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I'm reading the book "Practical Astronomy with your Calculator or Spreadsheet 4th Edition" and I want to implement formula 22: Converting between angles expressed in degrees and angles expressed in hours. It says that:

To convert between angles expressed in decimal hours and angles expressed in decimal degrees, simply multiply or divide by 15.

So, I have to convert a angle in degrees minutes and seconds into decimal degrees and then multiply it 15 (or divide it by 15?).

When do I have to multiply and when do I have to divide by 15?

Or

How to convert degrees minutes seconds to hour minutes seconds (and viceversa)?

Dave L. Renfro
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VansFannel
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  • Hint: The angle in degrees in the range $[0^\circ, 360^\circ)$ converts to the angle in hours in the range $[0, 24)$; note that $360=15\times 24$ so that is where the factor $15$ comes from. –  Feb 01 '20 at 16:14
  • So, to get degrees I have to multiply hours, and to get hours I have to divide it by 15. Thanks a lot. – VansFannel Feb 01 '20 at 16:16

4 Answers4

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Nope! 360 degrees is 24 hours. 360 divided by 24 is 15. So 15 degrees is 1 hour of right ascension.

Stephen Kosciesza
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In one day = $24$ hours the sky ''rounds'' $360°$, so: $$ 24:360=h:\alpha° $$

Emilio Novati
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Each hour is $360^\circ/24=15^\circ$. Each minute of time is $15^\circ/60=15^\prime$, i.e. $15$ arcminutes. Each second of time is $15^\prime/60=15^{\prime\prime}$, i.e. $15$ arcseconds.

J.G.
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Most clocks feature a $12$ hours dial and a full turn is $360°$. Hence an hour is $30°$ !