| MadSci Network: Astronomy |
The maximum altitude of the Sun in Northern latitudes (ie above the Equator) occurs on Midsummer Day (Jun 22)- the summer solstice. At this time, the axis of the Earth is tilted such that the North Pole is inclined 23.5 degrees from the vertical towards the Sun. At this time, at latitude 23.5 degrees North, the Sun is directly overhead ie altitude is 90 degrees. This latitude is known as the Tropic of Cancer, and includes the well of Syene in Upper Egypt, used by the Greek astronomer Eratosthenes, well before the Christian Era, to estimate the size of the Earth to within 5% accuracy. He used the difference between the due vertical angle of the Sun at midday on June 22 at Syene, and the 82.5 degree elevation at Alexandria 500 miles to the North at the same time and date, to arrive at the diameter of the Earth by simple trigonometry (500 miles subtended 7.5 degrees, therefore 360 degrees corresponds to 500 *360/7.5 ie 24,000 miles). New York's latitude is 40 degrees 45 minutes North. The Sun's maximum altitude is therefore 90 degrees (overhead) minus 40 degrees 45 minutes (latitude of New York) but plus 23.5 degrees (tilt of Earth towards the Sun at June 22 - mid summer). The final answer is therefore that the Sun is 72 degrees 55 minutes above the horizon or 17 degrees 5 minutes south of the vertical on that date - the maximum possible value. References: "The Fabric of the Heavens" by Stephen Toulmin and June Goodfield, Pelican Books 1961 The Sky III, Astronomical Software by Steve Bisque -- Michael Martin-Smith
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