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The Question

(Submitted February 10, 1997)

What are the altitudes of the Sun on the days of the Vernal and Autumnal Equinoxes, and on the Summer and Winter Solstices, knowing that the latitude of where we are measuring from is 40.3 degrees?

The Answer

Let's first define altitude. "Altitude" is the height an object is above the horizon. The altitude of the Sun varies throughout the day, but it reaches its maximum altitude around noon-time. So the most meaningful answer to your question would be the maximum altitude of the Sun on these dates.

At a north latitude of 40.3 degrees, the maximum altitude of the Sun is 49.7 degrees on the Vernal and Autumnal Equinoxes. This is because the Sun is crossing the celestial equator on those days, and the maximum altitude of the celestial equator is simply 90 degrees minus your latitude.

On the Summer Solstice, the maximum altitude of the Sun as seen from a north latitude of 40.3 is 73.2 degrees; on the Winter Solstice, it's 26.2 degrees. This is because the Sun travels along the ecliptic, which is inclined by 23.5 degrees from the celestial equator. On the day of the Summer Solstice, the Sun is at the point on the ecliptic which is furthest above the celestial equator (i.e. add 23.5 degrees to the equinox value). On the day of the Winter Solstice, it's at the point which is furthest below the celestial equator (i.e. subtract 23.5 degrees from the equinox value).

The 23.5 degrees should sound familiar, as it's the angle by which the earth's axis is inclined to its orbit. The celestial equator is an extension of the earth's equator onto the sky. The ecliptic is a projection of the earth's orbit onto the sky. The earth's orbit projected onto the sky is equivalent to the Sun's path across the sky through the course of the year. The maximum altitude of the Sun is just a matter of the geometry of these two orbits.

Jim Lochner
for Imagine the Universe!

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