Out walking the dog recently one of our colleagues was struck by how low in the sky the Sun was? It was almost midday and approximately halfway between the Winter Solstice and the Vernal Equinox, and the Sun seemed very low.
So he set about working out the Sun's elevation at the Solstices and Equinoxes at various Latitudes.
Can you produce equations for these three times of the year based on Latitude?
Let L be the location's Latitude.
At both Equinoxes the Sun's maximum elevation will be 90 - L degrees. At the Equator it will be overhead and at the Poles it will be on the horizon.
At the location's Winter Solstice the Sun's maximum elevation will be 66.5 - L degrees (that is 90 - 23.5, which is the Earth's tilt). At the Equator the sun will be at 66.5 degrees. At one of the Tropics it will at 43 degrees, the lowest it gets in the Tropics. At the Arctic/Antarctic Circle it will be on the horizon. And at the Pole it will be 23.5 degrees below the horizon.
It gets a little trickier for the Summer Solstice. The equation is 90 - ABS(L-23.5). At the Equator the sun will be at 66.5 degrees. At one of the Tropics it will be overhead. At the Arctic/Antarctic Circle it will be 47 degrees, And at the Pole it will be at 23.5 degrees.