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# Astronomy 103, Summer, 2006

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# The Method of Transit Times

Summary: This method provides a simple way of measuring the angular diameter of an object viewed through your telescope. As the Earth rotates, objects appear to move from East to West in the sky. Because we know that the Earth completes one circle in 24 hours, timing how long it takes an object to move past a given point in the field of view of your telescope tells you what fraction of 360° that object appears to occupy.

This method takes advantage of the same effect as does the field of view measurement in the Telescope Basics lab, but the measurements you make are a little different.

What you will measure with this method is the angular size of the object. To understand what this is, see How to Measure Angular Distances.

Equipment needed: Telescope, stopwatch (or watch with a second hand).

## Measurement of the Transit Time

These are the measurements you make at the telescope.

1. Make sure your telescope drive is on.

2. Center the object as perfectly as you can in the center of the field of view of your telescope. You can use any eyepiece. (You can even use the finder scope, but this method will not provide reliable results for any but the largest of objects if you use the finder scope.)

3. Turn off the telescope drive. Look through the eyepiece. Note the direction in which the object appears to drift. Really, it is you that is moving; as the Earth rotates, you rotate along with it, and your telescope is rotating out from underneath the object.

4. Turn the telescope drive back on.

5. Using just the right ascension fine adjustment, move the telescope so that the object is close to the edge of the field of view towards the direction it drifts with the drive off. Do not adjust the declination of the telescope!

6. Turn the telescope drive off.

7. Start timing the instant that the edge of the object you are measuring touches the edge of the field of view. That is, start timing when the object starts to leave the field of view.

8. Stop timing the instant that the object has fully left the field of view. 9. If you want more reliable results, repeat steps 1-8 three or more times. Make sure that the results you get are consistent with each other. If one result is different from the others by a lot more than the others are from each other, you probably made a mistake on that trial, and should perform another trial or two to make sure you got a good result. Finally, average together all of the trials you believe to be good to yield your best measurement of the transit time.

## Calculations

The time you measured above is the amount of time that it took for the Earth to rotate just enough so that the edge of the field of view of your telescope passed from one side of the object to the other side of the object. If the object is on the Celestial Equator (i.e. at 0° declination), then it's a matter of simple unit conversion to figure out the angular size of the object given that we know the Earth rotates through 360° in 24 hours:

t × (1 rotation/24 hours) × (1 hour / 3600 sec) × (360°/rotation) × (3600"/1°)

where t is the transit time you measured in seconds. If the object is at the equator, this will yield the angular size of the object in arcseconds ("). If you multiply out all the numbers above and cancel out units where applicable, the actual calculuation you need to do for an object at the equator is simpler:

t × (15"/1 sec)

where, again, t is the measured transit time in seconds.

As you observed in the Telesocpe Basics lab, objects appear at declinations away from 0° to move slower through the field of view of the telescope. Therefore, if the object you are looking at is not at 0°, you have to correct for this effect. You can do this using the following equation (which always works, even at the equator):

a = t × cos(d) × (15"/1 sec)

where t is the transit time you measured in seconds and d is the declination of the object you are looking at. This gives you a, the angular size of the object in arcseconds. For large objects, it may be convenient to convert this to arcminutes or degrees, which you can do knowing that 1'=60" and 1°=60'.

Note: If you've done the Yearly Rotation of the Sky lab, you may realize that the Earth rotates through 360° in a time that is slightly different from 24 hours. However, this will introduce an error of far less than 1% into your calculations, so you may ignore it for purposes of this method. (Do you understand why the error it introduces is less than 1%?)