Now, the year — Page 387, Lesson 342

Let’s pick this up right where the real Sun and the mean Sun left off, because those two examples are the whole reason we need to talk about the year and about hour angle. I want you to hold onto that idea: the real Sun and the mean Sun cross the meridian at different times, and that difference is what we call the equation of time. In November, the real Sun crosses at 1144 and the mean Sun crosses 16 minutes later at 1200 LMT, by definition. In February, the real Sun crosses at 1214 and the mean Sun crosses 14 minutes earlier at 1200 LMT. So the real Sun can be ahead of or behind the mean Sun, and that’s the heart of it. Now, the year. We have three different kinds of year, and you need to keep them separate. 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. That’s the Earth’s true orbital period relative to the fixed stars. 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 shorter than the sidereal year, and that’s because the seasons are tied to the Sun’s apparent position, not to the stars. A Calendar Year is normally 365 days. It’s kept in step with the tropical year by adding a day every 4th year, which is a leap year. And there’s a fine adjustment made on 3 occasions every 400 years. The rule is: at a centennial, when the first 2 numbers of the century are not divisible by 4, the leap year is omitted. So the year 2000 was a leap year because 20 is divisible by 4, but 1900 was not, because 19 is not divisible by 4. Now let’s move to Hour Angle. You already know declination is analogous to latitude. In the same way, Hour Angle is analogous to longitude. 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. It’s convenient to simplify this 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 we measure the hour angle westwards. Here’s the formal definition. The Hour Angle of a celestial body is the arc of the Equator, which we also call 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, its Hour Angle is 180°. Now, if the given meridian is Greenwich, the Hour Angle is known as the Greenwich Hour Angle, or GHA, which is directly analogous to longitude. 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, or equivalently the 090E meridian. So you see, GHA tells you exactly which meridian the body is over, measured westwards from Greenwich. Let me make sure you see the connection. The hour angle is measured westwards from the datum meridian, and when that datum is Greenwich, we call it GHA. That’s why a GHA of 050° puts the body over the 050W meridian, and a GHA of 270° puts it over the 270W meridian, which is the same as 090E. So the hour angle is just a way of saying where the body is in longitude, measured from your datum meridian going west. That’s the key idea you need to carry forward.