In November, the real Sun crosses an observer’s meridian at 1144 — Page 387, Lesson 342

Let’s start with the two examples at the top, because they set up the whole idea of why we need to distinguish between the real Sun and the mean Sun. In November, the real Sun crosses an observer’s meridian at 1144. The mean Sun crosses the same meridian 16 minutes later, at 1200 LMT — and that 1200 LMT is by definition. In February, the real Sun crosses at 1214, and the mean Sun crosses 14 minutes earlier, again at 1200 LMT by definition. So the real Sun can be ahead of or behind the mean Sun, and the difference changes through the year. That’s the heart of the matter: the mean Sun is a fictional, perfectly regular Sun that we define to cross the meridian at exactly noon, while the real Sun wanders a little. Now let’s talk about the year, because there are three different kinds and each has a precise definition. A Sidereal Year is the time taken by the Earth to complete an orbit of the Sun measured against a distant star. Its length is 365 days, 6 hours. The key word is “sidereal” — it’s measured against the fixed stars, so it’s the true orbital period. A Tropical Year, also called an apparent solar year, is the length of one cycle of the seasons. Its length is 365 days, 5 hours, and 48.75 minutes. Notice it’s slightly shorter than the sidereal year — about 11 minutes shorter — because the Earth’s axis precesses, and the seasons are tied to the position of the Sun relative to the equinoxes, not to the distant stars. A Calendar Year is normally 365 days. It’s kept in step with the tropical year by adding a day every 4th year — that’s a leap year. But there’s a fine adjustment made on 3 occasions every 400 years. The rule is: at a centennial year, when the first two numbers of the century are not divisible by 4, the leap year is omitted. So 1900 was not a leap year, but 2000 was, because 20 is divisible by 4. That’s how we keep the calendar aligned with the tropical year over the long run. Now let’s move to Hour Angle. We’ve already seen that the Declination of a celestial body — in our case, the Sun — is analogous to latitude. In the same way, Hour Angle is analogous to longitude. That’s the key parallel: declination is the celestial version of latitude, and hour angle is the celestial version of longitude. Here’s the physical picture. The Earth spins in an easterly direction, 360° in every 24 hours. So a celestial body — the Sun or a star — will transit across a given meridian at 24-hour intervals. To make this easier to think about, we simplify by considering that the celestial bodies circle the Earth in westerly directions. The Sun rises in the East, travels westerly to set in the West, and continues westerly to eventually rise again in the East. So the apparent motion is westward, even though the real motion is the Earth spinning eastward. Now the formal definition. The Hour Angle of a celestial body is defined as the arc of the Equator — also called the equinoctial — intercepted between the meridian of a datum and the meridian of the body, measured westwards from 0° to 360°. So when a celestial body transits a given meridian, its Hour Angle is 000°. When the body transits the anti-meridian — that is, the meridian exactly opposite — its Hour Angle is 180°. If the given meridian is Greenwich, then the Hour Angle is known as the Greenwich Hour Angle, abbreviated GHA, and it’s directly analogous to longitude. Let me make that concrete. A body with a GHA of 050° will be transiting the 050W meridian. A body with a GHA of 180° will be transiting the 180W meridian. But a body with a GHA of 270° will be transiting the 270W meridian — which is the same as the 090E meridian. So GHA tells you exactly which meridian the body is over, measured westward from Greenwich. That figure shows the Earth’s orbit, which is the context for why the real Sun and mean Sun differ. And the later figures — Figure 24.3, 24.4, 24.5, and 24.6 — show the inclination of the Earth’s orbit, the seasons, the side view of the orbit, and the declination of the Sun. Those are the pieces that explain why the real Sun’s meridian crossing time shifts through the year, which is exactly what the November and February examples at the top were showing you. So to tie it all together: the mean Sun is our regular reference that defines 1200 LMT, the real Sun wanders relative to it, and the hour angle — especially the Greenwich Hour Angle — is how we locate a celestial body in longitude, just as declination locates it in latitude.