Because the celestial sphere appears to be infinitely large, distances on it can only be measured as angles. For example, the apparent width of the Moon is half a degree, which means that two opposite edges of the Moon make a 0.5° angle with its vertex at the observer's eye (Figure 2.5). In similar terms, we can talk about two stars being ten degrees apart or the true field of a telescope being a quarter of a degree.
There are 360 degrees (360°) in a full circle. Each degree is divided into 60 arc-minutes or simply minutes (60'), and each minute is divided into 60 arc-seconds or simply seconds (60''). Thus 1' = 1/60° and 1'' = 1/3600°.
Some calculators have a built-in function to convert degrees, minutes, and seconds into decimal degrees and vice versa. If yours doesn't, the following examples will show how the conversion is done.
To convert 33°45'18'' into decimal degrees, simply add up its component parts:
If the angle is negative, the minutes and seconds are included within the negation:
It is probably easiest to ignore the minus sign until after the conversion.
Converting the other way is more complicated. First split the integer part from the fractional part:
Now convert the fractional part into minutes:
Figure 2.5. The apparent width of the Moon is half a degree. (From Astrophotography for the Amateur, Cambridge, 1999.)
If decimal minutes are good enough, you're done. Otherwise convert the fractional part of the minutes into seconds:
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