Now, why does that tilt matter to us as navigators — Page 387, Lesson 338

Let’s start with the big picture, because this whole chapter hangs on one geometric fact. The Earth’s orbit around the Sun lies in a flat plane, and the Earth’s equator lies in a different flat plane. Those two planes — the Plane of the Ecliptic and the Plane of the Equinoctial — are inclined to each other at an angle of 23.5°. That angle has a proper name: the obliquity of the ecliptic. So when I say “obliquity,” I mean that fixed 23.5° tilt between the plane of Earth’s orbit and the plane of the equator. Now, why does that tilt matter to us as navigators? Because it means the Sun is not always directly over the Equator. At a given time of year, the Sun sits either above or below the Equator, and that angle determines the season and affects the length of daylight and night. That angle is called DECLINATION. Think of declination as the Sun’s latitude in the sky — it is analogous to latitude on the Earth. Just as latitude tells you how far north or south of the Equator a point on Earth is, declination tells you how far north or south of the celestial Equator the Sun is. The Sun’s declination changes annually. It swings from 23.5°N, when the Sun is overhead the Tropic of Cancer, down through 0°, when the Sun is overhead the Equator, to 23.5°S, when the Sun is overhead the Tropic of Capricorn, and then it comes back through 0° up to 23.5°N again. That is the full annual cycle. And there’s a useful definition tied to this: when the Sun, or any planet, is overhead an observer at an altitude of 90°, it is at its Zenith. So “zenith” is the point directly above you, and when a body is at your zenith, it’s exactly overhead. Now, mathematically, you can model the Sun’s declination as following a sine wave. Its peak amplitude is 23.5°, and its cyclic period is one year. So the declination rises and falls smoothly, like a wave, between those two extremes over the course of a year. You’ll sometimes see the dates of the solstices and equinoxes quoted as about the 21st or 22nd of the month. That’s not sloppiness — the precise date depends on the relationship between the year in question and the leap year cycle. So the exact day shifts slightly from year to year, and you are not expected to calculate the precise date of these solar events. Just know they fall around those dates. Here’s the key relationship for navigation: the length of daylight and night at a given latitude varies with the declination of the Sun. And because of that, the rate of change of the length of daylight is greatest when the rate of change of declination is greatest. Look at that sine wave — the steepest part of a sine wave is where it crosses zero, and that happens at the equinoxes, around March 21 and September 21. So that’s when daylight length is changing fastest. But — and this is important — that situation is not true in several special cases. The exceptions come when the latitude considered is either the Equator itself, or is above 66°N/S. Those are the special cases we’ll discuss later. So for now, hold onto this: the general rule about daylight changing fastest at the equinoxes applies to most latitudes, but not at the Equator and not poleward of 66° north or south. Let me tie it together. You have the obliquity of the ecliptic, that fixed 23.5° tilt. That tilt produces the Sun’s declination, which swings between 23.5°N and 23.5°S over a year, following a sine wave. Declination drives the seasons and the length of daylight. And the rate of daylight change peaks at the equinoxes — except at the Equator and above 66°N/S. That’s the core of this section.