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In mathematics, a space is a set (sometimes known as a universe) ... The word "geometry" (from Ancient Greek: geo- "earth", -metron "measurement") initially meant a ...
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.
Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry. [1] Curved spaces can generally be described by Riemannian geometry , though some simple cases can be described in other ways.
Example: Terence and Stella are at an Earth-to-Mars space race. Terence is an official at the starting line, while Stella is a participant. At time t = t ′ = 0, Stella's spaceship accelerates instantaneously to a speed of 0.5 c. The distance from Earth to Mars is 300 light-seconds (about 90.0 × 10 6 km).
Image from space: The curved surface of the spherical planet Earth. Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth to a sphere.The concept of a spherical Earth gradually displaced earlier beliefs in a flat Earth during classical antiquity and the Middle Ages.
The extra pull of Earth's gravity decreases the object's orbital period, and at the L 2 point, that orbital period becomes equal to Earth's. Like L 1, L 2 is about 1.5 million kilometers or 0.01 au from Earth (away from the sun). An example of a spacecraft designed to operate near the Earth–Sun L 2 is the James Webb Space Telescope. [8]
An example of a quotient space of a manifold that is also a manifold is the real projective space, identified as a quotient space of the corresponding sphere. One method of identifying points (gluing them together) is through a right (or left) action of a group , which acts on the manifold.
A metric space M is bounded if there is an r such that no pair of points in M is more than distance r apart. [b] The least such r is called the diameter of M. The space M is called precompact or totally bounded if for every r > 0 there is a finite cover of M by open balls of radius r. Every totally bounded space is bounded.