for number 16 on homework number or homework chapter 17 for Esther 1:20 there's a three parts to an a B and C and it's all about the luminosity flux equation and it's beginning with you know the flux we receive from the Sun at Earth's distance is about thirteen hundred and seventy watts per square meter now we know that's above the Earth's atmosphere and it tells you what a watt is equivalent to you know one job per second and it also says and that same opening paragraph the star Sirius which is the brightest star in the sky besides our Sun is giving us a poultry flux of about one times ten to the negative seventh watts per square meter so okay clearly you know even though Sirius is a more powerful star it's more luminous than our Sun because of its vastly greater distance of course we receive a much lesser and a much smaller amount of flux from it that just makes good intuitive sense so in Part A it says all right you know based upon the fact that our Sun is a known distance away one astronomical unit but we need it in meters it says what is the sun's luminosity well you already know that we've calculated before but you know let's use it using the equation so you know no but I see this equal to 4 PI d squared times the flux received and if I would like this value to be in watts which I would then ID to be in meters and I want my flux to be in a watts per meter squared that way when you square the beers and this is Watts over meter squared the meter squared cancel don't they and you'll be left with just what's perfect that's exactly what I want so you know I write it down it's 4 pi times what's your Sun distance in meters it's about one point four nine six times 10 to the 11th meters don't forget to square it and what's the flex that we received it tells you in the opening paragraph it's about thirteen hundred and seventy watts per square meter so sure enough meter squared a meter squared here will cancel I'll have a final answer in watts we of course can look it up but punch it into your calculator and get a true value and my calculator spat out you know three point eight five times ten to the ear member it's ten to the 26 watts okay that's a and B it says all right let's do the same thing for serious you were talking the opening paragraph how much flex we receive from Sirius and you're told also that the distance in Part B this Sirius is eight point eight light-years which is you know accurate but it's not the units that I mean I need it to be in meters so what else have you told this is a Part B you're told that a light-years equivalent to nine point four six zero five three a lot of significant digits times tend to be a times 10 to the fifteenth excuse me meters so it says therefore calculate Sirius is luminosity okay in Part B same equation luminosity is serious this time it's gonna equal a four pi and now what goes in the parentheses here for D it's gonna be a multiplication so maybe eight point eight light-years multiplied by how many light here or how many meters that are per light here which again is you know nine point four six and then what's the extra digits zero five three all times sent to the fifteen meters an a whole thing there gets squared that could be the downfall if you put this into your calculator incorrectly but this you know I'd start here multiply eight point eight times this to the fifteenth and then take the whole quantity and square it that multiply it by four then multiply it by PI and finally got multiplied by the flux which you're told from the opening paragraph is one times ten to the negative seventh watts per square meter so again meters squared and meter squared will cancel on the final answer in watts perfect it's exactly what I want and you know I'm not going to solve all the problems for you so you don't just have to write them down but it's just a matter punch of them incorrectly isn't it right to get the nasty I'm serious the Part C is a little bit different it's more wordy and it says you know hypothetically if serious had a surface temperature of 15,000 kelvins it doesn't it's more like about 10,000 Kelvin so you're not gonna get the same answer here okay but it says if series had a surface temperature of 15,000 comments then what would its luminosity be how much total power would it have then and of course if the temperatures higher then it's luminosity is going to be higher - we know that it just kind of intuitively so it says you need to remember that the flux at the surface of a blackbody is given by a the stephane equation here which is you know flux equals Sigma T to the fourth and then where T effective is equal to the surface temperature and the Sigma of course is a constant it's the stefan-boltzmann constant and it says you can also assume that Sirius has a radius of about eight point R eight times ten to the eighth meters this is where the flux is measured for this surface flux from a black body so up here in Parts A and B you're just directly told what the flux was in Part C you've got to calculate the flux first and then actually use that and put it into your equation for luminosity so step one in Part C is to get the surface flux from series's surface so flux is equal to Sigma T to the fourth so if I plugged it in correctly Sigma of courses give it to you the problem it's just equivalent to five point six six nine seven I understand the very small number of times 10 to the negative 8 and that's a lot per meter squared Kelvin to the fourth bizarre bunch of units up but just make sure they all cancel out correctly in the end and that's just what Sigma is and you got to multiply it by the surface temperature of Sirius and it's in hypothetically let's make it 15,000 kelvins all right okay and there's the four now you see it don't you this is gonna be km/h to the fourth power and that's why this was over k2 the force of those K fourths cancel and I answer will then be in watts per meter squared which is what standard B fluxes measure didn't well good okay put this into your calculator start with the 15,000 then raise it to the fourth power remember the Y to the X key in your calculator punch you in 15,000 and then Y to the X and then for big number they multiply it by this very tiny number and it'll moderate a little bit for you so once you know what the surface flux is now the hypothetical serious is what do you do take this value of F and plug it into this equation here to get the luminosity so yeah you got luminosity equals four PI B squared times F but who's that business again this F is always a surface isn't it so if this F is a surface F then what does that DF to be it's going to be the distance to the surface of serious or simply its radius and that's why you've been told in Part C what the radius of series is okay so you know I substitute D for our right it's the radius really for your surface flux so do you see the difference here you know this is a flux at the surface of the star these EPS appear have been the flux that we received at Earth from a distance D from that object all the way to the earth so okay it I use this data for F and I plug it into this equation and they use the radius so they're serious I should be okay I will get four or five and the radius we were told to use was that eight times ten to the eighth meters that's meters so we're okay aren't we our deeds to be in meters don't forget to square that and then of course multiply that by the value that you got here if I call this value here of Z and of course multiply it by so again if this is actually hotter than seriously as normal later then I better hope that this luminosity of that I get here is going to be larger than the luminosity of the real series which is Part B so if you're finding all that to be true fantastic okay you know just got to be careful with the calculator hitting all those buttons correctly and that's it it's good practice though for doing these kind of problems