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The numbers below follow the inset numbers given in the figure above.
The visibility has three numbers, the first one is the rising time, the second one the transit time, and the last one the setting time. The difference between the rising and setting time is usually around twelve hours, and the transit occurs when the object is right above our head, when the object reaches the highest position in the sky on a given night.
It is always better to observe an object around the time of transit. Not exactly at the time of the transit, but around that time. If the difference between rising and setting time is twelve hours, then it takes approximately six hours for an object to reach the transit position after its rise. So, for example, if I see that the Andromeda galaxy will transit at 12 am, 16 Oct, then it must have risen at around 6 pm, six hours earlier. If it was near the horizon six hours ago, then it would be halfway toward its transit around 3 hours ago, meaning at around 9 pm.
The rising, setting and transiting can be explained using a protractor or goniometer shown above. It has 180 degrees marked from left to right and right to left. If we are facing toward north, east would be to the right and west to the left. There are 180 degrees from right to left, east to west.
If the observer is located at the center of the horizontal line, then the object is toward 0 degree during the time of rising, toward 90 degrees during the transiting time, and toward 180 degrees during the setting time. An astronomical object might go up or down by an angle of around 15 degrees in one hour, so a total of 180 degrees in 12 hours. The actual time taken depends on many other things which we will skip for now.
We can observe an object for around 4 hours on either side of its transit. If Andromeda transits, reaches its highest point, at 12 am, then we can observe it from 10 pm to 2 am, which suits us very well because our classes are typically from 10 am to 11 am.
The size of an object is also very important. It should not be too small or too big compared to the field of view (FoV) of the telescope. The size and FoV are measured in angles, so we need to understand the units of angle degree, arcminutes and arcsecond.
The angles within a complete circle are conventionally measured in degrees. A circle has a total of 360 degrees, each of the four quadrants having exactly 90 degrees. One degree is divided into 60 arcminutes (‘arcmin’ in short) and 1 arcmin is further divided into 60 arcseconds (arcsec). Arcmin is sometimes expressed using a single quotation mark ($'$), and arcsec sometimes by a double quotation mark ($''$). The symbol for a degree is $^\circ$. So we could write
$$ 1^\circ = 60' = 3600'' $$
$$ 1 \text{ deg } = 60 \text{ arcmin } = 3600 \text{ arcsec } $$
because $1'=60''$, that is 1 arcmin = 60 arcsec. Remember that 1 deg is the size of our pinkie finger, so 1 arcmin is a very small angle, and 1 arcsec even smaller.
In this course, you will encounter astronomical objects that have sizes of around a degree or a few arcmins. For example, the size of the sun or the moon is around 0.5 deg, that is around 30 arcmin. On the other hand, the size of the Andromeda Galaxy in our sky is more than 3 deg, too big for our telescopes.
Our telescopes have FoVs of around 1 deg.