Transcription
In a previous lecture, we talked about the concept of the year, which was certainly a concept you had heard of before. But by the end, hopefully, you had realized there was more to the year than maybe you had thought, and there was definitely a connection to astronomy.
Today, we are going to do something very similar with another concept or topic, the day. I think by the end of this lecture, you're going to realize that there's definitely a connection between the day and astronomy. And that the idea of the day is actually a little bit more complicated than maybe you had first thought.
In order to understand the day, we have to first, we have to talk about the concept of local noon. We say local noon is just the time each day when the sun transits. Remember, transit is just to reach your highest point. So, the sun, like any other star, rises over here somewhere to the east. Gets higher and higher in the sky until it reaches its highest point, it transits, local noon, and then it sets somewhere over here to the west.
Now, remember that when a star like the sun, or any star, transits, it's either going to be exactly north or exactly south. For us in Los Angeles, the sun will never transit to the north. The sun, when it transits, will always be exactly south. So, if you go outside and you measure the location of the sun and you discover that the sun is due south and is 180 degrees, then that means that you have caught the sun at local noon when the sun is transiting.
Now, does local noon always mean 12 o'clock on your watch? No, it doesn't. It used to mean that. It used to mean every little city or town that's out there would set their clock by local noon. And they would say, "When the sun transits, it's going to be noon, noon on our clock." But about 150, 200 years ago, they realized that was making setting things like train schedules very difficult, and they came up with the idea of time zones.
The continental United States is divided up into 4 time zones. Here's the Eastern Time Zone, way over here, we're in the Pacific Time Zone, the one in red. The way a time zone works is you say that any location inside this time zone, so any place inside the red here, has the same exact time on the clock. Because we have time zones, this means now that local noon does not always match up with noon on your clock.
In fact, the way it works is the farther east you are, so let's say you are over here in Palm Springs somewhere, the earlier the sun transits. So, the sun would transit earlier, say here in Palm Springs, than it does here in Los Angeles. And the sun would transit earlier in Los Angeles than it does, say, over here in Santa Barbara. So, the farther east you go, the earlier the sun transits. The farther west you go, the later the sun transits, the later local noon is. Local noon does not mean noon on our clocks.
Okay, so what's the connection to the day? Well, if I asked you, "What is a day?" you would probably give me one or both of these answers. You'd say, "Okay, a day is 24 hours long. A day is 24 hours." Sounds good. You might also tell me, "Okay, well, a day, astronomy connection here, a day is just the time it takes for the earth to rotate once, to spin around once." These are both great definitions for days, and believe it or not, you are actually talking about two completely different days here with these two definitions.
What do I mean? Well, the 24 hours in a day is what we call a solar day. Solar means measured by the sun. The solar day is just the time between two transits of the sun, two local noons. If the sun is transiting right now, we start our clock, we wait until the sun transits again. One solar day has passed. That is 24 hours. We call a solar day 24 hours.
Now, the other definition for the day, the time it takes for the earth to rotate once, is actually not a solar day. It's called a sidereal day. It looks like "side real," but it's pronounced sidereal, a sidereal day. And a sidereal day is the time between two transits of a star. And that star doesn't count the sun. Just the time between two transits of some distant star. It turns out, that is actually 23 hours and 56 minutes. 4 minutes shorter than a solar day.
Why do we have these two different definitions for the day? Why is a solar day not the same as a sidereal day? Let's look at this diagram here. Let's say we're sitting right here, and let's say that, of course, the sun is right here, and let's say there's some, a star that we're measuring that's way out here, right near the top of the PowerPoint slide. Okay, if this little person sitting here, this little person sitting here, right now the sun is directly overhead, so it would be local noon, and the star, which is really far away, way up here, is directly overhead.
Now, as the earth rotates, let's wait until we have the star directly overhead again. We wait for the star to rotate, the earth to rotate. It rotates once around, and when the guy is standing here, that star is directly overhead again. Remember, these stars are so far away that you don't have to worry about, "Oh, it's shifted a little bit." If you're looking straight up, that means that star is directly overhead. You have a sidereal day, the time it takes for the sun, the earth to go here, rotate around once, and then come back to here. One transit, time between two transits of a star.
But do we have a solar day yet? Has the sun come back to transit yet? No. The sun is over here. What happens? The earth has to rotate just a little bit more to bring the sun back in transit for this guy to finish the solar day. That little bit extra more rotation is about 4 minutes. That's why a solar day is about 4 minutes longer than a sidereal day.
The reason why there is this difference is because as the earth is rotating, the earth is also moving around the sun. If the earth wasn't moving around the sun, the earth was just sitting here and spinning around, then a solar day and a sidereal day would both be the same length. But because the earth is moving around the sun, the time it takes the earth to spin around once to bring that star back to transit again is not enough time to get the sun back to transit. You need an extra 4 minutes.
Four minutes. If you remember back to the lecture about the year and the Zodiac, we said that stars rise, set, and transit 4 minutes earlier on the clock each day. This is where that 4 minutes comes from. Since a sidereal day is 23 hours and 56 minutes, let's say right now, day 1 is at noon. By the time the star transits again, it will be 11:56, 23 hours and 56 minutes later, or if you're looking at it, 4 minutes earlier now on day 2 than it was on day 1. This is where we get that idea that stars rise 4 minutes earlier every single day, 2 hours earlier every single month.
Remember, important to remember here, it's all because the earth is going around the sun. If the earth was not going around the sun, a solar day and a sidereal day would be the same. Stars would always rise, set, and transit the same time every single day. But because the earth goes around the sun, a solar day and a sidereal day are different, and a sidereal day is 4 minutes shorter than a solar day. And stars rise, set, and transit 4 minutes earlier each day.