Continuum hypothesisIn mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that there is no set whose cardinality is strictly between that of the integers and the real numbers, or equivalently, that any subset of the real numbers is finite, is countably infinite, or has the same cardinality as the real numbers. In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to the following equation in aleph numbers: , or even shorter with beth numbers: .
Jordan algebraIn abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: (commutative law) (). The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra. The axioms imply that a Jordan algebra is power-associative, meaning that is independent of how we parenthesize this expression. They also imply that for all positive integers m and n.
Differential graded algebraIn mathematics, in particular in homological algebra, a differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. TOC A differential graded algebra (or DG-algebra for short) A is a graded algebra equipped with a map which has either degree 1 (cochain complex convention) or degree −1 (chain complex convention) that satisfies two conditions: A more succinct way to state the same definition is to say that a DG-algebra is a monoid object in the .
Launch padA launch pad is an above-ground facility from which a rocket-powered missile or space vehicle is vertically launched. The term launch pad can be used to describe just the central launch platform (mobile launcher platform), or the entire complex (launch complex). The entire complex will include a launch mount or launch platform to physically support the vehicle, a service structure with umbilicals, and the infrastructure required to provide propellants, cryogenic fluids, electrical power, communications, telemetry, rocket assembly, payload processing, storage facilities for propellants and gases, equipment, access roads, and drainage.
Rocket engineA rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accordance with Newton's third law. Most rocket engines use the combustion of reactive chemicals to supply the necessary energy, but non-combusting forms such as cold gas thrusters and nuclear thermal rockets also exist. Vehicles propelled by rocket engines are commonly called rockets.
Sea LaunchSea Launch was a multinational—Norway, Russia, Ukraine, United States—spacecraft launch company founded in 1995 that provided orbital launch services from 1999 to 2014. The company used a mobile maritime launch platform for equatorial launches of commercial payloads on specialized Zenit-3SL rockets from a former mobile/floating oil drilling rig renamed Odyssey. By 2014, it had assembled and launched thirty-two rockets, with an additional three failures and one partial failure.
Rocket propellantRocket propellant is the reaction mass of a rocket. This reaction mass is ejected at the highest achievable velocity from a rocket engine to produce thrust. The energy required can either come from the propellants themselves, as with a chemical rocket, or from an external source, as with ion engines. Rockets create thrust by expelling mass rear-ward, at high velocity. The thrust produced can be calculated by multiplying the mass flow rate of the propellants by their exhaust velocity relative to the rocket (specific impulse).
Analytical mechanicsIn theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the 18th century and onward, after Newtonian mechanics. Since Newtonian mechanics considers vector quantities of motion, particularly accelerations, momenta, forces, of the constituents of the system, an alternative name for the mechanics governed by Newton's laws and Euler's laws is vectorial mechanics.
Water rocketA water rocket is a type of model rocket using water as its reaction mass. The water is forced out by a pressurized gas, typically compressed air. Like all rocket engines, it operates on the principle of Newton's third law of motion. Water rocket hobbyists typically use one or more plastic soft drink bottle as the rocket's pressure vessel. A variety of designs are possible including multi-stage rockets. Water rockets are also custom-built from composite materials to achieve world record altitudes.
Solid-propellant rocketA solid-propellant rocket or solid rocket is a rocket with a rocket engine that uses solid propellants (fuel/oxidizer). The earliest rockets were solid-fuel rockets powered by gunpowder; they were used in warfare by the Chinese, Indians, Mongols and Persians as early as the 13th century. All rockets used some form of solid or powdered propellant up until the 20th century, when liquid-propellant rockets offered more efficient and controllable alternatives.
Gravity of EarthThe gravity of Earth, denoted by g, is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude is given by the norm . In SI units this acceleration is expressed in metres per second squared (in symbols, m/s2 or m·s−2) or equivalently in newtons per kilogram (N/kg or N·kg−1).
Continuum (set theory)In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by . Georg Cantor proved that the cardinality is larger than the smallest infinity, namely, . He also proved that is equal to , the cardinality of the power set of the natural numbers. The cardinality of the continuum is the size of the set of real numbers. The continuum hypothesis is sometimes stated by saying that no cardinality lies between that of the continuum and that of the natural numbers, , or alternatively, that .
