Transcripts of greatCircleTutorialEarth520
The formula for the great circle path distance is like this. The cosine of the distance is the sine of the latitude of one point and the sine of the latitude of the other point multiplied together plus the cosine of the latitude of the first point, the cosine of the latitude of the second point and the cosine of the absolute value of the difference between their longitudes. If we use station BFO as an example, its location is 48.33 N, and its longitude is 8.33 E The earthquake happened at 42.7226 N, and 13.1871 east. ok. That means that this is "a" right here, this quantity here is "b," and the difference in between these two is c. So you are going to do the sine of this, and the sine of this and then cosine of this, and cosine of this and the cosine of the difference between these two. It doesn't matter which one of these you subtract from each other because it enters into the equation as an absolute value. So multiply the sines together, add them to the product of all the cosines, take the inverse cosine of that answer, and you wind up with "d" which is the distance between the points in degrees. I think it is important that you know that there is such a thing as the great circle path formula and I'm giving it to you, and it will help you later if you have to look it up, but I don't really want this class to be about calculator skills, so I think you should automate this. You should do maybe about one or two by hand to make sure that the automated thing you set up does it correctly. Same as if you look it up on a website. You should do one or two by hand to make sure the web is giving you the answer you think is right. But after that, the point of computers is to do repetitive calculations quickly and accurately and probably it's more accurate than you so that's what you should use. There's a couple of things that I should tell you and one is that if you have a latitude that's in the southern hemisphere then you need to put it in to the equation as a negative number. And also, if your two longitudes are not in the same hemisphere, then you should make them into the same hemisphere first before you subtract them, otherwise you will be wrong. So for example, if one of them is in the western hemisphere then in order to make that into an east longitude, you will want to multiply your western hemisphere number by negative 1. Then it becomes an east longitude. Then you can subtract. And still it doesn't matter which one you subtract from the other, but you need to transform them into the same system of coordinates first, otherwise you will not get the right answer when you go to calculate the distance.