 Greetings and welcome to the Introduction to Astronomy. And in this lecture, we will go through numbers and light travel time, how numbers are used in astronomy, some of the different units that we measure, measure values in, and what it means to think about light travel time and how long it takes light to travel through various distances. So let's start off looking at numbers. What are some of the numbers in astronomy? One of the difficulties with them is that in astronomy we have both very large and very small numbers, and because of that we express those numbers in what we call scientific notation in order to make them easier to write out. Well, an example I give you here is that the distance from the Earth to the Sun can be written as 150 million kilometers. That's a very big number, lots of zeros to write out and keep track of. So what scientists do to write numbers like that is instead of writing out all of those zeros, they move the decimal point to, so that there is just one non-zero number to the left, and then write the rest as a power of 8, which, power of 10, which represents all of those zeros. So we can write 150 million kilometers as 1.5 times 10 to the 8th kilometer, which is really convenient for the incredibly large distances that we will deal with. In order to convert a number to scientific notation, we move the decimal point until there is only one non-zero number to the left, and we count the number of decimal places that we moved. So if we move the decimal point to the left, the exponent is going to be positive. If we move it to the right, the exponent is going to be negative. So the direction that we move it will give us what the sign of that exponent is going to be. Let's look at a couple of examples here. So a couple of examples, first of all, we have the number 314 million. Now we can write that out, but we can also write that in scientific notation. The decimal point would be here at the very end, and if we want to leave one non-zero number to the left, what we do is we move it 1, 2, 3, 4, 5, 6, 7, 8 places, and we're left with 3.14. Now we moved it 8 places to the left. That means it's going to be positive. So 3.14 times 10. How many places did we move it? We moved it 8, so 10 to the positive 8. So we can write 314 million as 3.14 times 10 to the 8th power. Our second example, we're going to go the other direction. So now we have a very small number, .0004563. Now we're going to move the decimal point to the right. It starts here and we go 1, 2, 3, 4, 5 places until we get 4.563. And now we've moved it to the left, so it's going to be negative. So it's going to be 10 to the negative 5th. So we can write .0004563 as 4.563 times 10 to the negative 5th power. And we will find that that is much easier to represent all of these large and small numbers that we will deal with. Now the units that we use, we use what we call the metric system of units, and or system international SI units, both mean the same thing, and all scientific measurements would be done in the metric units. And that means that we would use things like the meter as a unit of length, the second as a unit of time, and the kilogram as a unit of mass. Now you may be familiar with some of these and you can divide them up into other units. So like in English units we divide feet into inches and we add up feet into yards or into miles. We can do the same thing in the metric unit, but everything here is based on powers of 10. So you may be familiar with things like millimeters or centimeters or kilometers. Well millimeters, milli just means one one thousandth. So a millimeter is one one thousandth of a meter. Centi means one one hundredth. So a centimeter is one one hundredth of a meter. And kilo means one thousand, so a kilometer is one thousand meters. So very easy to do conversions between those. Kilogram, you can see the same thing. Kilogram would have, you could do milligrams for very very small masses, and grams as well as a unit. Now other units are then devived from these specific values that we get. So things like velocity here is just the distance or the length, how far something moves in a specific time. And that might give you, for example, if we use the standard units, meters per second. So you can measure velocities in how many meters something moves in a certain number of seconds. Density is another one. Density is mass divided by volume. We know that the mass is in kilograms, for example. And the volume would be related to the length. And for example, the volume of a cube is just the length to the third power. So you make the length, multiply it by the length, and multiply it by the length again, and that would give you the volume of the cube. Densities can tell you how dense an object is. So an astronomical object, a planet, or a comet, or a star will have a certain density, depending on how much mass it has compacted into a specific volume. Now in looking at some of these distances that we use, let's look at some of them, we have the nearest star. The nearest star is about 40 trillion kilometers away from the Earth, a very large number and much too large to easily write out. Here we have it written out as 40 trillion. That's a lot of zeros to keep track of. We can write this in scientific notation using the method shown before, and that would be 4.0 from the numbers I've given you here, times 10 to the 13th power. We still can't really comprehend things like trillions. Our mind just cannot get wrapped around a number that is so large. So in order to simplify that, astronomers use another term that they call the light year for measuring these very large distances. We know that the speed of light in a vacuum is a constant. It is 300,000 kilometers per second. So it always travels at the same speed, and that allows us to define a light year as the distance that light travels in one year. So it is a measure of distance, not time. And that is about 10 trillion kilometers. So in terms of light years, the nearest star is a little over 4 light years away. Well now that's a number at least we can comprehend. We know what it means to have 4 of something, and if we want to compare a star that's 4 light years away to one that is 8 light years away, it's a lot easier to compare the numbers 4 and 8 than it is to compare 40 trillion and 80 trillion. Just because the numbers are something that we can comprehend that our brains can actually decipher for us. So that's one of the problems is that distances in astronomy are so large that it is difficult to kind of wrap your mind around those numbers. Let's look at a couple other examples here that we have. A light year is way too big to be used in the solar system. You can use things like light minutes or light hours. How far light travels in a minute? It takes about 8 minutes from light to get from the Earth to the Sun. So 8 minutes from the Earth to the Sun. We use, even easier within the solar system, we use what is called the astronomical unit, which is simply the average distance between the Earth and the Sun. So how far away are the Earth and the Sun on average? Well, that's about 150 million kilometers, and that is what we define to be one astronomical unit. So instead of trying to compare planets and give their distances in kilometers, we can now compare them directly to the Earth. Mars would be 1.5 astronomical units from the Earth. Neptune would be about 30 astronomical units from the Earth. So it's much easier to comprehend these numbers and to be able to understand, comparing 1.5 and 30, than it would be to give those distances in kilometers. As an example, in the English system of units, just to think about what you're used to every day, perhaps, is that one mile is a lot easier to think about than 5,280 feet or 63,360 inches. All of them are correct for the distance of a mile, but they're much less manageable. So make using these definitions of the astronomical unit and the light-year make the numbers in astronomy much more manageable. Now, let's talk... The last thing I wanted to talk about is light travel time, and what we understand in astronomy is that light does have a certain speed limit. It does not travel instantly fast. So it does not get someplace instantaneously. It takes time to get to us. I mentioned earlier that light from the Sun takes about 8.5 minutes to get here on the Earth. That means that we see the Sun not as it is right now, but as it was 8.5 minutes ago. If the Sun had just vanished 7 minutes ago, it would still take another minute and a half before we would even know about it, because the light had not yet gotten to us. If we look at the nearest star, Alpha Centauri, it would take about 4 years for it to get to us. So the light that we see coming from Alpha Centauri now is not the light currently leaving it, but the light that left it a little over 4 years ago. If we look at the nearest large galaxy, the Andromeda galaxy is about 2.5 million light-years away. So it takes about 2.5 million years to get to us. So the light would then take 2.5 million years to get here. Now what does that mean? That means that we see nothing in astronomy as it is right now. We see the Sun as it was 8.5 minutes ago. We see Alpha Centauri as it was a little over 4 years ago. And we see the Andromeda galaxy as it was 2.5 million years ago. In astronomy we know nothing about how anything looks right now, but we do know a lot about how things looked in the past. And as we go on, look at this a little bit more detail. That means, as I've just said, we do not know, we never see any object as it is right now. What does the Andromeda galaxy look like right now? Well, let's wait 2.5 million years for that light to get here, and that would allow us to see what it looked like at this instant. However, at that point it would still be 2.5 million years from now, so the light that's just leaving Andromeda at that point would still take another 2.5 million years to get here. It also tells us that when we look out into space, we are looking back into time. We see things, we can see objects as they looked long ago. So we can see some very distant galaxies as they looked very early in the history of the universe. They don't look anything like that anymore. There are likely objects out there that we see that no longer even exist. But we are still seeing the light traveling from them from many billions of years ago, and that means that we can still see them because the information about, say, their destruction has not yet gotten to us. So let's finish up here and summarize a little bit. And what we have is that just kind of what we reviewed here, we talked about scientific notation. We use that for the very large and the very small numbers that we will work with in astronomy. We know that we use the metric set of units, or the SI System International, set of units in astronomy and in all sciences. And we have also defined a couple different terms, the AU or astronomical unit and the light year, to measure the vast distances that we have in astronomy. Finally, last thing here to look at would be that because light does not travel infinitely fast, it doesn't get here instantaneously, we can never see any object as it is at this instant. Even looking at the moon, it took a couple of seconds for the light to get here from the moon. So we know what the moon looked like a second or so ago, we know what the sun looked like eight and a half minutes ago, we know what Alpha Centauri looked like four years ago, and we know what the Andromeda Galaxy looked like two and a half billion years ago. But we have no idea what they look like today because it does take time for light to travel. So that concludes this lecture. And until next time, have a great day, everyone. And I will see you in class.