Transit Measuring

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What is Vega's maximum altitude in the sky as observed from?

What is Vega's maximum altitude in the sky as observed from the Scottish Highlands (latitude 57°N, longitude 4° W)?
(Vega's right ascension is 18.5° and its declination is +39° )

Will Vega ever disappear from the sky and, if not, what will its minimum altitude be?
this is the question and it can be answered with the information provided

From any location at latitude L in northern hemisphere:

Looking at the southern horizon, the celestial equator crosses the meridian at altitude 90-L.

Declinations are measured from the celestial equator.

Therefore, altitude of a star above southern horizon = (90-L)+DEC.

If this angle is greater than 90 degrees, then the star's azimuth is north instead of south (however, mathematically, it is OK to say that the altitude is 110 degrees above the southern horizon).

In your problem:
L = 57
D = 39

Altitude at upper transit (measured above south horizon):

Alt = (90-57)+39 = 72 degrees.

For a fixed star, upper transit (a.k.a. meridian passage) is the highest altitude that a star can reach in your local sky.

Will the star set?

The altitude of the celestial pole (DEC=90) over the northern horizon, is the same as the latitude. At lower transit, the body is (90-D) degrees below the celestial pole. Therefore, altitude is L - (90-D)

For Vega in the Highlands, at lower transit:
Alt = 57 - (90-39) = 57 -90 +39 = +6

By definition, lower transit is the minimum altitude that the star can reach. Since Vega is still 6 degrees above the horizon at lower transit, then it does not set (it's altitude never decreases to zero).

However, in the highlands, you may be located where there are mountains blocking your northern horizon, higher than 6 degrees above the theoretical horizon (defined as 90 degrees from the zenith). So, depending on your exact location, it is possible that Vega "sets" behind a mountain.

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