How Much Does the Earth Weigh?

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In order to measure the mass of the Earth, the density must first be determined. Discover how to measure the weight of the Earth in kilograms with help from a science teacher in this free video on calculating mass and physics.

Part of the Video Series: Physics Help
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Video Transcript

Hi, I'm Steve Jones, and I'm going to try and tell you how much the earth weighs. Well, this is a real problem, but of course we know some rough, ideas of size. And I'm using a radius of 5,000 kilometers, or five times ten, to the power six meters, is the actual radius of the earth. Ten to the sixth is a million, so five million meters. So when we're starting with a number like that, and then we're going to multiply it by itself, twice, we have to use these powers of ten, five times ten to the sixth. So let's look at the actual volume of this sphere, because, if we can find the volume of the sphere, then we can use a density equation to find the mass. And I'm giving it a density of eight kilograms per cubic meter, it might be, sorry, 8,000 kilograms per cubic meter, it might be 5,000. Doesn't really matter, it's the method that we're doing. So first of all, let's look at the volume of the sphere. Four thirds, pie, r cubed. Well pie, and three are near enough the same, so it's four times the radius, which is five, times ten to the sixth, all of that cubed. Now, well that's not to difficult to work out. Five, times five, times five, is 125. So it's four, times 125, times ten to the power, well, to multiply ten to the sixth by itself, it becomes ten to the twelfth, and again ten to the power 18. That's one with 18 zeros. It's getting to be a quite big number. So this is, checking it, this is meters cubed. So that is the number of cubic meters. Now, let's have a look at the density. We know, that each of these is 8,000 kilograms. So the mass, is therefor, the volume, this that we've just worked out, well, four times 125, is 500. That's nice and easy, isn't it. So it's 500, multiplied by ten to the power 18. So that's the volume, and we'll multiply it by the density, which is 8,000, and this will be in kilograms. That's quite a lot of kilograms. If you want it in tons, we can divide by 1,000 later. So if we get rid of some of these knots, we've got, ten to the power 18, and we've got one, two, three, four, five knots. So it's ten to the power, 23, and five eighths of 40. So 40 times 10 to the 23, which is four times ten to the power 24, kilograms. Okay, now if we're going to draw 10 to the 24, well we've got three, six, nine, 12. Three, six, nine, 12. Well that's 10 to the power 24. There you are. And it's four. It's that number of kilograms, is the mass of the earth. So if we want to measure the mass of the earth, we should first of all establish exactly what the density is. I'm not sure it's exactly 8,000, but somewhere around there. Know exactly the radius of the earth, and using the calculation I've shown you, you can work out that it is this huge number of kilograms. That is how to weigh the earth.


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