Project #2 Astrometry and the Scale of the Telescope.

Preparation

The objective of this exercise is to relate the distances and sizes you measure on the CCD to what you see in the sky. It is the fundamental calibration for all our measurements of angular size in the sky. So do it carefully. What you will need is a chart of a particular region of the sky and a good CCD picture of that same region. We will use the region near (field of) Lambda Orionis . You have two charts of the field, one in blue and one in red. They correspond roughly to what our CCD camera measures in the B filter and the R filter. What you see is somewhere in between - yellow = V filter. You also have a list of the coordinates of the stars on the chart. Take some time to match up a few coordinates with their star. The list is in order of right ascension. The brightness in red (and sometimes blue) is listed.

One further note, lambda Ori is really a visual binary star. However, the components are just over 1 arcsecond apart so it is unlikely you will see them as two stars.

Observations

To find the scale of the CCD.

  1. Move to lambda Ori RA=5h 35m 8.3s, Dec=+9° 56' 03.0" (2000).
  2. Center it in the finder. It is a fairly bright star so you should not confuse it. It is a visual binary star and so you might see two stars close together. It is very close so it might blur into one blob.
  3. Center lambda Ori in the visual eyepiece.
  4. Move the telescope to the center of the group of stars around lambda Ori and check that you see them in the visual eyepiece. (The orientation may not be the same as on the chart. The chart is set for the CCD.)
  5. Take a picture of the lambda Ori field. You should be able to get the two stars next to lambda Ori and the two north of it also. Try R or I. Don't be afraid to go to 10 -20 seconds. Lambda Orionis will have to be overexposed. It is just too bright!
  6. Make sure your CCD picture is something like what you see in the central box on your chart. You might have some fainter stars also.

Be sure to get a good focus for the telescope. This will help you locate the stars precisely. You have two charts: one taken in the red and one in the blue. As you can see the brightness indicated for the stars on the charts depends on the colors of the stars. Again, if you use the R filter to take a CCD picture it should resemble the red chart. If you use the B filter it should resemble the blue chart.


Reduction and Analysis

Hint: The reductions are MUCH easier using a spread sheet.  If you make an error you can correct it and a spreadsheets calculations will be done automatically.

  1. Measure the x, y position of all of the stars on your image. The fainter stars can use the fitting tool. Lambda Orionis is over exposed so can't be fit. In fact since it is a visual binary, what you see as the center is not the location of either star separately. You might even want to leave l Ori out of the list entirely.
  2. Pair the star images you choose with the RA (x) and Dec (y) position of the same stars. Be careful.
  3. Calculate all possible pairs of differences in x's and y's and RA's and Dec's (three stars gives you 3 pairs, 4 gives you 6, 5 gives you 10, etc.). Do the RA in seconds and the Dec in arcseconds and the x's and y's in pixels. You may do your own labeling for the stars. Try to get some spread in x and in y. The more pairs you have the more accurate your result will be.
  4. Remember that the distance between any two points with coordinates (x,y) and (x',y') is

distance in pixels =  SQRT ((x-x')2 + (y-y')2 )

When you have calculated all the differences in x and y convert them to distances in pixels for each pair.

  1. The distance RA and Dec is more complicated. That is because RA is a) measured in seconds not arcseconds and b) depends on where you are on the celestial globe between the equator and the pole. At the equator 1 second in RA equals 15 arcseconds (360° / 24hours). At the pole all 24 hours of RA are in one point so the conversion is nonsense. In between it goes as the cosine of the latitude. At Dec +10° for lambda Ori the conversion between seconds and arcsecond is 15 x cos(10°) = 15 x .9848. So, before finding the distances in the sky, convert seconds RA into arcsecond by multiplying all of them by 15 x .9848.
  2. Now find the distance between each pair in arcseconds as above

distance in arcseconds = SQRT ((RA-RA')2 + (Dec-Dec')2 )

  1. Divide the distances in arcseconds differences by the differences in pixels
  2. Check to see if they are close to the same number. If not, check your measurements and your star identifications.
  3. Average the ratios

How accurate do you think your measurement is? If you know how to do a standard deviation calculation or have one on your spreadsheet, do it and quote it as your accuracy.

Remember the arcseconds/pixel number! You will need it for later exercises!

The CCD camera on the UGA telescope is an Apogee U6. It is 1014 x1024 pixels with each pixel 24 microns (2.4 x10-5 m). How large is the field of view of the CCD in arcseconds?

The scale of a telescope in arcsec/mm is related to the focal length of the telescope by

scale (arcsec/mm) = 206265/focal length (in mm)

You have the scale, so what is the focal length of the UGA telescope? Be careful of the units. The focal length is the distance from the mirror to where the telescope comes to a focus. Is your answer reasonable? (You should always try to answer that question.)

You can also use the formula above to find out how large the image of an object will be on the CCD. For example, how much of the CCD will Jupiter cover?

size of an image = angular size in arcseconds x focal length/206265

The f ratio of a telescope is found by:

f ratio = focal length/aperture

The aperture is 0.6m. F ratio is often quoted for cameras as well as telescope as f/? , where ? is usually a number 1 -20. What is the f ratio of the UGA telescope?

Lambda Orionis and the stars next to it to the west are members of the same star association. (The stars to the north are not necessarily part of the group.) That is they are in the same region of space not just in the same direction. Therefore they are approximately at the same distance from the Earth (about 1000 light years). If we assume this, then we can calculate their approximate distance from each other.

The small angle equation states

q = 206265 x d/D

Where d is the distance between the stars, D is the distance to the group of stars and q is the angular distance between the stars. Pick a pair of stars and find out how far they are apart.

Write Up

As you describe your work, show the data you used (in tabular form if it is convenient.) If you use a spreadsheet to do calculations be sure to label everything and indicate what formulas you used.

Be sure to answer every one of the questions posed in the above section (with enough information to know which questions you are answering.)