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AC4.1.1. Distance to Asteroid1998wt

A Changing Cosmos Cover

{ A Changing Cosmos Contents } { All GSS Books }

by Rich Lohman

Materials

Image Processing software such as

Images :

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 SalsaJ software open the three Yerkes (y) images and place them side by side. Click on the “Brightness and Contrast” icon and click “Auto” once or twice to see the images clearly. 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.  Click on the “Images” menu.  Click “Stacks”.  Click “Images to Stack”. 
  3.  Once again click the “Images” menu. Click “Stacks”. Click “Start Animation”. You will now see the asteroid in motion as it moves across the image.You can stop the animation by clicking anywhere on the image.
  4.  Move the slider on the bottom of the stack to the left so you are viewing the image 0245y. Put your cursor over the asteroid, and look up in the orange bar to see the x and y coordinates of this point (pixel). 
    Record those coordinates (x, y) = (_______, _______)
  5.  Close all 3 of the Yerkes images. Then open all 3 of the Gettysburg (g) images and place them side by side.Adjust the Brightness and Contrast as before.
  6. 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.  Go through the same process as above by creating a stack and starting the animation to locate the asteroid moving across the images.  You may find that zooming the image will help you see it more easily.
  7. Once you have located the asteroid in the 0245g image identify the (x,y) coordinates and record them:
    (x, y) =  (_______, _______).  
  8. Close all but the 0245g image.  Then open the Yerkes 0245y image.  Place them side by side.  You now have open the 2 images which were taken at the same time from the two locations.  Recall the location of the asteroid in each image.  

Now you’re in a position to measure 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 superimpose one of the “g” images onto 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. 

Here are two methods:

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 sausage-like 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 inverse-gray 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.