Using the

celestial sphere, it becomes quite easy to calculate the what the height of the sun at noon will be for any given day, if you know your

latitude. To start off, I'll define a few terms.

Imagine the earth is encased in an

arbitrarily large crystal sphere: this is the

celestial sphere. The

celestial equator is the circumfrencial line that would appear if the

equator on Earth was expanded outward until it was resting on the celestial sphere. Another important circumfrence on the sphere is the

ecliptic. This is the

plane that most of the planets orbit in. If the

rotational axis of the Earth was perfectly

perpendicular to the ecliptic plane, then the celestial equator and the ecliptic line on the celestial sphere would be the same. However, the Earth's axis is angled 23.5

degrees away from perpendicular.

When looking up at the celestial equator on

Earth, the peak of the

arc it describes in the sky is directly related to your

latitude. If you're standing on the

terrestrial equator (latitude = 0), then the peak of the celestial equator is at an

elevation of 90 degrees. If you're at the one of the poles (

absolute latitude = 90), then the celestial equator's elevation is 0 degrees. The height of the celestial equator is always equal to 90 minus your absolute latitude.

The celestial equator is an important land (sky?) mark because its height when observed from Earth is always easy to

calculate, and the postion of other celestial objects relative to it can also be calculated. On the two equinoxes, the plane of the ecliptic describes the same arc as the celestial sphere. During the solstices, the ecliptic varies from the celestial equator by 23.5 degrees, the amount by which the Earth's axis varies from the ecliptic. During the

winter solstice, for those in the northern

hemisphere, the height of the ecliptic will be 90 - your latitude - 23.5 .

Again, the height of the ecliptic is useful because all objects in its plane (i.e, the Sun), are found at that height. So if you know your latitude, and want to calculate the height of the Sun at noon during the

summer solstice (and you live in the northern hemisphere), the elevation will be: 90 - your latitude + 23.5 degrees. Ta da!

"Aah," you say. "That's sort of interesting, but what would be a lot cooler would be if I could do that for

*any* given day."

Well, that's not too much harder. Imagine taking some

cosmic scissors and

*snipping* the juncture between the ecliptic and celestial equator at the

spring equinox. Now peel these two lines off the sphere, and lay them on a graph, with the celestial equator as the x-axis. If the y-axis is elevation, the ecliptic will form a

sine wave, with an

amplitude of 23.5 degrees. To calculate the difference between the ecliptic from the celestial equator, the

function is (where x = number of days past the spring equinox):

Difference = 23.5 * ( sin ( x * 360 / 365)) Make sure you use

degrees to calculate sin(x)!

The inside function ( x* 360 / 365) converts the day of the year to degrees. To find the actual height of the sun at noon, take the difference, and add it to the height of the celestial equator for your observing location. Voila!