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Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
Earth radius (denoted as R 🜨 or R E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of nearly 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).
One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.
Knowledge of the location of Earth has been shaped by 400 years of telescopic observations, and has expanded radically since the start of the 20th century. Initially, Earth was believed to be the center of the Universe , which consisted only of those planets visible with the naked eye and an outlying sphere of fixed stars . [ 1 ]
Stripping out unit conversion and uniform scaling, the formulae may be written: = = where is the longitude from the central meridian (in radians), is the latitude, and R is the radius of the globe used as the model of the earth for projection.
The unit for radial distance is usually determined by the context, as occurs in applications of the 'unit sphere', see applications. When the system is used to designate physical three-space, it is customary to assign positive to azimuth angles measured in the counterclockwise sense from the reference direction on the reference plane—as seen ...
Earth's surface is the boundary between the atmosphere, and the solid Earth and oceans. Defined in this way, it has an area of about 510 million km 2 (197 million sq mi). [12] Earth can be divided into two hemispheres: by latitude into the polar Northern and Southern hemispheres; or by longitude into the continental Eastern and Western hemispheres.
Posidonius calculated the Earth's circumference by reference to the position of the star Canopus.As explained by Cleomedes, Posidonius observed Canopus on but never above the horizon at Rhodes, while at Alexandria he saw it ascend as far as 7 + 1 ⁄ 2 degrees above the horizon (the meridian arc between the latitude of the two locales is actually 5 degrees 14 minutes).