The Method of Transit Times

Summary:T he method of transit times is a simple technique that makes use of the diurnal motion (i.e. the daily rotation of the Earth) to measure the apparent (or angular) diameter of a celestial object. We used a variation of this method to determine the angular diameter of the field of view. Knowing the diameter of the field of view allows you to estimate the size of objects you view through the telescope but for small objects like planets, or for more precise measurements, the method of transit times is to be preferred.

How it works: As the celestial sphere (the sky) appears to rotate in one day, celestial bodies drift through the field of a stationary telescope. Since the rotation of the sky is well known and constant (360^o in 24 hours), we can use that fact to measure the diameter of an object by simply timing how long it takes to cross the edge of the field of view with the telescope drive turned off. This is illustrated in the figure below. The object is about to enter the field of view (#1) and when it has reached (#2) it has traveled a distance equal to its own diameter. The angular distance traveled in the sky is simply the transit time (t₂-t₁) multiplied by the angular speed of the object.

Example:

The above example is strictly valid for an object located on the celestial equator (declination =0^o). Objects located away from the celestial equator also make one turn in the sky in 24 hours, but their apparent motion takes place on smaller circles than the celestial equator and their angular speed across the sky is correspondingly smaller. An extreme example is the pole star, Polaris. It is located about 1^o from the North Celestial Pole and if you point your telescope at it with the drive turned off, you will see that it hardly moves at all. This is exactly the same situation as we have on Earth. Someone standing at the North pole would make one turn in one day, but would remain stationary all along! At the same time, people on the Equator are the ones who are moving the fastest due do the Earth's rotation. We can correct for this effect in our measurement by introducing the cosine of the declination (the latitude in our analogy with the Earth ) of the object you are measuring. The angular diameter is correctly given by:

(Note: 24 hours = 86400 seconds.)

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Procedure:

1. Refer to the figure above.

2. With the telescope drive ON, acquire the object in the telescope, using the 25 mm eyepiece. If the object is small, switch to the 10mm eyepiece so that it has an appreciable size. Put the object in the center of the field of view. Focus precisely.

3. Turn the drive OFF. Using the RA slow motion knob (East-West motion), move the object to just outside of the field of view so that it will drift back in on its own. As it crosses the field of view, it should go through the center, i.e. travel along the diameter of the field of view. Alternatively, you can move the object near the edge of the field of view so that it will drift out.

4. Using a stopwatch, time how long it takes for the object to cross the edge of the field of view (between point #1 and point #2 on the figure). One lab partner looks through the eyepiece and the other keeps an eye on the stopwatch. Repeat the measurement 2-3 times, re-centering the object each time.

5. In your logbook, note the date and time, the name of the object and its declination (read off the star chart or using the declination dial on the telescope; to the nearest degree) and enter each of your transit time measurements.

6. Average your transit time measurements.

7. Determine the diameter with the following formula:

   Apparent diameter (in ") = (transit time in seconds) * cos (declination) * 15"

   Convert the diameter into minutes of arc (') if appropriate.

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Note the following conversions for a star located on the celestial equator:

Recall that 1^o (degree)= 60' (minutes of arc) =3600" (seconds of arc)