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Relating Angles to Hours

“I am amazing.  Everyone knows it.”

Narcissus

 

If we're ever going to master the physics that allows us to calculate star temperatures, we need to understand the sky.  For starters, the Earth moves beyond rotation and revolution.  For example, nutation and precession of the equinoxes.  Since the planet has an axis tilt of about 23.5 degrees, the precessional motion is determined by the tilt of the axis relative to the plane of its ecliptic, and one spin takes 25770 years to complete.

To create a system of interrelationships between planets and stars, we divide the celestial dome into two hemispheres separated by the equator.  The stars in the northern hemisphere have positive declinations, while those in the southern hemisphere have negative declinations.  Thus, the North Star, which at this moment is exactly aligned with the North Pole of the Earth, has a declination of +90⁰.

As we know, the largest circumference of the earth is measured at the equator.  By analogy, we assume that the positions observed from the celestial equator are known as right ascension, whose zero point is the moment when the Sun crosses the celestial equator, at the beginning of spring, a phenomenon called the spring equinox.

Finally, we come to units of measurement.

On Earth, when we use angles in our calculations of longitude and latitude, the celestial measurements are made in hours, minutes, and seconds.  Therefore, the degrees of the angles correspond to the Earth's rotation time.  That is, the planet rotates on itself in 24 hours, completing 360 degrees.

And then things get simpler.  One hour equals 15 degrees; 1 minute (or 15 degrees divided by 60) equals 15" (or fifteen arcseconds).  For example, the star Alpha Ophiuchi, in the constellation of Ophiuchus, is located at 17h34m56s, with a declination of +12° 33′ 38.1.″

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