### Andromeda's Scale

Purpose:  Get a feel for angular size and scale, and what they mean.

Background:  Astronomers use degrees to specify both the location and the size of objects in the skies.  To a person observing from Earth, the heavens form a dome, 360 degrees around the outside edge, or circumference, and 180 degrees from one horizon to the other, through the highest point, the zenith.  An object's apparent, or angular, size is given by the angle it takes up moving parallel to the horizon  and the number of degrees moving perpendicular to the horizon.

Degrees are divided in to tenths and hundredths, or into arc minutes and arc seconds, with 60 arc minutes in a degree, and 60 arc seconds in an arc minute. One can express the same angular height as 10.2 degrees, or 10 degrees, 12 arc minutes. The Sun and Moon, which are the largest naked- eye objects in the sky, each appear to be about half a degree. Angular size is not the same as physical size, and the angular size of an object changes as its  distance from the observer changes. This may happen in a short time with cars and even pedestrians on Earth, but not so much with celestial objects!

 Suppose we want to find and measure the angular size of an extended object like a galaxy.  The angular size of a patch of sky where we look can be very important.  If we use a telescope to examine an area of large angular size, like 20 x 20 degrees, the galaxy may almost disappear, like a needle in a haystack.  A whole galaxy can look like just another star. In fact galaxies weren't discovered until well after the invention of the telescope for this reason.If we get a better telescope (increase the magnification), we are examining a smaller patch of sky in greater detail. This is fine as long as the area still includes the galaxy. Then the galaxy occupies more of the image.  It's the same when you zoom in on a friend with a camera lens; the photograph is the same size, but you get a "close up." Can an image have too much magnification?  Yes, because the size  of the film limits the size of the picture: zoom in too much and you might see only your friend's nose!  In astronomy too, the size of the telescope's field of view (lens), and the light detecting device (film) attached to it, are limited. In this exercise, we will vary the angular size and magnification of an image, keeping the physical size of the image the same. This is like the  photography example above, in which the photographer is able to change the distance to his subject.   This is not entirely realistic, as our distance from most large objects like Andromeda does not change.  The image producing engine we will use is able to simulate this effect by manipulating the pixels of large images.As a general rule, the larger the angular area of sky that is visible in your image, the lower the magnification. The higher the magnification, the smaller the area of sky shown in the image.  Your goal is to determine the best magnification for measuring the angular size of the object Andromeda, and to estimate its angular size. Procedure:  Read all instructions through #5 before you begin.  Go to the Skyview site:  http://skyview.gsfc.nasa.gov/easy.html.  Skyview is an interface to an archive that supplies images of many astronomical objects at various wavelength and magnifications.  Enter the name "Andromeda" into the space labeled "Coordinates of Source,"  The librarian recognizes common names for many objects, so you don't need numerical coordinates.  In the table labeled "Survey[s]" check optical, for a visible light image.   Go down to the "Optional Parameters" and use the pull-down menu (click and hold) to change the "Image Size" to 0.1x 0.1 degrees. Scroll back up to "Initiate Request" and click on the "submit" button.

Your image should appear after a few seconds in a new window. Write down your answers to these questions:

1. What do you see?   Describe the image.
2. Can you pick out Andromeda in the center of the image?   If so, how did you identify it?
3. Look below to see the image dimensions in pixels (picture elements). What is the angular size of each pixel in this image (degrees x degrees)?  Use a calculator if you need to.

6. Go Back to step 3 and change the size to 1.0  x 1.0 degree, and get a new image.

1. What do you see now?
2. Where in the image is Andromeda?
3. The relative magnification of this image with respect to the first one is  the angular size of the first image over that of the second.  What is the relative magnification of this second image?
4. What do you think its angular size  is? (degrees)  Hint:  you can use the pixel size you calculated last time, if you multiply it by the relative magnification, to account for the change in pixel sizes. Calculate for the largest and shortest dimensions that include the center.
5. Have you changed your mind about what you saw in the first image?

7. Go Back and change the size to 3.0 degree by 3.0 degrees.

1. How much of the image does the object take up now?
2. Has your estimate of Andromeda's angular size changed?  If so, what is it now?
3. What did we change by changing the angular size of the image?
4. What is the magnification of the third image with respect to the first one? Write down your answer.
 x1/3 x10 x1/30 x100
5. Do you see anything else in the image that looks similar to Andromeda? What is its angular size?
6. What is the fraction of the sky's dome shown in the 3 degree x 3 degree image? Remember, it is 360 degrees around, but only 180 degrees from horizon to horizon.