Take an observer at a point Q on the Earth’s surface — Page 426, Lesson 388

Let’s pick this up with twilight, because it’s the first thing that ties the Sun’s position to the time of day. Before sunrise there’s a period when it becomes light, and after sunset a period when it stays light — those are both called twilight. The Sun is below the horizon, but its rays are being refracted in by the atmosphere, which gives us that extended period of light. So to understand twilight properly, we have to be careful about what we mean by the horizon. Take an observer at a point Q on the Earth’s surface. His Sensible Horizon is the tangent to the Earth’s surface, ignoring terrain features. In other words, it’s the flat plane that touches the Earth at his feet — the horizon a spirit level would sense, the one instruments like a spirit level would detect. That’s why it’s called the sensible horizon — it’s the one that can be sensed by a level. Now, because of atmospheric refraction, the visual horizon — the one you actually see — sits below the sensible horizon by about 34 minutes of arc. That’s the first key number. When the top lip of the Sun passes below the visual horizon at sunset, the centre of the Sun is another 16 minutes of arc below that — and 16 minutes of arc is the radius of the Sun as viewed from Earth. So at sunset, the centre of the Sun is roughly 50 minutes of arc below the sensible horizon: 34 from refraction plus 16 from the Sun’s radius. Here’s the time connection. Fifty minutes of arc equates to 3 minutes of time. So at sunset, the centre of the Sun is already 3 minutes of time below the sensible horizon. The same argument works at sunrise — the centre of the Sun is 3 minutes of time below the sensible horizon then too. That’s why the length of day at the Equator is approximately 6 minutes longer than the length of night: 3 minutes gained at sunrise and 3 minutes at sunset. So twilight is that period before sunrise and after sunset when refracted light from the Earth’s atmosphere gives an amount of illumination. And that amount of illumination varies with two things: the Sun’s depression below the sensible horizon, and the atmospheric conditions. Now the first specific type — Civil Twilight. Civil twilight occurs when the Sun’s centre is between 0° 50’ and 6° below the sensible horizon. So it starts right at that 50 minutes of arc depression we just calculated, and runs down to 6 degrees. During civil twilight, illumination is such that you can carry out daytime tasks without additional artificial lighting — for example, a daytime visual approach is possible. And importantly, this is the only twilight period considered in the Air Almanac. Let me show you the geometry — the sensible horizon, the visual horizon sitting 34 minutes below it, and the Sun’s centre 50 minutes down at sunset. So the key numbers to hold onto: 34 minutes of arc for refraction, 16 minutes for the Sun’s radius, 50 minutes total, which is 3 minutes of time, giving 6 minutes extra daylight at the Equator. And civil twilight spans from 0° 50’ to 6° of depression.