have so okay here we go moving forward form for the rest of this discussion let's assume that we used parallax or any other method available to astronomers to find the distance so let's assume that we know the distance for every star out there for the rest of this discussion okay all right the next property the next property that's important is is how bright stars are okay and the the thing that we're going to use to talk about how bright stars are is a property called luminosity and here you can kind of think of the lumen part as meaning light right so luminosity is it's the total amount of light produced per second okay the total amount of light energy there we go total amount of light energy produced per second okay total amount of light energy produced per second it's the total light that a star is sending out in all directions per second okay now two things here two things let's figure out if this is direct or indirect and let's figure out what the units of it are okay let's first say direct and indirect okay let's first talk direct and indirect check it out here we go let's take a boat is the total amount of light produced per second something that is direct or indirect are we going to be able to directly see that or is that something we're gonna have to figure out take a vote in the discord well I adjust some some things here there we go okay I'm getting some votes coming in let's see what we're gonna wear we're gonna put it okay I'm getting multiple answers here let's see what it is so most of you guys got it and it's okay if you didn't get it a lot of times people think that this is direct but it is indirect okay I'm gonna go ahead and write it down and I'll explain why and we use a capital L for luminosity because a lowercase L looks like a 1 we don't want that okay so why is luminosity indirect instead of direct so it sounds like the total light coming out of a star per second is something we can measure but we can't because which direction does a star put out light which direction does a star put out light all directions so if you were going to measure the total light that a star put out in one second where would you have to view it from if in order to catch all of the light that a star put out in that second where would you have to view that star from in order to get a direct measurement yeah you would have to be on all sides of the star essentially what's the problem is is this oh you come on the problem is that the star is putting out light come on you can do it one moment technical difficulties again this is just killing me okay let me reload come on you can capture it it's not wanting to capture my my powerpoint presentation anymore okay so give me one moment we're gonna do this a very clunky way here it goes this final stream guys it's working out really well final try please work please work sorry guys okay here's how it's gonna have to go there we go okay so I'm back I'm back sorry guys here we go now here we go so um I've just got this open over here I'm just gonna have to show you guys the full screen so I like we were saying the problem with luminosity is that it goes the total light goes out in all directions okay so the light is coming out like this and we're only able to catch the stuff that hits us we could probably assume that this light going in all directions is the same as the light coming at us but that's still indirect because we're not for sure that the light coming out over here is exactly the same as ours but because this is a ball shaped star and the star is pretty uniform we expect that the light going out in all directions is the same as the light coming at us so how do we distinguish all of this so essentially sorry I just kind of threw me off my flow here but I can get this essentially we need to make a distinguishment between as distinguishment is that a word whatever it's a word now here we go we need to distinguish between the light going out in all directions and the light that's hitting us so we call the light that goes out in all directions the luminosity and we call the light that hits us the apparent brightness okay the apparent brightness so let me pop back up the lists we're going to put apparent brightness over here in the direct pile with a lowercase B and we're gonna leave luminosity over there okay so again luminosity is the total light it sends out in all directions per second and the apparent brightness is the stuff that hits us now those two things are related okay because if the if the luminosity of a star is higher if it makes more light per second in all directions what will that do to the apparent brightness if the star makes more light in all directions what will it do to apparent brightness if the luminosity is higher what happens to the apparent brightness you guys still here it would be higher that's correct it would be higher so if the star makes more light it's going to look brighter okay but the apparent brightness the brightness we see is not just related to the luminosity it's also related to one other important thing that we've already listed okay what else on our list is the apparent brightness going to depend on the distance right right you probably learned as a little kid if there's like a light bulb on do you want to put it way up in your face no because that's gonna make it look way brighter and it's gonna hurt your eyes if you go further away from a light bulb it's not gonna be as bright and therefore it's not gonna hurt as much so that means the apparent brightness depends on the luminosity and the distance if the luminosity goes up the apparent brightness goes up but if the distance goes up if the star is farther away it's gonna look dimmer so that means the apparent brightness will go down okay everybody good all right now well we have to get here though is this why like everybody knows that things that are farther away look dimmer why do they look dimmer why is it that stuff looks dimmer when it's farther away this is a hard question so give it a try see if anybody can figure it out why is it that things that are farther away you'd look dimmer and I'm gonna give you guys a hint I'm gonna bring up my power point again this picture will help you answer it so it's definitely that less light gets to your eye but why why does less light get to your eye when when you go further away from this star Oh somebody is saying that the gases between you and the star would absorb more of the light well remember space is mostly a vacuum so this works things that are farther away are dimmer even when there's nothing between you and that object somebody got it looks like somebody got it what's happening to this light right here as it goes away from the star what's happening to this light so if this is the amount of light it made per second what's happening to that light as it goes away it spreads out it spreads out so you're looking at less and less of it by the time it gets to your face somebody described this in terms of angles that's basically right essentially imagine this let me kind of get myself kind of small here we go if I were looking at this star from here see how a bunch of the lines are crossing my face I would see all of this light right and if I go further away see how less lines are crossing my face now now I only have three crossing my face and if I go further away now only two are crossing my face and if I go even further away eventually only one will cross my face so because the light spreads out as it goes away from the star you're catching less and less of it on you become a smaller target as you go away so you catch less of that light so it's a spread because the light has spread out on the surface of essentially a ball you end up missing more and more of it the farther away you go okay now here we go looks like somebody has a question so I'm gonna brief pause for that to come in and then I am going to I'm gonna switch over to this but if show you guys an equation that says what we just said okay let's get this down this is not part of our lists I'm just gonna put them over here here we go the equation is this B equals L over 4 PI d squared B equals L over 4 PI d squared okay let's see what this means don't freak out you're not gonna have to plug numbers into this equation you're not gonna have to do math like that on the on a test you're not gonna need a calculator we just need to see what this equation says now just to make sure if we look on here check this out this over here is our apparent brightness this up here is the luminosity and that's the distance squared okay but what is this saying um this is a fraction right here and if we want it to be really super fancy we'd call the top a numerator and the bottom of denominator but let's not get super Matthew and crazy here let's just call this the top part and the bottom part okay if we have a fraction and we increase the top part what happens to the total if we were to increase the L here what would happen to the total we would get if we were to actually calculate this if you increase the top of a fraction what happens to the total does it go up or does it go down it increases it increases so one thing this equation is saying is that wait I'm losing something there we go one thing this equation is saying is that if we increase the luminosity it's gonna look brighter which is what we said before okay but distance is in the bottom part if we increase the distance if we increase the bottom of this fraction what would happen to the total if we increase the D right here because it's in the bottom of the fraction we're making the bottom of the fraction bigger what would happen to the total it decreases it decreases the overall total so in other words if you make it if you have a fraction and you had like a 1/2 and then you made it a 1/3 and then a 1/4 you're making your total smaller by increasing the bottom of the fraction okay so anytime we have something like this if we increase the top the total will go up and if we increase the bottom the total will go down okay now what is this 4 PI d squared here geometry is not a prereq for this class but does anybody know what this bottom formula is for 4 pi we brought say it in a different way what have you ever seen the formula for PI R squared that is the formula for the surface of a ball okay it's the formula for the surface of a ball and remember in the picture I said that the light of the star the luminosity of the star is spread out over the surface of a ball right so that's why the equation for the brightness you see is the luminosity over the surface of a ball so it's kind of putting into an equation the words we were saying okay let's put this all together there's a reason I'm putting this here remember if an astronomer is trying to figure these properties out they've already found the distance so in this equation we already know D right is the astronomer gonna have to use this equation to find the apparent brightness or are they going to use this equation to find the luminosity is this equation for finding the apparent brightness or for the luminosity it's the luminosity right because the brightness is what you see okay the brightness is what you see so that means that we don't need to use this equation to find B so what I'm gonna do don't freak out I'm gonna do some quick algebra here check it out if we solve this for L I would do that by taking this bottom part and multiplying it over to the other side remember you're not gonna have to do algebra this is just for us for now okay so check this out if I multiply that to the other side I get 4 PI d squared B equals L so that means when an astronomer wants to know the luminosity the total light of a star they're going to use this equation okay and if they want to use this equation to find L here is a possible test question I could ask okay if an astronomer wants to know the luminosity of a star what two things do they need to know first put it in the discord if the astronomer wants to know the luminosity of a star what two things does it have does that astronomer have to find first distance and apparent brightness okay so I could ask you a question like this I'm not gonna ask you a question where you have to write this equation out or actually plug it in but it does tell you how these things are related to each other if you need this then you have to get the distance and brightness to get it does that make sense so if I asked you that question on the test distance and apparent brightness would be the answer okay if I asked you that on a test okay