Link: walter.bislins.ch/bloge/?page=Knowledge+Database&qs=Radius&mask=3
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#44 | Author: MCToon | Type: Website | Keywords: Measurements, Radius, Historical Documents
Encyclopædia Metropolitana, Volume V, Article: Figure of the Earth
George Biddel Airy, Esq., A.M, F.R.S., Astronomer Royal; 1830; Pages 185-260, Specific numbers on Page 240
Account of the Observations and Calculations, of the Principal Triangulation; and of the Figure, Dimensions and Mean Specific Gravity of the Earth as Derived Therefrom
Alexander Ross Clarke; 1833; Survey of Great Britain
Bestimmung der Axen des elliptischen Rotationssphäroids, welches den vorhandenen Messungen von Meridianbögen der Erde am meisten entspricht
Geh. Rath und Ritter Bessel; 1837; Astronomische Nachrichten 333
An Account of the Measurement of Two Sections of the Meridional Arc of India
Sir George Everest; 1847
The Transcontinental Triangulation and the American Arc of the Parallel
Henry S. Pritchett; 1900; Treasury Deparment; U.S. Coast and Geodetic Survey
Shows triangulation with spherical excess; Page 221 for Spherical Excess
A History of the Determination of the Figure of the Earth from Arc Measurements
Arthur D. Butterfield, M. S.; 1906
#49 | Author: Walter Bislin | Type: Website | Keywords: Radius, Measurement, Curvature, GNSS, GPS, Bonneville, Salt Flats, Salt Lake, Road, Utah
Measuring the radius of the earth in the Display Geo Data App at the Route 80 at the Great Salt Lake Desert near Salt Lake City (Bonneville Salt Flats, Utah) from GNSS data gathered by the geodetic surveyor .
#209 | 6/30/2021 | Author: Walter Bislin | Type: Math | Keywords: Radius of Earth, Hidden
Good approximation formula to calculate R if we know the distance to an object (d), how much of the object is observed to be hidden (x) and the observer height (h) without having to know the distance to the horizon. This values can be figured out by researching the target without even having to go there or to the horizon. My formula is:
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This formula can now be used for simple observations. d, x, and h are easy measurable without having to go to the horizon or target, if we know the size and elevation of the target. The refraction coefficient k corrects for atmospheric refraction (k = 0.17 for standard refraction, or k = 0.143 for 7/6R).
Error calculation:
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#163 | 1/1/2019 | Author: The Maine Surveyor | Type: Youtube | Keywords: Measuring, Radius, Dip Angle, Al-Biruni, Geodesy
Earth's radius can be calculated with reasonable accuracy from a very simple method: Measuring Horizon Drop. Ancient Mathematician Al-Biruni worked out an excellent equation for this.
R = h · cos(a) / (1 − cos(a))
#222 | Author: Wabis | Type: Math | Keywords: Measurement, Radius, Al-Biruni, Accuracy, Error, Refraction
Al-Biruni measured the Dip Angle θ between eye level and the horizon from a mountain of height h. Using some trigonometry he could solve for the radius of the earth R. Refraction can be taken into account by the refraction coefficient k (k = 0.143 for 7/6R refraction):
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The accuracy of R is very dependent on the accuracy of the measured angle θ. Here is equation to calculate the accuracy for small angles
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Al Biruni was certainly aware of atmospheric refraction. His slightly older contemporary, Ibn al-Haytham, devoted one of the 7 volumes of his Kitab al Manazir (Book of Optics) entirely to refraction and reflection, then dealt with refraction further in the final volume. That is why al-Biruni didn't simply take one measurement once, but lugged his huge astrolabe up and down the mountain on various occasions in different conditions. ~ Martin James
#81 | 7/18/2017 | Author: StormsHalted | Type: Website | Keywords: Measuring, Radius, Dip Angle, Trigonometry, Astrolabe
Al-Biruni developed a new method of using trigonometric calculations based on the angle between a plain and mountain top which yielded more accurate measurements of the Earth's circumference and made it possible for it to be measured by a single person from a single location.
From the top of the mountain, he sighted the dip angle which, along with the mountain's height (which he calculated beforehand), he applied to the law of sines formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines.
#80 | 8/3/2019 | Author: Saildrone | Type: Website | Keywords: Saildrone, Circumnavigation, Antarctica, Radius
A seven-meter (23-foot) long, wind-powered unmanned surface vehicle (USV) called a saildrone has become the first unmanned system to circumnavigate Antarctica.
The 196-day mission was launched from Southport in Bluff, New Zealand, on January 19, 2019, returning to the same port on August 3 after sailing over 22,000 km (13,670 miles or 11,879 nautical miles) around Antarctica.