lowest altitude of Alkaid?

Can anyone help me with this question?
I need to calculate the lowest altitude of Alkaid at my latitude which is
55
deg 45.9'

I found a formula for calculating the altitude at meridian transit facing
south but not sure if I can use it to calculate the altitude looking
directly north.

The formula was
objects altitude = (90 - observers latitude) + stars declination
This works out as
(90° - 55° 45.9') + 49° 18.795'
= 83° 32.895'
Obviously this is for transit of the observers meridian looking south


I modified the formula to
objects altitude = stars declination - (90 - observers latitude)
Because it appears to give me the correct answer (15° 4.695' ) but i'm not
sure its right and im having trouble getting my head round it lol

Does it look right?
comments?

In article . 38,
Paul Stephen writes:
I need to calculate the lowest altitude of Alkaid at my latitude which is
55 deg 45.9'

Start with the north celestial pole, which has an elevation equal to
your latitude. Then think in terms of polar distance, which is 90°
minus declination. The declination of Alkaid is 49° 18.795', as you
give, so its polar distance is 40° 41.205'. At "upper culmination"
Alkaid will be 40° 41.205' higher in the sky than the pole. (This is
greater than 90 degrees, so it will be beyond the zenith or in the
south.) At lower culmination, Alkaid will be lower than the pole by
its polar distance: 55° 45.9' - 40° 41.205' = 15° 4.695'.

Looks like the formulas you gave are correct, but maybe the above
will be easier to understand. Just remember how to interpret
negative angles or angles greater than 90°.

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
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