 Greetings and welcome to the Introduction to Astronomy. In this lecture we are going to discuss determining ages of solar system objects. So how do we figure out how old something is in the solar system? Now there are a couple of ways that we can do this and we can look at two things that we call either the relative age or the absolute ages or the true age. So a relative age would be one way to do it. That shows how things are related to each other and the absolute ages are actual ages that we can determine. So there are a couple ways we can determine how old objects are in the solar system by looking at them or by getting samples of them. So relative ages is done by looking at the object. You don't need a sample of anything and it's essentially based on superposition. That if something is on top of something else then the thing on top must be more recent. So if you see craters and one crater is on top of another crater then the crater that is on top is the one that must have formed more recently. If you see something cutting through a feature, so if you have a crater and you have some kind of fault crack going through it, then that fault must have come later. So it tells you relatively how old things are. Now essentially what this means is that the more craters you see on the object the older the surface is. Remember that everything in the solar system is about four and a half billion years old but that does not mean that their surfaces have been unchanged all that time. Things like the moon have been relatively unchanged over the last few billion years. It's essentially looks the same now as it did a billion or two billion years ago. Other surfaces like the earths look nothing like they did a couple of billion years ago. So it tells you really not how old the surface, how old the object is, but how long it's been since it's has been resurfaced. So the moon was last resurfaced, worked a long time ago, whereas the earth has been relatively recently reworked. And we can use this throughout the solar system because the cratering rate has been effectively the same. Now the absolute ages are based on radioactive materials and radioactive decay. The way the radioactive material decays is in a very predictable manner and we can use that to figure out the exact age of a sample of a rock and how long it was since that rock solidified from molten lava. So let's look at these in a little bit more detail. And first of all looking at determining relative ages, first of all it's just countering the crater. Since cratering rates have been about the same for the last few billion years that tells you how old an object surface is. So if we look at an object when we see it we see more craters on the surface. That's the longer that surface has been exposed to space and to impacts. And what happens is that there are effects that will then wipe that out and that can be geological effects, volcanic eruptions, lava flows, can wipe out craters, and weathering effects can slowly wear down craters over time. So craters that formed a million years ago on the earth are now long since, could be long since gone, could have been wiped out. Especially smaller craters would not no longer exist. And craters that formed a billion years ago would no longer exist at all on the earth. However on the moon we can see craters that formed a billion or two billion or even three billion years ago. They are still present because there are far fewer weathering effects there. So a couple things like geological activity, weathering effects, and the presence of an atmosphere can really affect the number of craters that we will see on an object. So if we look at our example here, the earth has very few craters while the moon has many. That tells us that the earth's surface is younger and has been reworked by geological and weathering processes over the last, since the craters have formed. So over billions of years the earth's craters have been wiped out leaving only the most recent ones while many of the craters that ever formed on the moon are still there. So let's take a quick look at our moon here. And what we see are that there are regions that have lots of craters and regions that have very few craters. So the maria are the dark regions which have few craters and are a younger surface. And you can see some of the maria here and here. And these darker regions have fewer craters than the highland regions which are the lighter colored regions which have far more craters. So the rest of these regions you can see lots and lots of impact craters scattered around in between the maria and those are the older regions. So we know that the maria are younger and that the highlands over here are older regions. So we can tell the regions just by looking at the number of craters. Now if we were to actually do crater counts and how many craters there are per square mile, square kilometer, how many craters actually existed we could actually determine relatively how old these various sections are. However to get actual ages we really need a sample of the rock from the surface. So we can really tell which areas are younger or older here and we could even compare that among different objects. We could compare the moon to the earth but we could also compare things like Mars and Mercury and Venus and kind of get the ages for them as well. Now if we want to determine absolute ages or actual ages that requires a little bit more. If we want to find out how old it actually is we do need a sample of rock from the surface. So what happens is when rocks solidify they all have some radioactive minerals that will decay over time and we can look at the relative concentrations of these to determine how old that rock is. Once we can figure out how old the rock is that helps us get absolute ages and lets us calibrate our crater counts that we would use to determine other ages because we do not have samples of the entire moon for example. We have samples from various regions that the Apollo astronauts explored so we have to then use the ages that we determined there to help us to extrapolate and determine ages elsewhere on the moon. So let's look at how this process works and it uses a concept of half-life and what half-life means is that it's the amount of time required for one half of the parent atoms to decay into the daughter atoms. So however many half-lifes it is if we look at an object with a half-life of say one year as an example so let's look at a one year example half-life that means if you start off with 100 percent of your parent atom then after one half-life or one year you are down to 50 percent you have lost you have decayed half of those original atoms that had formed after two half-lives or two years you're now down to one quarter after three half-lives you've cut that in half and you're now down to just about 12 and a half percent so if you want to write that in 12 and a half percent of the atoms left after three years so what we can do is then compare the ratio of parent to daughter atoms to just discover the age so if they were equal we would know it is one half-life old if you have three times the number of daughter atoms that you have parent atoms then you would be able to say it's two half-lives old and so on you can just look at the relative ratios how many parent atoms relative to the daughter atoms do you see so this works very well when the curve is changing quickly here when you get out to the far end it doesn't work very well it's very hard to get the difference between six and seven and eight half-lives so if you were looking here to try to determine something it would be hard to tell whether it was six years or seven years or eight years old because the ratios would become very similar but in this part of the curve it's very easy to determine and that's why we look for minerals that have half-lives that are in this range that several half-lives would be about the approximate age of the of the rock so let's look at it let's make it into an example here for potassium 40 and what we can do is make a little table to look at how this changes over time so we can talk about the number of half-lives we'll do half-life here in the first column of the table how many half-lives have we passed then we want to put the age or the time that is passed and then we want to put the number of atoms that we see so we would have potassium 40 which potassium symbol is k and argon 40 argon is ar and what we want to look at is how much we'd have of each of these so let's just start off with the half-life zero which is time zero so when the when the object formed and let's just give it a number just to count here and we could say 1000 atoms of potassium 40 and since we haven't started the clock yet we would have no argon 40 and then we can continue and make tape make a table here for one half-life the half-life is 1.3 billion years so this would be 1.3 billion years which sometimes abbreviated as gyr for giga years or giga meaning billion and at that point you would have had one half of the potassium 40 decay so you would now have 500 potassium 40 atoms and they would have decayed into argon 40 so you would now have 500 argon 40 atoms if we wait another half-life so after two half-lives we double this this would now be 2.6 giga years now we would cut this in half again it's not the original amount it's the amount you had here that gets cut gets cut in half so it's not that you'd have zero potassium 40 you would now have half of the 500 or 250 atoms and you would now have gained that 250 in argon and have 750 argon 40 atoms let's just do a couple more here after three half-lives or 3.9 giga years 3.9 billion years you'd now be down to 125 potassium and 875 argon and finally if we went to four half-lives you would be at 5.2 billion years and that would get you down to 62 and a half atoms of potassium and 937 and a half atoms of argon 40 now you might wonder how do we get half of an atom it is because this is a probability each half-life each had an atom remaining has a 50 chance of decaying so what this means is that you have an equal chance of there being 62 or 63 potassium 40 atoms that would be present and then you would of course have either 937 or 938 argon atoms you cannot have an atom halfway decay but then you can look at the ratios how do they compare as I said a one to one ratio here you could have a one to three ratio here you could have a one to seven ratio here so when we determine that ratio how many daughter atoms there are relative to the parent atom that then tells us where we fall in this and what the age would be so let's finish up with our summary here and what we find is that we can measure we can determine ages of objects in the solar system it is something we can figure out and we talked about relative ages using crater counts how many craters there are in different regions to determine relatively how old they are and that works for regions on a planet or or moon or regions between different planets and different moons and we looked at how we can determine absolute ages by looking at the radioactive decay of minerals from rock samples brought back from an object's surface so that concludes our lecture on 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