Calculating Distance Between Tow Points on Earth Surface Using Gps Coordinates

DISTANCE CALCULATION Because of the near-spherical shape of the Earth (technically an oblate spheroid) , calculating an accurate distance between two points requires the use of spherical geometry and trigonometric math functions. However, you can calculate an approximate distance using much simpler math functions. For many applications the approximate distance calculation provides sufficient accuracy with much less complexity. The following approximate distance calculations are relatively simple, but can produce distance errors of 10 percent of more. These approximate calculations are performed using latitude and longitude values in degrees. The first approximation requires only simple math functions: Approximate distance in miles: sqrt(x * x + y * y) where x = 69. 1 * (lat2 lat1) and y = 53. 0 * (lon2 lon1) You can improve the accuracy of this approximate distance calculation by adding the cosine math function Improved approximate distance in miles: sqrt(x * x + y * y) where x = 69. 1 * (lat2 lat1) and y = 69. 1 * (lon2 lon1) * cos(lat1/57. 3) If you need greater accuracy, you can use the Great Circle Distance Formula. This formula requires use of spherical geometry and a high level of floating point mathematical accuracy about 15 digits of accuracy (sometimes called double-precision). In order to use this formula properly make sure your software application or programming language is capable of double-precision floating point calculations. In addition, the trig math functions used in this formula require conversion of the latitude and longitude values from decimal degrees to radians. To convert latitude or longitude from decimal degrees to radians, divide the latitude and longitude values in this database by 180/pi, or approximately 57. 9577951. The radius of the Earth is assumed to be 6,378. 8 kilometers, or 3,963. 0 miles. If you convert all latitude and longitude values in the database to radians before the calculation, use this equation: Great Circle Distance Formula using radians: 3963. 0 * arccos[sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 lon1)] If you do NOT first convert th e latitude and longitude values in the database to radians, you must include the degrees-to-radians conversion in the calculation. Substituting degrees for radians, the formula becomes: Great Circle Distance Formula using decimal degrees 963. 0 * arccos[sin(lat1/57. 2958) * sin(lat2/57. 2958) + cos(lat1/57. 2958) * cos(lat2/57. 2958) * cos(lon2/57. 2958 -lon1/57. 2958)] OR r * acos[sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2 lon1)] Where r is the radius of the earth in whatever units you desire. r=3437. 74677 (nautical miles) r=6378. 7 (kilometers) r=3963. 0 (statute miles) If the software application or programming language you are using has no arccosine function, you can calculate the same result using the arctangent function, which most applications and languages do support. Use the following equation: 3963. 0 * arctan[sqrt(1-x^2)/x] where x = [sin(lat1/57. 2958) * sin(lat2/57. 2958)] + [cos(lat1/57. 2958) * cos(lat2/57. 2958) * cos(lon2/57. 2958 lon1/57. 2958)] If your distance calculations produce wildly incorrect results, check for these possible problems: 1. Did you convert the latitude and longitude values from degrees to radians? Trigonometric math functions such as sine and cosine normally require conversion of degrees to radians, as described above. 2. Are the equations implemented correctly with necessary parentheses? Remember the old math precedence rule MDAS multiply, divide, add, subtract. 3. Does your software application or programming language provide sufficient mathematical accuracy? For best results, you need about 15 digits of accuracy. 4. When you imported the data from the text files your latitude/longitude values may have been truncated. Make sure you did not lose any of the digits to the right of the decimal point during import. 5. Have you lost any precision of your decimal values due to rounding during importing or calling custom math functions

Short answers about Introduction to Political Economy Essay - 2

Short answers about Introduction to Political Economy - Essay Example Another cause of monopolies occurs when one firm expands to the point where it has tremendous economies of scale; other competitors drop out of the market because they cannot compete. Companies are likely to collude with each other if there are very few firms in an industry. Because of this, a change in one firm is likely to result in a change in another firm so that market forces remain the same. On the other hand, companies are likely to compete with each other when there is free market economy that allows consumers to pick and choose from many different companies. Regulations can cause a huge shift in the market, particularly in the labor market. When the government stipulates that employees must certain type of social security, employers have to respond to those changes. This can often mean that a business downsizes because it cannot afford to employ the same number of workers. Regulations primarily stifle business because of all the extra red tape that comes along with it. Capture theory stipulates that a government agency may allow the industry that it is charge of to dictate policy that favors the industry as a whole. On the other hand, public-interest theory deals with the interest of consumers. For example, when the market is not efficient as it could be, a regulatory body can act to make changes in regulations. The abolition of private property and the application of all rent to public purpose is designed for zoning laws that allow the government to own property. Progressive income tax makes all Americans pay their fair share. The abolition of all rights of inheritance offers limited inheritance through tax statues. Confiscation of property of rebels allows the government to seize property belonging to terrorist groups. Centralizing the credit system gives the state control over loans. Centralizing communication and transport allows the state to set regulations. Corporate capacity allows land to be improved. Equal labor

Martin Luther King and the Church Essay Example | Topics and Well Written Essays - 250 words

Martin Luther King and the Church - Essay Example All social groups ranging from the ruling class to the peasant class had a strong reason to accept Luther’s reasons and support him. The princes and kings resented the overarching control of the Church, while the peasants resented the wealth of the Church and revolted against the social, political and religious authorities. It was the context and time that played a huge role in the success of Luther. As reformation spread from Germany throughout Europe, it gave rise to violence, religious struggles, wars and civil unrest. The widespread conflicts involving Catholics killing Protestants, Protestants killing Catholics and the Thirty Years War can certainly not be justified, whatever the reason was, given the bloodshed and other serious consequences. However, Reformation alone cannot be held solely responsible for these wars as even otherwise there would have been political and social struggles leading to wars at that time in Europe. There was an increasing social and political discontent all over Europe. Reformation offered the opportunity to either establish authority or to break away from it. This context should not be ignored while discussing the stormy period in Europe during the Reformation. Such a political and social unrest should be seen as a significant trigger for the wars and civil unrest all over Europe during Reformation. Brutal wars and bloodshed cannot be hailed or celebrated, but without Reformation, Europe would not have undergone significant changes in its political, economic and social institutions. Change is inevitable, and Reformation was one such a change within the Church but one which led to a larger scale conflict and war because of the contemporary socio-political conditions. It was only an opportunity seized by the society of that time, and if it had not been a Reformation, it would have been some other revolution that would have erupted to