At the summer solstice, the Sun is 23.5 degrees north of the celestial equator. Love Field, Dallas, TX is at 32.8 degrees north.
A "noon fix" is achieved by observing the altitude of the Sun at "local apparent noon", when the Sun is at its highest point in the sky. You can calculate your latitude by taking 90 degrees minus the observed angle above the horizon, or "altitude", and subtracting the declination, or Sun's angle north (or south) of the equator.
In this case, we need to work the problem backwards. So take 90 - (latitude) + declination, or 90 - 32.8 + 23.5 = 80.7 degrees.
Oh, one other thing; this is the altitude of the Sun above the SOUTHERN horizon. The Sun will never appear north of Dallas at noon. The question asks about the northern horizon. We could calculate the angle above the northern horizon as 180-80.7 or 99.3 degrees above the northern horizon.
If you are in the northern hemisphere, the altitude of the celestial equator above the southern is equal to your latitude.
If you're in the Southern Hemisphere, the celestial equator is above your NORTHERN horizon. But the angle is still your latitude.
That completely dependes on where you are on Earth ... your latitude.
The altitude of the sun above the southern horizon at noon on March 21 is
90 degrees minus (your latitude).
(Southern latitudes are negative, northern ones are positive.)
-- South pole . . . latitude = -90 . . . sun altitude = 90 - (-90) = 180 degrees = on the northern horizon
-- Equator . . . latitude = zero . . . sun altitude = 90 - (0) = 90 degrees = overhead
-- North pole . . . latitude = 90 . . . sun altitude = 90 - (90) = 0 = on the southern horizon
It all depends on your latitude. At the equinoxes the sun follows a path across the sky that is 90 degrees minus your latitude at noon. So if you live at the equator, since your latitude is zero, the sun is 90 degrees minus zero degrees, or 90 degrees overhead. If you live at 45 degrees latitude, north or south, then the sun is 90 minus 45, or 45 degrees high in the sky. If you live on the arctic, or antarctic, circle then the sun is 90 minus 66 1/2 degrees which makes it 23 1/2 degrees above the horizon.
Since you mentioned "southern horizon", you're probably in the northern Hemisphere,
so the following answers all refer to the northern Hemisphere:
At equinoxes, it's [ (90 degrees) minus (your latitude) ].
At June solstice, it's 23.5 degrees higher.
At December solstice, it's 23.5 degrees lower.
That's a great question! It's well written, and the conditions you describe are all
consistent and appropriate ... right up until almost the end of the question, and
that's where you hit a snag.
Whose Summer solstice are you specifying, the northern hemispheres' or the southern ?
You've forced me to answer it both ways.
-- On June 21, the summer solstice in the northernhemisphere, the sun's declination
is +23.5°. If you were on the equator, the sun's peak elevation would occur when it's
23.5° north of your zenith, so 66.5° above your northern horizon. At 4° south latitude,
it's 27.5° north of your zenith, and 62.5° above your northern horizon.
-- On December 21, the summer solstice in the southern hemisphere, the sun's declination
is -23.5°. If you were on the equator, the sun's peak elevation would occur when it's
23.5° south of your zenith, so 66.5° above your southern horizon. At 4° south latitude,
it's 19.5° south of your zenith, and 70.5° above your southern horizon.
This depends on your location and the date. If you are in Hawaii in June, the angle above the horizon can be 90 degrees; the Sun can be "straight up". In Hawaii (the only part of the US where this can happen) they call it "Lahaina Noon". From northern Canada at midwinter, the Sun might be only 15 or 20 degrees above the southern horizon.
And if you live in Australia, the Sun is generally above the NORTHERN horizon at mid-day.
That varies, depending on the time of the year, and on the latitude.
On the Tropic of Capricorn the Sun is overhead at the summer solstice and 47 degrees off the vertical, or 43 degrees above the horizon, at the winter solstice. So the observer here must be 7 degrees further north than the tropic of capricorn: the latitude is 16.4 degrees south.
summer solstice
The observer must be 15.5 degrees south of the Arctic circle, so 51.1 degrees north approximately.
At the June Solstice, the Sun is about 23.5 degrees north of the equator. London is at 51.5 degrees north latitude. So at midnight around the solstice, the Sun is (90-51.5) + (90-23.5) degrees north of London. So, the Sun is 105 degrees away from London. The northern horizon is 90 degrees, so the Sun is only 15 degrees below the northern horion.
The eastern horizon. Note: The sun does not rise due east, and the specific location changes throughout the year. The furthest south (on the eastern horizon) the sun rises is at the winter solstice (in the northern hemisphere), and vice versa.
On the Tropic of Capricorn the Sun is overhead at the summer solstice and 47 degrees off the vertical, or 43 degrees above the horizon, at the winter solstice. So the observer here must be 7 degrees further north than the tropic of capricorn: the latitude is 16.4 degrees south.
About 23.5 degrees
The latitude of the observer is equal to the altitude of Polaris. Therefore, if the altitude of Polaris is 43 degrees, then the latitude of the observer is 43 degrees.
summer solstice
summer solstice
summer solstice
summer solstice
The observer must be 15.5 degrees south of the Arctic circle, so 51.1 degrees north approximately.
Perth is at 32 degrees south and on the summer solstice the Sun's declination is 23½ degrees south. Therefore the Sun is 32-23½ degrees or 8½ degrees from the zenith, that is 81½ degrees above the horizon.
latitude of the observer
At the June Solstice, the Sun is about 23.5 degrees north of the equator. London is at 51.5 degrees north latitude. So at midnight around the solstice, the Sun is (90-51.5) + (90-23.5) degrees north of London. So, the Sun is 105 degrees away from London. The northern horizon is 90 degrees, so the Sun is only 15 degrees below the northern horion.
The Arctic Circle is the southernmost latitude in the Northern Hemisphere at which the sun can remain continuously above or below the horizon for 24 hours (at the June solstice and December solstice respectively).