Expert: Tom Whiting - 9/28/2008

Question
Dear Expert, yesterday i asked the follwoing question:
" How can we calculate the altitude of the Sun along the meridian on the first day of summer for an
observer at latitude 52 degrees north? What would the maximum altitude of the Sun be on the first day of winter at the same altitude?" But i was refused a reply. Today i was wondering whether you could comment on my answer? If so, that would be a great help. All i wanted was to double-check my answer from an expert - thank you for your help.
My answer is:

"First day of summer - means Summer Solstice - therefore Sun at highest point on the sky - at the furthest point furthest on the ecliptic, above the equatorial plane; the angle between the ecliptic and equatorial planes is 23.5 degrees.

Altitude  - therefore in the Horizon system.

Now, we need to combine information between the Horizon and Equatorial co-ordinate systems.  

When we talk about Equinoxes and Solstices we are talking about the positions of the Sun in relation to the Equatorial system.

Now, altitude of NCP (north celestial pole - equatorial system) = latitude of Observer = 52 degrees
Altitude of Equatorial plane = 90 degrees - latitude of observer i.e 90degrees - 52 degrees = 38 degrees.

Considering first the easier case of the altitude of the Sun, had the Sun been at the Vernal Equinox, which would mean its at the Equatorial plane: its altitude would be
90 degrees-52 degrees = 38 degrees.

But as it is at the Summer Solstice point - and the ecliptic is 23.5 degrees north of the equatorial plane, then altitude of Sun is= 38degrees + 23.5 degrees = 61.5 degrees.

On the Winter Solstice , the Sun is at its lowest point from the equatorial plane, therefore, altitude of Sun = 38 degrees - 23.5 degrees = 15.5 degrees. "

Would this be an acceptable answer?? thank you again fro your time, sincerely, Elsa.  

Answer
Hi Elsa,
Sorry, I mis-interpreted your question, as I thought you wanted me to do your homework.  Yes, you are exactly correct, except for an arithmetic error in Part 2, as 38 minus 23.5 equals 14.5 degrees high, not 15.5.  I would do the problem from more a descriptive standpoint, as opposed to mathematical.

We know at the North Pole on those dates, the sun is +23.5 degrees high on June 21 and -23.5 below the horizon on December 21.  Since 52 degrees (say, London) is 38 degrees farther south than the North pole, the sun in both instances would be 38 degrees higher than the North pole sun's position. Therefore,

for June 21, 23.5 plus 38 = 61.5 degrees high, and for Dec 21... 38 minus 23.5 equals 14.5 degrees high. (at 52 degrees N. Latitude).
Different way, but same answer.
Hope this helps,
Clear Skies,
Tom Whiting
Erie, PA