 |
Business | Industries | Finance | Tax |
| Index: > A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |
|
|||||
| First Prev [ 1 2 ] Next Last |
Between any two points on a sphere which are not directly opposite each other, there is a unique great circle. The two points separate the great circle into two arcs. The length of the shorter arc is the great circle distance between the points. Between two points which are directly opposite each other (called antipodal points) there infinitely many great circles, but all have the same length, equal to half the circumference of the circle, or , where r is the radius of the sphere.
Because the Earth is approximately spherical, the equations for great circle distance are important for finding the shortest distance between points of the surface of the Earth, and so has important applications in navigation.
Let δ1 and φ1 be respectively the latitude and the longitude of the first point, and δ2 and φ2 those of the second. Let r be the Earth's radius. Then the great circle distance is:
An alternate formula is
Although this formula appears more complicated at first sight it is useful for small distances since it is less subject to rounding errors. It can be used for all distances, however, since it is equivalent to the previous expression. For more explanation, and a slightly different version of this formula, see the haversine formulaThe haversine formula is an equation important in navigation, giving distances between two points on a sphere from their longitudes and latitudes. It is a special case of a more general formula in spherical trigonometry, the law of haversines relating the.
The shape of the EarthA geoid is a close representation, physical model, of the figure of the Earth. According to C. Gauss, it is the "mathematical figure of the Earth", in fact, of her gravity field. It is that equipotential surface (surface of fixed potential value) which co more closely resembles a flattened spheroidA spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. If the ellipse is rotated about its major axis, the surface is called a prolate spheroid (similar to the shape of a rugby ball). If the mi with extreme values for the radius of curvature of 6336 km at the equator and 6399 km at the poles. Using a sphere with a radius of 6367 km results in an error of up to about 0.5%.
In order to use this formula for anything practical you will need two sets of coordinates. For example, the latitude and longitude of two airports:
You will have to convert these coordinates to a more mathematically friendly form using a simple methodGeographic coordinates consist of latitude and longitude. There are many ways of writing coordinates, and converting between the different ways is non-obvious but also quite trivial. Ways of writing coordinates All of the following are valid and acceptabl before you can use them effectively in a formula. After conversion, the coordinates become:
You'll need to convert these coordinates to radians instead of degrees for them to be useful in the formula:
Now you can simply substitute numbers in the formula above:
Substituting r with 6367 kilometers, we get:
The distance between LAX and BNA is then 2884.6 km or 1792 miles.
| Politics | Business | Finance |
 |
 |
 |
|