Spherical Coordinate Systems

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Spherical Coordinate Systems Exploring Space Through Math Pre-Calculus let's examine the Earth in 3-dimensional space. The Earth is a large spherical object. In order to find a location on the surface, The Global Pos~ioning System grid is used. The Earth is conventionally broken up into 4 parts called hemispheres. The North and South hemispheres are separated by the equator. The East and West hemispheres are separated by the Prime Meridian. The Geographic Coordinate System grid utilizes a series of horizontal and vertical lines. The horizontal lines are called latitude lines. The equator is the center line of latitude. Each line is measured in degrees to the North or South of the equator. Since there are 360 degrees in a circle, each hemisphere is 180 degrees. The vertical lines are called longitude lines. The Prime Meridian is the center line of longitude. Each hemisphere either East or West from the center line is 180 degrees. These lines form a grid or mapping system for the surface of the Earth, This is how latitude and longitude lines are represented on a flat map called a Mercator Projection. Lat~ude , l ong~ude , and elevalion allows us to uniquely identify a location on Earth but, how do we identify the pos~ion of another point or object above Earth's surface relative to that I? NASA uses a spherical Coordinate system called the Topodetic coordinate system. Consider the position of the space shuttle . The first variable used for position is called the azimuth. Azimuth is the horizontal angle Az of the location on the Earth, measured clockwise from a - line pointing due north. Elevation is the angle of the EI object above the horizon . Finally, the radial distance or the actually distance the object is space is from the surface of the Earth. Ir, fl, Az) Using these three measurements we can identify the specific location of an Az object above the Earth's surface using a spherical coordinate system. Ir, fl, Az) The final slide showing our observer standing on the Az surface of the Earth! Well done! .

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TYPHOONS and DEPRESSIONS OVER the FAR EAST Morning Observation, Sep Teinber 6, from Rasa Jima Island by BERNARDF
SEPTEMBER1940 MONTHLY WEATHER REVIEW 257 days west of the 180th meridian. In American coastal appear to be independent of the typhoon of August 28- waters fog was noted on 10 days each off Washington and September 5, are the following: The S. S. Steel Exporter California; on 4 days off Oregon; and on 3 days off Lower reported 0700 G. C. T. September 6, from latitude 20'18' California. N., longitude 129'30'E.) a pressure of 744.8 mm. (993.0 nib.) with west-northwest winds of force 9. Also, the TYPHOONS AND DEPRESSIONS OVER THE FAR EAST morning observation, Sep teinber 6, from Rasa Jima Island By BERNARDF. DOUCETTE, J. (one of the Nansei Island group) was 747.8 mm. (997.0 5. mb.) for pressure and east-northeast, force 4, for winds. [Weather Bureau, Manila, P. I.] Typhoon, September 11-19) 1940.-A depression, moving Typhoon, August %!-September 6,1940.-A low-pressure westerly, passed about 200 miles south of Guam and area far to the southeast of Guam moved west-northwest, quickly inclined to the north, intensifying to typhoon rapidly developing to typhoon intensity as it proceeded. strength, September 11 to 13. It was stationary, Sep- When the center reached the regions about 250 miles tember 13 and 14, about 150 miles west-northwest of west of Guam, the direction changed to the northwest, Guam, and then began a northwesterly and northerly and the storm continued along this course until it reached course to the ocean regions about 300 miles west of the the latitude of southern Formosa.
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Prime Meridian ×
This website would like to remind you: Your browser (Apple Safari 4) is out of date. Update your browser for more × security, comfort and the best experience on this site. Encyclopedic Entry prime meridian For the complete encyclopedic entry with media resources, visit: http://education.nationalgeographic.com/encyclopedia/prime-meridian/ The prime meridian is the line of 0 longitude, the starting point for measuring distance both east and west around the Earth. The prime meridian is arbitrary, meaning it could be chosen to be anywhere. Any line of longitude (a meridian) can serve as the 0 longitude line. However, there is an international agreement that the meridian that runs through Greenwich, England, is considered the official prime meridian. Governments did not always agree that the Greenwich meridian was the prime meridian, making navigation over long distances very difficult. Different countries published maps and charts with longitude based on the meridian passing through their capital city. France would publish maps with 0 longitude running through Paris. Cartographers in China would publish maps with 0 longitude running through Beijing. Even different parts of the same country published materials based on local meridians. Finally, at an international convention called by U.S. President Chester Arthur in 1884, representatives from 25 countries agreed to pick a single, standard meridian. They chose the meridian passing through the Royal Observatory in Greenwich, England. The Greenwich Meridian became the international standard for the prime meridian. UTC The prime meridian also sets Coordinated Universal Time (UTC). UTC never changes for daylight savings or anything else. Just as the prime meridian is the standard for longitude, UTC is the standard for time.
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THE JOURNAL OF NAVIGATION (2019), 72, 1660–1664. c The Royal Institute of Navigation 2019 doi:10.1017/S0373463319000341 FORUM GMT and Longitude by Lunar Distance: Two Methods Compared From a Practitioner’s Point of View Eric Romelczyk (E-mail: [email protected]) This article discusses the technique of observing lunar distance - that is, angular distance between the moon and another celestial body - to establish universal time and longitude, from a practitioner’s point of view. The article presents a brief overview of the principles underlying the lunar distance observation and its use in celestial navigation. A discussion follows of two different methods for finding universal time by observing lunar distance, Dr. Wendel Brunner’s calculator-based method and the specialised inspection tables created by Bruce Stark. The article compares the two methods against each other for ease of use and accuracy. The author concludes that either method will provide satisfactory results, but that the technique of observing lunar dis- tance is unlikely to regain relevance in the modern-day practice of navigation and is primarily useful as a skill-building exercise in making sextant observations. KEYWORDS 1. Navigation. 2. History. 3. Nautical. 4. Time. Submitted: 8 August 2018. Accepted: 14 April 2019. First published online: 2 May 2019. 1. INTRODUCTION. 1.1. History of the lunar distance method. For centuries of seafaring history, a method for accurately measuring time to the degree of precision necessary to establish the navigator’s longitude was out of reach for practical purposes. It had been understood since the mid-16th century that the navigator’s longitude could be established either by reference to the moon’s angular distance from other celestial bodies - the “lunar distance”, measured by careful sextant observations - or by reference to a timepiece of sufficient accuracy.
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