Astrometry
Astrometry is the science precision measuring of stellar and planetary positions and motions. Important applications include measuring the positions of newly discovered variable stars, supernovae, comets, and asteroids. Future applications will include extremely accurate measurements of the positions of stars in an attempt to find extrasolar planets.
Astrometry is one of the oldest branches of astronomy. The earliest known star catalog came from the Greek astronomer Hipparchus. Tycho Brahe, the noted Danish astronomer, produced a star catalog at the end of the Dark Ages.
Astrometry in the 19th century was accomplished with transit telescopes. These telescopes measured the precise altitude and time of stars crossing the celestial meridian. The measurements provided a fundamental reference frame upon which other measurements could be based.
The advent of space based astronomy has given astrometry a big boost. The Hubble Space telescope requires the knowledge of stellar positions to accurately point the telescope. Hence the birth of the Hubble Guide Star Catalog, which contains the positions of 15 million stars down to 14th magnitude. That catalog has been overtaken by the Hipparcos and Tycho catalogs. Hipparcos measured, with the unprecedented accuracy of 0.002 arcseconds, the positions of 118,000 stars. The Tycho catalog contains 1,058,000 stars to an accuracy of 0.05 seconds. The US Naval Observatory has two catalogs, the USNO-A2.0 and USNO-SA2.0, that contain over 57 million stars.
Astrometric accuracy depends on having a precise reference frame within which the position of celestial objects can be measured. The above catalogs provide the necessary reference frames. The exercise below demonstrates how to make precise positional measurements of objects within a CCD frame.
Step 1: Load the image “Ah102dad.fts”. This image contains three asteroids and can be found in the astrometry directory on your computer. Click the Measure—Astrometry menu item.
Step 2: You need to create the reference frame for this image. This has already been done for you, but you could use one of the above mentioned catalogs to do so. The overlay we will use here was created using the Hubble Guide Star Catalog. First, enter the focal length of the telescope used in this image (1909 mm, not a telescope at Mt.Cuba). Next, you want the image to have North on top and East on the left. That has already been done for this image. Now click the “Load Ref Data” button. Click the “Reference File” button since we already have a reference file and don’t need to create one from the catalogs. Find the file “AH102.gsc” and open it.
Click the “Toggle Overlay” button until the overlay appears. It will appear as a collection of red circles, with a blue cross marking the center of the field.
Step 3: Align the overlay to match the stars. There are arrow keys on the Astrometry Tool that you can use to move the overlay up/down and left/right. You can change the speed of movement by clicking the center button marked X1. You must also rotate the overlay a bit (Parallactice Angle)
Question: What is the best parallactic angle for this image?
Step 4: Select a set of reference stars. Select the circled star in the center of the image with the mouse and click the “Select as Reference” button. A green circle will surround the star with the label R1. Select two more reference stars. Try to pick nice, isolated stars that will give a good centroid. Remember to only select stars that appear on the overlay. Once you have selected three stars, click the “Recalculate Focal Length” button. The three stars can be used to give a very accurate measurement of the focal length of the telescope. What is the new value?
Select a few more reference stars. You will need at least 4 stars for the following steps.
Step 5: Select your target. Zoom in so you can see the fainter stars better (use zoom button on the Display Control. The overlay will disappear, but if you click “toggle overlay” when you are finished zooming, it will reappear. There are three asteroids in this image. The first one is at X=115, Y=48. Click on it with the left mouse button. Then click “Select as Target”. Enter a name for the target and click OK. A yellow circle will appear around the target with the label T1. If the circle centers on the brighter star below this object, click “Clear Target(s)” and try again with a smaller search radius
Step 6: Now click the “Measure” button. The Astrometric Residuals window will appear, showing the residuals (“errors”) from the calculation. Open the Data Log window from the taskbar. In it you will see the calculated right ascension and declination for this object, the error for both coordinates, and the magnitude of the object.
Question: What are your residuals in right ascension and declination? How does this compare with the accuracy of the Hipparcos catalog?
Click the “report” button. Select the verbose option and type in an object name, time, and date. Click “Save” to save the report. If you still have your floppy, save it there so you can include the report in your journal. If you don’t have your floppy, ask for one.
Step 7: Repeat the above using “ah102.ref” as your overlay. This overlay was created using the USNO A2.0 catalog. Use the asteroid at X=94, Y=109 as your target.
Questions: 1) How does this overlay differ from the Guide Star Catalog overlay?
2) How does increasing the number of reference stars affect your accuracy?
Part 2: Pluto
You will need three images, plutojuly12.fts, plutojuly13.fts, and plutojuly16.fts. The files are located in the astrometry directory on your computer.
Step 1a: Open the three Pluto images. Examine the fits header (under Edit Fits header) and record the date and time of each observation.
Step 1b: Locate Pluto. You will need to compare the stars in the July 12 and 13th images to locate the planet Pluto. First, register the images (under multi-image). Pick either the 12th or 13th image as your reference image and the remaining image as your subject image. You need to identify two stars that are present in each image. The Register window only displays a small fraction of the image. Use the slide bars to move around in x and y to locate identical stars. When you have located the same two stars in each image, click “apply”. A new window appears, which has cropped your subject image to match your reference image.
Step 1c: Now blink the images (under multi-image). Blink your original reference image with the referenced image. Try to ignore the edges. You should see Pluto jumping back and forth as the images switch. This is the technique Clyde Tombaugh used to initially discover Pluto, except he used the actual photographic images and a special machine called a “blink comparator”.
Step 2: Now we need to determine how far Pluto moves between observations.
Start with the July 12th image. The bright star at X=216, Y=271 has the coordinates right ascension =17 hours, 1.031 minutes, declination= -12 degrees 42.868 minutes. You need to create an overlay for this field. You will need the Hubble Guide Star Catalog CD. Insert the CD into your CD drive. Click “Preferences”, then “Reset astrometric database locations”. You will need to tell AIP where to find the Guide Star Catalog CD.
Step 3: Click “Measure Astrometry”. The astrometry window will appear. Enter a preliminary focal length of 4600 mm for the 24 inch telescope. Click “Load ref data”, and click the button for the Hubble GSC. You will need to enter the right ascension and declination for the star at X=216, Y=271. When you have finished, click “Ok”. The program may ask you to locate the GSC CD. Direct it to the proper drive, and then to the directory “Tables” on the CD. When your overlay is complete, save it to a file.
Step 4: Go back to the Astrometry tool. Click “Toggle Overlay” until the overlay appears. If AIP asks for a camera type, Ap7 is the correct response. Now you need to align the overlay and the stars. Bear in mind that North should be up and east on the left. You may need to “mirror x” or “mirror y” to get the stars to align.
Question: What is your best parallactic angle?
Step 5: Select three reference stars and recalculate the focal length.
Question: What is the new focal length?
Step 6: Select a few more reference stars, and select Pluto as a target. Click “Measure”.
Question: Record the right ascension, declination, standard deviations, and magnitude of Pluto.
Step 7: Repeat for the July 13th and July 16th images. Make sure to enter the correct focal length before you begin each measurement!!
Question: How far does Pluto move in 1 day (answer in both pixels per day and arcseconds per day)?
Question: Given that Pluto will move 360 degrees (1 orbit) in 248 years, do you think your answer above is sensible?