Let's pick up with the practical side of time conversion — Page 393, Lesson 349

Let's pick up with the practical side of time conversion. I want to walk you through how we actually turn arc into time using a scientific calculator, because that's the tool you'll use for these problems. The key relationship we're working with is that the Sun takes 1 hour to travel 15° of longitude. So to convert arc to time, we divide the arc by 15. The calculator's `dms` function handles the degrees, minutes, and seconds for us. Let me show you with the example: convert 137°36' of arc to time. The exact buttons depend on your calculator, but with the Casio series that Oxford recommends, the `dms` button is marked ° ' ". Here's the sequence: you press 1 3 7, then the `dms` button — you'll see 137° in the window. Then press 3 6, then `dms` again — you'll see 137° 36° in the window. Then press ÷ 1 5 = — and you'll see 9°10°24, which reads as 9 hours, 10 minutes, and 24 seconds. So that's the mechanical process. The point is that you practise this conversion and check your answers against the arc/time table from the Air Almanac. Now let's move to the concept of Local Mean Time, or LMT. The Earth rotates daily around its geographic axis, anticlockwise if observed from above the North Pole. But it's convenient sometimes to consider the Earth as stationary and the Sun travelling around the Earth once a day in a clockwise direction. This alternative fits well with our perception that the Sun rises in the East and sets in the West. So for our discussions, we'll use that alternative — and unless otherwise stated, the Sun we refer to is the 'mean' Sun. Here's the core definition: when the mean Sun transits — that is, crosses — a particular meridian, the Local Mean Time at all places on that meridian is 1200 hrs, which is midday or noon. Similarly, when the mean Sun transits the anti-meridian of a point — that's the meridian exactly opposite — the LMT at that point is 0000 hrs, or 2400 hrs, which is midnight. There's a convention here about midnight. Midnight of a particular night, say the night of the 6th/7th, is regarded as 2400 hrs LMT on the 6th, or 0000 hrs on the 7th. So both are valid ways to express the same instant. Let me illustrate with Figure 25.1. It shows the situation when the mean Sun is transiting the meridian of 45°E on 16th May — the date is just for illustration. So the LMT at all places on the 45°E meridian — that includes Baghdad, Aden, Madagascar — is 1200 LMT on 16th May. Now, remember the key fact: it takes the Sun 1 hour to travel 15° of longitude. So let's work eastward from 45°E. At 90°E, which is approximately India, the LMT is 1500 hrs on 16th May — the Sun passed the meridian 3 hours ago, because 45° divided by 15° per hour gives 3 hours. At 135°E, approximately Japan, the LMT is 1800 hrs. At 180°E, mid-Pacific in the Eastern hemisphere, the LMT is 2100 hrs. Now working westward from the 045°E meridian. At 0°E/W, the Greenwich Meridian, the LMT is 0900 LMT on 16th May. And here's an important naming point: LMT at the Greenwich Meridian is known as Greenwich Mean Time, or GMT, also called Zulu, 'Z'. GMT used to be the Earth's standard time. The present standard time is called Co-ordinated Universal Time, or UTC, which for all practical purposes is the same as GMT. Continuing west: at 45°W, Newfoundland, the LMT is 0600 LMT on the 16th May. At 90°W, mid USA, the LMT is 0300 LMT. At 135°W, Alaska, the LMT is 0000 LMT on the 16th May — and this time may be considered also 2400 hrs LMT on the 15th May. So the pattern is clear: going east, time increases by 1 hour per 15°; going west, time decreases by 1 hour per 15°. And that's the foundation for all the time problems you'll solve in navigation.