Terminology
Pairs of points on a sphere that lie on a straight line through its center are called antipodal points In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite it — so situated that a line drawn from the one to the other passes through the centre of the sphere and forms a true diameter. A great circle A great circle of a sphere is a circle that runs along the surface of that sphere so as to cut it into two equal halves. The great circle therefore has both the same circumference and the same center as the sphere. It is the largest circle that can be drawn on a given sphere is a circle on the sphere that has the same center and radius as the sphere, and consequently divides it into two equal parts. The shortest distance between two distinct non-antipodal points on the surface and measured along the surface, is on the unique great circle passing through the two points. Equipped with the great-circle distance The great-circle distance or orthodromic distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere . Because spherical geometry is rather different from ordinary Euclidean geometry, the equations for distance take on a different form. The distance between two points in, a great circle becomes the Riemannian circle In metric space theory and Riemannian geometry, the term Riemannian circle refers to a great circle equipped with its great-circle distance. In more detail, the term refers to the circle equipped with its intrinsic Riemannian metric of a compact 1-dimensional manifold of total length 2π, as opposed to the extrinsic metric obtained by restriction.
If a particular point on a sphere is (arbitrarily) designated as its north pole, then the corresponding antipodal point is called the south pole and the equator The equator is the intersection of the Earth's surface with the plane perpendicular to the Earth's axis of rotation and containing the Earth's center of mass. In simpler language, it is an imaginary line on the Earth's surface equidistant from the North Pole and South Pole that divides the Earth into a Northern Hemisphere and a Southern Hemisphere is the great circle that is equidistant to them. Great circles through the two poles are called lines (or meridians A meridian is an imaginary arc on the Earth's surface from the North Pole to the South Pole that connects all locations running along it with a given longitude. The position of a point on the meridian is given by the latitude. Each meridian is perpendicular to all circles of latitude at the intersection points. Each is also the same size, being) of longitude Longitude , identified by the Greek letter lambda (λ), is the geographic coordinate most commonly used in cartography and global navigation for east-west measurement. It is the angular distance measured east or west and usually expressed in degrees (or hours), minutes, and seconds, from the prime meridian, defined to be at the Royal Observatory,, and the line connecting the two poles is called the axis of rotation A rotation is a movement of an object in a circular motion. A two-dimensional object rotates around a center of rotation. A three-dimensional object rotates around a line called an axis. If the axis of rotation is within the body, the body is said to rotate upon itself, or spin—which implies relative speed and perhaps free-movement with angular. Circles on the sphere that are parallel to the equator are lines of latitude Latitude, usually denoted by the Greek letter phi gives the location of a place on Earth (or other planetary body) north or south of the equator. Lines of Latitude are the horizontal lines shown running east-to-west on maps (particularly so in the Mercator projection). Technically, latitude is an angular measurement in degrees (marked with °). This terminology is also used for astronomical bodies such as the planet Earth Earth is the third planet from the Sun. It is the fifth largest of the eight planets in the solar system, and the largest of the terrestrial planets in the Solar System in terms of diameter, mass and density. It is also referred to as the World, the Blue Planet,[note 3] and Terra.[note 4], even though it is neither spherical nor even spheroidal A spheroid is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters (see geoid The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest, and extended through the continents . According to C.F. Gauss, who first described it, it is the "mathematical figure of the Earth," a smooth but highly irregular surface that).
<<Table of Contents A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the radius of the sphere. The | Next>> | Show All>>
