Monday, December 12, 2016

Latitudes and Logitudes

I came across this youtube video while looking into how sextants work:
https://www.youtube.com/watch?v=CycmCFb-6VU
And I was surprised by how simple it all is.

In the northern hemisphere, if you keep your watch horizontal and point the hour hand at the sun, then halfway between the hour hand and noon is due south!

Likewise, longitude is really just the Greenwich Mean Time at which noon happens where you are. However, since there are 360degrees of longitude and only 24 hours on the clock, each hour is equivalent to 15 degrees of latitude. So if noon is at 18:30 GMT where you are, then your longitude is (18.5)*15 = 277.5W degrees. But since longitude is expressed in 180W to 180E, we convert 277.5W to (360-277.5)E = 82.5E which is the meridian of the timezone of India.

Likewise, for the moment let us assume the sun were perfectly above the equator all the time. That is, the earth's axis is not tilted 23.5 degrees. Then the angle between the sun and the horizon gives you an idea of the latitude you are at. At equator, the angle will be 90 degrees. At the poles the angle will be 0 degrees. So your latitude = 90 - angle between sun and horizon. But this only works at sharp noon, when the sun is at the highest point in the sky. At all other times, the sun will be lower in the horizon because the spot you are at is not facing directly at the sun.

So if you had a way to measure the angle of the sun, say a protractor with a string suspending a weight, or a sextant, you could compute your latitude.

But since the earth's axis is tilted 23.5 degrees, at various spots on the earth's orbit around the sun, the sun will be various angles off from the perfectly equatorial. This difference/correction is known as declination, and is available in the form of declination tables such as these:
https://www.starpath.com/blog_files/Table of the Declination of the Sun.pdf

So now, if we could tell precisely when noon happens where you are, we can find the latitude and longitude of where you are. So how exactly do we do that.

This is actually pretty simple. Around noon as you can guess it, make a few observations of the sun, and plot the observations on a graph. The sun's angle will form a bell curve, and the highest point on the curve is noon.Voila!

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