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### Appendix B

# Method of Transit Times

**Summary:** The method of transit times
is a simple technique that makes use of diurnal
motion (i.e., the daily rotation of the Earth) to measure the diameter of
a celestial object. In order to be
used effectively, the object must be magnified to a reasonable size and
resolved. For this reason, the method of transit times is limited to
measuring the diameter of the moon, a few planets, and some surface
features of the moon and planets.

**Mathematical Basis:**

- Cosider the object of interest to be at distance D
from Earth.

- Assume the object is found in the sky at
declination angle
*delta* (i.e., at angle *delta* with
respect to the celestial equator). [See Figure 1 in
ClassPak, Appendix B]

- If we could observe the object for 24 hours, it would appear
to travel all the way around the sky -- a full 360 degrees --
because of the Earth's rotation. The size of the circle in the
sky that the object appears to travel has a radius r, where
r = D x cosine(
*delta*). The rate of drift is then

v = circumference of orbit / period of orbit = 2 x Pi x D x cosine (*delta*) / 24 hours

v = Pi x D x cosine (*delta*) / {12 hours x (3600 seconds/hour)}

v = Pi x D x cosine (*delta*) / 43,200 seconds

- Now, if we measure the time T required for an entire object to move
across a reference line in the field of view of the telescope,
then the diameter d of the object is given by the formula

d = v x T = Pi x D x T x cosine (*delta*) / 43,200 seconds

- Note: if the measured dimension (e.g. the rings of Saturn) is
* not * along the east-west axis, then you would need to make
an additional correction of this formula.

**Procedure:**

- Align the western edge of the object you wish to measure with
the crosshairs visible through the 10 mm eyepiece. (If the 25 mm
eyepiece is used, you may use an edge of the field instead of the
crosshairs, but this is harder to do.) Your answer does not depend on
which eyepiece you use, although the accuracy of your answer may change.

- Be sure the telescope drive is
** on ** to assure
the crosshair reference remains aligned with the object.

- Using your watch as a timer,
** switch the drive off
** and measure the time it takes for the entire object to
drift across your reference line (the crosshairs or the edge of the field).
The measured time is the transit time T.

- In order to obtain the current declination angle of the object,
the polar axis of the telescope must be aligned with the celestial
equator. The declination can then be read from the declination setting
circle after centering on the object. If you have not polar aligned
your telescope, you would need to determine the declination from a
reference table or by determining the position of the object in the
sky and comparing it to star maps with marked declination circles.