## Degrees minutes and seconds

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:

60 3600

If the angle is negative, the minutes and seconds are included within the negation:

60 3600

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:

Moon

Observer

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: