Time transcripts of greatCircleDistance1 [00:00:00:010] We need to calculate the distance between our earthquake and each station [00:00:04:020] that recorded the tsunami. The way to do that is to use the [00:00:08:030] great circle path formula. Here is the formula: [00:00:12:050] The cosine of the distance [00:00:16:060] equals the following: [00:00:20:070] [00:00:24:080] [00:00:28:090] In this formula "a" is [00:00:32:100] the latitude of the earthquake. "b" is [00:00:36:100] the latitude of the other point, here. [00:00:40:110] "a" latitude, "b" latitude, and "c" is the difference between their longitudes. Take the [00:00:44:120] absolute value of that. So you are going to take the sine of this number, [00:00:48:120] the sine of this number, and then you are going to take the cosine of this number and the cosine [00:00:52:130] of this number and you are going to subtract the longitudes from each other. It doesn't matter [00:00:56:150] which because you are going to take the absolute value of that, and take the cosine [00:01:00:170] of that. Multiply all the cosines together, multiply the sines together [00:01:04:180] add those two. Then you have to take the inverse cosine of the answer [00:01:08:190] and you'll get the distance in degrees. Then you multiply by [00:01:12:200] 111.32 and you'll get the distance in kilometers. [00:01:16:200] Here are the things that I want to point out that are important. It is important that you know [00:01:20:210] that when you calculate the distance between two points on the surface of a sphere [00:01:24:210] you need to use the great circle path formula. And I think it's important [00:01:28:230] that you know what that formula is, and I wrote it down right here. [00:01:32:240] But, this class is not really meant to be about calculator skills so if you can automate this [00:01:36:240] in a spreadsheet program or whatever, or you know of a website that will [00:01:40:260] calculate it for you, then that's what you should use because it will actually minimize the errors [00:01:44:270] of you typing stuff in. I've found a good website [00:01:48:280] that works. This is it. I've given you the link to this in the course pages. [00:01:52:290] But, you need to be smart [00:01:57:010] about using websites just like you would if you were looking up information on a [00:02:01:020] web site. That is, you should do a couple of problems [00:02:05:020] yourself and trust your own math and then check if the website [00:02:09:030] gives you the same answer or not. I have checked with this one. [00:02:13:050] So, here, I've entered in the latitude and longitude of the earthquake and the latitude and [00:02:17:060] longitude of our station, and it gives me the distance. It is important [00:02:21:060] when you use a website like this one, that if you have [00:02:25:070] points that are in west longitude or south latitude [00:02:29:090] that you enter them in here as negative numbers or else you won't get the right answer. [00:02:33:100] But I wrote all those down correctly for you in your table of values so hopefully [00:02:37:120] that won't trip you up. All right, that's all there is to it! [00:02:41:120]