 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to look at ways we can determine ages of objects in the solar system, and we'll look at a couple different methods that can be used to help determine how old objects are. So how do we measure ages? That's a good question. How can we figure out how old something is? Well there's two methods we're going to look at. One is a relative age, which is based on crater counts and overlapping objects. Essentially we look at more craters means it's an older surface. Now what that means in terms of older is how long it's been since that surface has been reworked. So planets that are subject to weathering effects and geological effects, volcanoes, etc. Those will be younger surfaces. The more craters we see the longer that system has been unchanged and that is the older surface. Then we will look at the absolute ages. That is actually figuring out the exact age by looking at the concentrations of radioactive materials in rock samples. Now the difference is this one requires a sample of the material. So you actually have to get a piece of the object you want to figure out the ages for. This one can be done from a distance. So let's start off by looking at relative ages and we look at relative ages. Ideally what you do is count the craters and what we find is that cratering rates have been essentially the same throughout the solar system for billions of years and that means it doesn't matter whether you're in the inner solar system or the outer solar system. That everything's been hit just about as much so that if we see a certain number of craters per square kilometer on the moon that we can use that as a comparing ages to other objects in the solar system whether they be in the inner solar system or whether they be in the outer parts of the solar system. So what we look at is the number of craters we see, the more craters we see the longer that has been exposed to space, the longer since that surface has been unchanged. What will change that are geological and weathering effects. Those will change and wipe out the craters. So that was what will get rid of craters. So looking at an example the earth has very few craters the moon has many craters. So the earth's surface is younger. That does not mean that earth is younger than the moon. It means that they still formed at the same time. However the earth's surface is younger because it's been reworked by geological effects, earthquakes, volcanoes, plate movements and by weathering processes, wind and rain and ice that have weathered the surface and removed craters from the surface. Now let's take a look at the moon here because even on the moon we can see there are two different regions and we will talk about the moon in more detail later but we have the maria which are the dark regions which have very few craters here and we can see several of those large basins here with very few craters in them. We see the highlands which are the lighter colored regions and we see some of that down here which has a lot of craters. Now you'll see the craters primarily as you look toward the terminator line the dividing between night and day. When you look out here it's a lot harder to see craters because they're not casting very long shadows. But what we find is that the maria are younger regions because they have very few craters so they are younger the highlands have are older and once we could calibrate this we can actually use the crater density to figure out areas even in the outer solar system but we have to be able to calibrate it and that's what we're going to do with our moon. So the moon we have the most samples of and the most regions that we've been able to figure out ages. So how can we figure out the actual ages? How do we get an absolute age of how old a surface actually is? Well I can't tell you how old any specific surface is and that's because it varies from places on the object. There are areas on the moon that are older and some that are younger. Same with earth. Some areas are older and some are younger but in order to determine the age of that part of the surface we need a rock sample and if we need that rock sample in order to study the radioactive materials within it every rock has radioactive materials in it that decay over time. Their relative concentrations of these can tell us the age of the rock and this is by using the concept of a half-life. What is a half-life? Well a half-life is defined as the amount of time it takes for one half of the original atoms to decay into the new atoms. So we can look at this here when you start off with a rock it has a full concentration of say whatever material it was, whatever radioactive element we're looking at after one half-life it will be down to half of that. After two half-lives it doesn't lose as much it loses half again so it's down to a quarter and an eighth and a sixteenth and a thirty-second. So it keeps cutting it in half every time. Essentially you can think of it as every half-life the atom flips a coin and if it's heads it decays and if it's tails it doesn't so each time each half-life it has a fifty percent chance of decaying. Now of course the actual numbers will vary and you could have a little bit of variance just as you could if you flip a coin ten times you won't necessarily get five heads and five tails but that is a more likely outcome than getting ten heads or ten tails. So by comparing these ratios we can then get ages. Let's look at an example of this in a table form and we can look at the decay of potassium. Potassium 40 has a half-life of 1.3 billion years. So that means every 1.3 billion years half of the potassium 40 that was there will have decayed into argon 40. So if we look at the ratio of potassium 40 to argon 40 that will tell us the age. So when the star when the rock forms that's time zero let's just give a number and that's just 1,000 we have 1,000 potassium atoms. You'd have far more than this in any rock and you would have zero daughter atoms. We have not yet had time for anything to decay. Well after 1.3 billion years half of those would have decayed and you will now have 500 of each. 500 of the parent to daughter. So you would have a one-to-one ratio and if you saw a one-to-one ratio that would then mean it was a it was one half-life old, you know the half-life and then you can figure out that this would be 1.3 billion years old. After another 1.3 billion years again half of those decay leaving you 250 you now have 750 of the daughter element so now it is a one-to-three ratio. You have three times as many daughter atoms as you have parent atoms. You can continue the process going down to 125 and then to 62.5 and the ratios will continue to increase. So if we did this again this would be a one to seven ratio so seven times as many of the parent of the daughter atoms as we have of the parent atoms and the process can continues and will go on forever. We would then have here if you look at this one this would be a one-to-15 ratio so you have 15 times the amount of the daughter element as you did of the parent and as that you can continue this down all you do is keep cutting this one in half and they have to add up to a thousand you can't lose any atoms so if you figure out this ratio you can then figure out where you fall on this scale now of course you might be somewhere in between and you could estimate in between that if it was one to two and you might say it somewhere between 1.3 and 2.6 billion years. Now there is an exact way to calculate this using exponentials I'm not going through that in this class for you you don't need to worry about that if you're doing anything with it a simple table like this will give you a very basic approximation of what you need to do to measure the absolute age of the sample that you are looking at and then this can be used to calibrate the crater counts once we figure out different regions on the moon and say so many craters per square kilometer say relates to a certain age we can then use that to get estimates of ages of other objects in the solar system for which we do not have samples so let's go ahead and finish up here with our summary and what we've looked at this time we talked about how we can measure ages of objects in the solar system and we looked at the relative ages done by crater counting and we looked at the absolute ages done by radioactive decay using the half life so that concludes this lecture on determining ages in the solar system 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