 Greetings and welcome to the Introduction to Astronomy. In this lecture, we are going to continue our introduction into astronomy and look at things like some of the numbers that we have to deal with and the concept of light travel time and how we can use that to measure distances. So, let's go ahead and get started today. And what we find is that for numbers, we look at really big and really small numbers. So, we will see a combination of these and we need to be able to express these numbers in scientific notation. Now, why do we need to do this? Well, the Earth and Sun are 150 million kilometers across. And we deal with numbers even far bigger than that. How what we can do is instead to compress writing out all of those zeros is to write this as 1.5 times 10 to the 8th kilometers. Now, these two are exactly the same. So, they express the same number of kilometers, but it is far more convenient to use the scientific notation version. So, how do we convert a number into scientific notation? Well, what we do is we move the decimal point until there is only one number to the left and you count how many places you had to move it. And then if you move the decimal point to the left, you get a positive exponent and if you move it to the right, you get a negative exponent. So, whether this exponent here is positive or negative depends on the direction that you had to move that decimal point. Now, let's look at a couple of examples of this and we will see that let's look at a relatively large number and a relatively small number. So, here we have the number 314 million. Well, the decimal point, even though it isn't printed, would be here at the end. So, we have to move the decimal point how many places 2, 3, 4, 5, 6, 7, 8 and once we've done that, we have moved the decimal point 8 places to the left. Now, because it's left, that means that the exponent will be positive. So, it becomes 3.14, we can drop all the rest of those zeros and then times 10 to the 8th power and that represents all of those zeros that we have just gotten rid of. Let's look at an example for a small number. Here, the small number is 0.0004563 and we're going to now have to move the decimal point here 1, 2, 3, 4, 5 places to the right. Now, this time we've moved it to the right, that means that the exponent is going to be negative and we write the remaining number 4.563 times 10 to the negative 5th power. So, that's how we can convert numbers and often our first lab will let us look at a few examples of using some numbers in scientific notation. Now, how about units? What kind of units do we use? Well, from almost everything we give in the class, we will be using the metric system and that is using the meter for length, the second for time, and the kilogram for mass. Now, that means that there's a standard unit. Now, often when you hear me say something, I may give you a conversion into miles or feet or pounds or something because those are the numbers that those taking the class, at least in the United States, are most familiar with. However, the standard measurements in science are all going to be in meters, seconds, and kilograms or they're different variations. Sometimes you'll see things measured in centimeters for smaller versions or millimeters or just grams for smaller amounts of mass. All the other units that we use will come from these so like velocities can be given in meters per second. So we're using two different ones of these. It's a length divided by a time. Density can be given in kilograms per cubic meter. Density is a mass, kilogram, divided by a volume. Well, a volume is the meter but is the third power of that. So, such as the volume of a cube is the length times the width times the height. That would give you a third power or meters cubed but other units that we use will come from these. Now, there are several other basic measurement units but these are really the ones that we will use. These are the standard ones and the ones that we use primarily in this class. Now, let's go ahead and look at some of these distances. Again, numbers get very big. The nearest star other than our sun is 40 trillion kilometers away from Earth. Now, that gets to be big numbers and very hard to comprehend. Now, we can write this in scientific notation as 4 times 10 to the 13th but how can we even imagine 40 trillion of anything? It is a much larger number than our brains like to try to comprehend. So, what we often use is the light year. The light year is another way of measuring distances and that depends on the speed of light which is 300,000 kilometers per second. The light year is the distance that light travels in one year so even though it has year in it it is a distance. So, it is about 10 trillion kilometers so that means since the nearest star is 40 trillion kilometers one light year is 10 trillion kilometers that means the nearest star is about four light years away. Does that make the distance any different? No, it's still the same distance but the number is more manageable. We can comprehend the number 4. We know what 4 if something is and if we want to compare that to another star that is six light years away we have a pretty good sense of comparison of relative distances. Now, let's continue here and we will see again the light year within our solar system is too big. The sun is about eight and a half light minutes away so light minutes, a light year gets us well outside the solar system so things within the solar system we could use the light minute would be one example of something we could use here. So let's look at the light minute here and what we have is so there's our light minute we don't often use that but it is something that would work we could talk about things being light minutes or even light seconds away within the solar system for things that are close. Typically within the solar system though we use what is called the astronomical unit. Now this does not depend on light but actually depends on the Earth-Sun distance so the average distance between Earth and Sun here and that one astronomical unit is 150 million kilometers. So if we want to talk about distances it's a lot easier to say one and a half astronomical units than 225 million kilometers. Neptune is 30 astronomical units away. Now why is this more comprehensible? Well we can comprehend one mile better than 5,280 feet or 63,360 inches even though those are all exactly the same amount of distance. If somebody just gave you without this comparison something was about 60,000 inches away you probably wouldn't be able to get a sense of actually how far that was without doing some kind of conversion. The whole idea of using these definitions is to make the numbers more manageable and easier to understand. So what does this have to do with light travel time? Well we find that light travels at a finite speed it does not travel infinitely fast so the light from the Sun gets here in about eight and a half minutes the light from Alpha Centauri that nearest star takes about 4.3 years to get here the light from the Andromeda Galaxy takes nearly two and a half million years to get here What that means is we don't see anything in astronomy as it is right now the Sun we see as it was eight and a half minutes ago has it changed in eight and a half minutes? Very unlikely we see Alpha Centauri as it was four years ago the stars don't change in just four years so it's going to be essentially the same even a galaxy two and a half million years ago is essentially unchanged Andromeda probably still looks almost exactly as we see it today but it does mean that we never see anything exactly as it is right now we never see that object as it is at this instant this is important because we are also looking back into time when we look out into space which is a good thing in that we can now see what objects looked like a long time ago so when we start to talk about galaxies we will be able to see that we can see what galaxies looked like 10, 12 billion years ago at the very early history of the universe simply because their light has taken that long to reach us so let's go ahead and finish up here with our summary and what we see is we talked about scientific notation as a way to express both very large and very small numbers we talked about scientific measurements being made in the metric system of units and we said that we use distances are so large that we use things like the astronomical unit and light year to measure these great distances and finally we talked about how light not traveling infinitely fast means that we can never see any object as it is at this instant in time so that concludes this lecture on numbers and light travel time we'll be back again next time for another topic in astronomy so until then, have a great day everyone and I will see you in class