Anderson Video - Intensity of the Sun Example

Professor Anderson
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<font color="#ffffff">And let's ask the following question:</font> <font color="#ffffff">what is the total --</font> <font color="#ffffff">what is the total power output of the sun?</font> <font color="#ffffff">What is the total power output of the Sun? And let's say that we know a couple</font> <font color="#ffffff">things. We're going to say that the intensity at the earth is equal to</font> <font color="#ffffff">1,390 watts per square meter,</font> <font color="#ffffff">this is the intensity of the sunlight at the earth.</font> <font color="#ffffff">All right, let's draw a picture of this thing. Here's our sun. Okay, it is spitting</font> <font color="#ffffff">out electromagnetic waves in all directions. Some of those we collect</font> <font color="#ffffff">right here on the earth. Okay, and we know that we are a distance, capital R, away from</font> <font color="#ffffff">the sun. So if I want to think about how much power is emitted by the Sun in</font> <font color="#ffffff">total, I have to worry about this sphere right here, of radius capital R. Okay, the</font> <font color="#ffffff">total power emitted through that sphere is hopefully something we can calculate</font> <font color="#ffffff">based on the intensity at the earth. All right, how do we do it? Well at the earth</font> <font color="#ffffff">the intensity that we measure is just power over area and that is what we said</font> <font color="#ffffff">was 1390 watts per square centimeter. But the total power coming out of the</font> <font color="#ffffff">sun is going to be that intensity that we measure here,</font> <font color="#ffffff">multiplied by the area of this giant sphere.</font> <font color="#ffffff">Okay, we know S, what is the area of this giant dashed sphere? It is four PI capital R</font> <font color="#ffffff">squared. Now take our little intensity and multiply it by the area of the</font> <font color="#ffffff">sphere. And as you can imagine that's going to be a pretty big number so we</font> <font color="#ffffff">have 1390 for S, we have a four, we have a pi, and now we need this number R, and this</font> <font color="#ffffff">you can look up in your textbook -- how far is the Earth from the Sun? It is 1.5</font> <font color="#ffffff">times 10 to the 11 meters and so you're gonna square that. And somebody</font> <font color="#ffffff">double-check my calculation, I ran this earlier but maybe you can double check,</font> <font color="#ffffff">I get 3.93 times 10 to the 26 watts.</font> <font color="#ffffff">Okay, 3.93 times ten to 26 watts for the total power coming out of</font> <font color="#ffffff">the Sun, which is a pretty big number right? When we were talking about how</font> <font color="#ffffff">much power your hairdryer uses, it was like one-and-a-half kilowatts, right?</font> <font color="#ffffff">It was like 10 to the 3 watts and here's something that is 23 orders of</font> <font color="#ffffff">magnitude bigger. It's not like you would expect -- it's lot of power coming out of the sun.</font> <font color="#ffffff">Okay, but if that's the total power coming out of the Sun, let's ask a</font> <font color="#ffffff">follow-up question. What is the intensity at the sun's surface?</font> <font color="#ffffff">Okay, how do we do that? Well, we're going to need to know the radius of the Sun</font> <font color="#ffffff">and if we do that, then we can calculate the intensity at the sun's surface, because</font> <font color="#ffffff">it's just going to be that total power divided by the area of the Sun. And we</font> <font color="#ffffff">know the total power, and the area of the Sun is four pi times the radius of the</font> <font color="#ffffff">Sun squared. And so now again you can look up that number and let's punch it</font> <font color="#ffffff">in right here. So P total we said was 3.93 times 10 to the 26 watts, we've got a 4</font> <font color="#ffffff">pi and then we have R squared, which if you look it up is 6.96 times 10</font> <font color="#ffffff">to the 8th meters. That's the radius of the Sun and if you put all this together</font> <font color="#ffffff">you get 6.42 times 10 to the 7 watts per square meter.</font> <font color="#ffffff">Okay, which is a big number, right? Think about a square meter, it's like that and it's</font> <font color="#ffffff">going to have 64 million watts in that square meter,</font> <font color="#ffffff">that is a lot of electromagnetic intensity.</font>
<font color="#ffffff">And let's ask the following question:</font> <font color="#ffffff">what is the total --</font> <font color="#ffffff">what is the total power output of the sun?</font> <font color="#ffffff">What is the total power output of the Sun? And let's say that we know a couple</font> <font color="#ffffff">things. We're going to say that the intensity at the earth is equal to</font> <font color="#ffffff">1,390 watts per square meter,</font> <font color="#ffffff">this is the intensity of the sunlight at the earth.</font> <font color="#ffffff">All right, let's draw a picture of this thing. Here's our sun. Okay, it is spitting</font> <font color="#ffffff">out electromagnetic waves in all directions. Some of those we collect</font> <font color="#ffffff">right here on the earth. Okay, and we know that we are a distance, capital R, away from</font> <font color="#ffffff">the sun. So if I want to think about how much power is emitted by the Sun in</font> <font color="#ffffff">total, I have to worry about this sphere right here, of radius capital R. Okay, the</font> <font color="#ffffff">total power emitted through that sphere is hopefully something we can calculate</font> <font color="#ffffff">based on the intensity at the earth. All right, how do we do it? Well at the earth</font> <font color="#ffffff">the intensity that we measure is just power over area and that is what we said</font> <font color="#ffffff">was 1390 watts per square centimeter. But the total power coming out of the</font> <font color="#ffffff">sun is going to be that intensity that we measure here,</font> <font color="#ffffff">multiplied by the area of this giant sphere.</font> <font color="#ffffff">Okay, we know S, what is the area of this giant dashed sphere? It is four PI capital R</font> <font color="#ffffff">squared. Now take our little intensity and multiply it by the area of the</font> <font color="#ffffff">sphere. And as you can imagine that's going to be a pretty big number so we</font> <font color="#ffffff">have 1390 for S, we have a four, we have a pi, and now we need this number R, and this</font> <font color="#ffffff">you can look up in your textbook -- how far is the Earth from the Sun? It is 1.5</font> <font color="#ffffff">times 10 to the 11 meters and so you're gonna square that. And somebody</font> <font color="#ffffff">double-check my calculation, I ran this earlier but maybe you can double check,</font> <font color="#ffffff">I get 3.93 times 10 to the 26 watts.</font> <font color="#ffffff">Okay, 3.93 times ten to 26 watts for the total power coming out of</font> <font color="#ffffff">the Sun, which is a pretty big number right? When we were talking about how</font> <font color="#ffffff">much power your hairdryer uses, it was like one-and-a-half kilowatts, right?</font> <font color="#ffffff">It was like 10 to the 3 watts and here's something that is 23 orders of</font> <font color="#ffffff">magnitude bigger. It's not like you would expect -- it's lot of power coming out of the sun.</font> <font color="#ffffff">Okay, but if that's the total power coming out of the Sun, let's ask a</font> <font color="#ffffff">follow-up question. What is the intensity at the sun's surface?</font> <font color="#ffffff">Okay, how do we do that? Well, we're going to need to know the radius of the Sun</font> <font color="#ffffff">and if we do that, then we can calculate the intensity at the sun's surface, because</font> <font color="#ffffff">it's just going to be that total power divided by the area of the Sun. And we</font> <font color="#ffffff">know the total power, and the area of the Sun is four pi times the radius of the</font> <font color="#ffffff">Sun squared. And so now again you can look up that number and let's punch it</font> <font color="#ffffff">in right here. So P total we said was 3.93 times 10 to the 26 watts, we've got a 4</font> <font color="#ffffff">pi and then we have R squared, which if you look it up is 6.96 times 10</font> <font color="#ffffff">to the 8th meters. That's the radius of the Sun and if you put all this together</font> <font color="#ffffff">you get 6.42 times 10 to the 7 watts per square meter.</font> <font color="#ffffff">Okay, which is a big number, right? Think about a square meter, it's like that and it's</font> <font color="#ffffff">going to have 64 million watts in that square meter,</font> <font color="#ffffff">that is a lot of electromagnetic intensity.</font>