Field of View and Pleiades Observations

In this short lab you'll get more experience using the telescope by comparing what you see through it (and through binoculars) with a star chart. For this lab you'll determine the field of view of each of your optics and the pointing uncertainty of your guide scope.

Background Reading: Stars & Planets, p. 385 to 392 (Binoculars and telescopes), and star charts for the proper month

Understanding how astronomers measure angles is very important for observing. With the cross-staff ,or by holding your hand up to the sky, you've seen how we can measure relatively large angles. The field you see through an eyepiece is usually much smaller, and to make sense of a star chart its essential that you know how big this is. We call the angular diameter of the part of the sky that you can see through an eyepiece (either telescope or binoculars) the field-of-view (or just FOV). Remember that we measure relatively big angles in units of degrees. For example you know that the moon is about 1/2 degree across (as is the Sun). For most telescope observing (and some binoculars) this is a very big angle. We will often measure angles in arcminutes where 60 arcminutes are equal to one degree -- so the lunar diameter is about 30' (and notice that the 'minute' symbol to the upper right of the number is used to indicate arcminute units rather than writing out the word). Even arcminutes can be too large when we talk about the diameter of saturn (for example) and we will often talk about arcseconds as an angle unit. There are 60 arcseconds to an arcminute. The diameter of the moon is now about 1820'' (notice the 'seconds' symbol to the upper right is used to indicate arcseconds).

In the first part of this lab you must align your telescope guide scope cross-hairs with the center of the field of your 25mm eyepiece/telescope combination. Do this by pointing the telescope at a distant street light (or anything else that you can see through the telescope that doesn't move). You can adjust the pointing of the guider using the alignment screws so that the distant object is centered on the cross-hair and in the field of your telescope eyepiece. Sketch what you see for your lab writeup. Now look at the same object using the other eyepieces you have and sketch what you see. Do the same for the binocular view of the object.

Now estimate the angular size of what you're looking at. You can pick two edges of the street light or any other two points in the scene you see through your 25mm eyepiece. We'll do this only approximately since we have to guess two lengths to use the small angle formula. First guess the physical separation between the two points you've picked in the eyepiece. Guess this distance in feet and call this s. Be sure to write down and show on your sketch what this distance is. Now estimate how far it is from you to the object you're looking at. We're only guessing here so there is no right or wrong answer, but try to be as accurate as possible. For example the distance across Kapiolani park toward the ocean is about one football field or 300 feet and the length of the park is almost one mile or about 5000 ft. Call this distance d and mark it in your writeup. The small angle formula says that the angle (call it a) is a=s/d and the units of the angle will be in radians. This isn't a traditional astronomer's angle unit so we convert to arcseconds using a=206000s/d, where now a is in arcseconds (and this strange number just comes from factors of `pi' and the number of arcseconds in 360 degrees). What is the angular size of your object in arcseconds and in arcminutes? From this size and your sketch estimate the FOV of your eyepieces and guider in arcminutes or degrees.

Now we'll look at the sky to get a better idea of the telescope FOV. Use your text star charts to get your bearings and, by eye, locate the Pleiades. This is also known as Messier 45 (it was the 45th entry in Messiers catalog) or just M45. Below I've included three different charts plotted on three different angular scales. Make a sketch of what you see with the largest and smallest focal length eyepiece and with your binoculars. Now using these charts determine the FOV for each of these. Notice that the orientation of each of the charts is the same, but in general they will not be aligned with the horizon or east-west direction.

Lab Writeup Ingredients

Include sketches and a sentence or two describing how you aligned the guider.
Include sentences describing your calculations and how you estimated the FOV in each eyepiece and binoculars.
Include sketches and explanation for how you measured FOV using the Pleiades in two eyepieces and binoculars.
Now that you know the FOV, estimate how far off your guider pointing is from being perfectly centered.
BONUS point: Now that you know the FOV use this information to determine the angular size of the distant object you used to align the guider and then improve on your guess of the distance to this object.

Donald L. Mickey (mickey@ifa.hawaii.edu)

Last modified: March 10, 2005
http://www.ifa.hawaii.edu/users/mickey/ASTR110L_S05/Pleiades.html