ASTRONOMY FUNDAMENTALS - Chapter 2, Exercise 1 Solution
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Converting Right Ascension from Hours to Degrees

PROBLEM
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A star has a right ascension of 6 hours, 30 minutes. Convert this to
degrees.

SOLUTION
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Using the real conversion: 1 hour of right ascension = 15 degrees.

Step 1 - convert the whole hours:
    6 hours x 15 degrees/hour = 90 degrees

Step 2 - convert the remaining 30 minutes:
    30 minutes is half an hour, so it converts to half of 15 degrees:
    30 minutes x (15 degrees / 60 minutes) = 7.5 degrees

Step 3 - add the two parts together:
    90 degrees + 7.5 degrees = 97.5 degrees

ANSWER: A right ascension of 6h 30m equals 97.5 degrees.

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WHY THIS WORKS AS AN ANSWER

Right ascension is measured in a time-based unit specifically because
astronomers historically tracked a star's position by timing when it
crossed the meridian as Earth rotated - one full rotation takes 24
hours and corresponds to one full 360-degree circle. Dividing 360 by 24
gives exactly 15 degrees per hour, which is why that conversion factor
works for any right ascension value, not just this one. The same ratio
applies to the smaller units too: since 1 hour = 60 minutes = 15
degrees, 1 minute of right ascension equals 15/60 = 0.25 degrees (or
equivalently, 15 arcminutes) - the same proportional relationship,
just at a finer scale.