may have decided
to use “subtraction” with these
images as well. In any case, use the Auto
Aperture tool to measure the coordinates of
the asteroid in the three Gettysburg images. Record
that information.
6. Now you’re at the point of measuring
the parallax shift of the asteroid. If
the two telescopes were identical and using
the same cameras, then this process would be
very simple. You would subtract one of
the “g” images from one of the “y” images. Then
you would measure the pixel shift and convert
the pixels to an angle using the Plate Scale. It’s
not possible here since the plate scales and
image sizes are different. So another
procedure is called for. The following
is a broad outline.
7. Using the HOU software open one image
from each telescope. The two images must
be of the same time (0245, 0250 or 0255). Shrink
down the window of the “g” image
so that you can place the two images, side by
side, on the screen. Identify the asteroid
in each image by using the Auto Aperture tool.
8. You now need to do a determination
of how far the asteroid has shifted from one
image to another, due to the two positions of
the observatories. This is where you’ll
need to use your creativity. You have
all the raw data you need in the images, along
with the plate scales for each (given below). You’ll
undoubtedly want to make some approximations
and/or some assumptions which may introduce
some error. If you have time you can try
several, perhaps more accurate, approaches. But
take one approach all the way so you can calculate
the distance to 1998wt.
You’ll probably need to use a reference
star, common to both images, that’s reasonably
close to the asteroid….but not necessarily. Initially
you’ll measure in pixels and, later, convert
those pixels to an angle in arcsecs. Keep
in mind that, because of the different plate
scales, the pixel measurements between any two, fixed
stars will be different, but the
angular spacing will be the same. You
might want to check that by using the plate
scales below.
Plate Scales: Yerkes = 0.62 “/px.; Gettysburg
= 1.09 “/px.
9. Now that you have the parallax shift
in arcsecs, use the equation for parallax and
calculate the distance to 1998wt. The
baseline between the telescopes is ~970 km.
10. Convert the distance above to AU’s. What
do you notice about this number? Does
it seem reasonable or surprise you? You
might check on the following website for more
information about this asteroid and further
information on parallax: http://spiff.rit.edu/richmond/parallax/1998wt/par_1998wt.html.
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