Software method:
9. 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.
10. 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.
d
= (b/p") x 206,265
d = distance to asteroid
b = baseline
p" = parallax angle (arcseconds)
11. 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.

Paper and Ruler Method:
9. Zoom the Yerkes image (0245y)
to 100%. Do you see a figure of stars
that appears to be a distorted pentagon with the sausagelike asteroid as one
of the vertices? Now see if you can
find the same pentagon figure in the Gettysburg image, but very small. Zoom that area in the 0245g image to
200%. Locate the pentagon of stars and
the position of the asteroid in this image.
10. If you examine
and compare the two images now, you should be able to notice a difference in
the position of the asteroid. If we use
the star pentagon as a reference, then the 4 stars which are not the asteroid
are very far away and show no shift or parallax. But the asteroid DOES show parallax
shift. It is this shift that we can
measure to determine the distance to the asteroid from the Earth.
11. Print out the following document: 2 pics astrd 1998wt.doc
It shows the views of the the pentagon you are seeing on your computer
screen. The images are printed in
inversegray scale (sky is light and stars are black) so that lining them up is
easier. The scales have been adjusted so
that the stars match reasonably well with each other.
12. Using a pencil or
pen and a ruler, connect the 5 “stars” (one is the asteroid) with straight
lines to form the pentagon in each image.
Cut between the two images to separate them. Now place the Yerkes image (the one with the
sharper stars) on top of the Gettysburg
image and hold them up to the light and/or against a window pane. Mark the Gettysburg asteroid position on the Yerkes
image.
13. Set aside the Gettysburg image and put
your attention to the Yerkes image. You
now have 2 different positions of the asteroid in this one image. One was viewed from Yerkes. One was viewed from Gettysburg.
The difference between the two points is the parallax shift. Measure the distance between the two points
in mm and record your result:
Parallax shift = _________ mm.
14. To determine the
distance to the asteroid we need to know the ANGLE between the two points. The scale factor that converts the shift from
mm. to arcseconds (") has been previously determined to be: 1.5 arcsecs/mm. (The process to determine this scale factor
required knowledge of the two telescopes and their cameras.) Use this scale factor to determine the
parallax angle:
Parallax angle = p" = 1.5 x (shift in mm.
from #14 above)
p" = __________ arcsecs or “
15. [same as step 10 in software method] 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.
d
= (b/p") x 206,265
d = distance to asteroid
b = baseline
p" = parallax angle (arcseconds)
16. [same as step 11 in software method] 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.
