Then it descends vertically to the western horizon, where it sets — Page 432, Lesson 392

Let’s start with the idea that gets corrected right away: it is a romantic, but false, idea that after sunset at the Equator it becomes dark immediately. I want to walk you through why that’s wrong, and then we’ll build the whole twilight picture from there. Picture yourself standing on the Equator on or about March 21st or September 21st — those are the Equinoxes. Looking east, the Sun rises and travels apparently vertically upwards until it is directly overhead you. Then it descends vertically to the western horizon, where it sets. So the Sun’s path is a straight vertical line in the sky. Now, at the moment of sunset, we define a position called position A. At position A, the top edge of the Sun has just passed below the visual horizon. But here’s the key: the Sun’s centre is not yet at the horizon. At position A, the centre of the Sun is 50 minutes of arc below the sensible horizon. Let me unpack that. The sensible horizon is the horizontal plane through the observer’s eye — the true geometric horizon. The visual horizon is what you actually see, and because of refraction and the Sun’s finite size, the top edge disappears while the centre is still 50 arc-minutes below that sensible horizon. So that 50’ is the angular distance the Sun’s centre has already sunk. Then we move to position B. At position B, the centre of the Sun is 6 degrees below the sensible horizon. And that 6 degrees marks the end of evening civil twilight. So civil twilight is defined as the period from sunset until the Sun’s centre is 6 degrees below the sensible horizon. Now, the duration of twilight is the angular arc the Sun travels between position A and position B. That’s 6 degrees minus 50 arc-minutes. Since 6 degrees is 360 arc-minutes, subtracting 50 gives 310 arc-minutes, which is 5 degrees and 10 minutes of arc. And that angular arc corresponds to 21 minutes of time. So at the Equator, twilight lasts 21 minutes — and that is the minimum period of twilight anywhere on Earth. That’s the equatorial baseline we’ll use. Now let’s see how twilight changes as you move away from the Equator. We’ll call the equatorial case case (i) — the baseline, 21 minutes minimum. Case (ii) is an observer whose latitude is farther north than the declination of the Sun. In this example, that’s an observer in the Northern hemisphere. Declination is the Sun’s angular distance north or south of the celestial equator — so here, the observer is north of the Sun’s declination. For this observer: the Sun rises in the East, travels westward, at 1200 LMT — that’s local mean time, noon — the Sun is due south of the observer, and it sets in the West, following a slanted path. The key result: the duration of twilight will be longer than 21 minutes. Case (iii) is the mirror image: an observer whose latitude is farther south than the declination of the Sun — in this example, the Southern hemisphere. Again: the Sun rises in the East, travels westward, at 1200 LMT noon the Sun is due north of the observer, and it sets in the West. And again, the duration of twilight will be longer than 21 minutes. So the pattern is clear: at the Equator you get the minimum, 21 minutes; anywhere north or south of the Sun’s declination, twilight lasts longer. And in both case (ii) and case (iii), the duration of twilight can be calculated using the Air Almanac — that’s the reference publication that gives you the data to work out twilight times for any latitude and date. Let me tie the geometry together. The reason twilight lengthens away from the Equator is that the Sun no longer sets vertically. At the Equator it drops straight down, so it crosses the 6-degree twilight band in the shortest possible time. Away from the Equator, the Sun’s path is oblique — it slides down at an angle — so it spends more time between the 50-arc-minute point and the 6-degree point. That extra angular travel is exactly why the duration stretches beyond 21 minutes. So the three things to hold onto: civil twilight ends when the Sun’s centre is 6 degrees below the sensible horizon; at the Equator that takes 21 minutes, the global minimum; and anywhere else, north or south of the Sun’s declination, twilight is longer, with the Air Almanac used to calculate the exact duration.