Outer Space Treaty

The Outer Space Treaty, formally the Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies, is a treaty that forms the basis of international space law. The treaty was opened for signature in the United States, the United Kingdom, and the Soviet Union on 27 January 1967, and entered into force on 10 October 1967. As of September 2015, 104 countries are parties to the treaty, while another 24 have signed the treaty but have not completed ratification. In addition, the Republic of China (Taiwan), which is currently only recognized by 21 UN member states, ratified the treaty prior to the United Nations General Assembly's vote to transfer China's seat to the People's Republic of China (PRC) in 1971.

Key points

The Outer Space Treaty represents the basic legal framework of international space law. Among its principles, it bars states party to the treaty from placing weapons of mass destruction in orbit of Earth, installing them on the Moon or any other celestial body, or otherwise stationing them in outer space. It exclusively limits the use of the Moon and other celestial bodies to peaceful purposes and expressly prohibits their use for testing weapons of any kind, conducting military maneuvers, or establishing military bases, installations, and fortifications (Art.IV). However, the Treaty does not prohibit the placement of conventional weapons in orbit. The treaty also states that the exploration of outer space shall be done to benefit all countries and shall be free for exploration and use by all the States.

Outer space

Outer space, or just space, is the void that exists between celestial bodies, including the Earth. It is not completely empty, but consists of a hard vacuum containing a low density of particles, predominantly a plasma of hydrogen and helium as well as electromagnetic radiation, magnetic fields, neutrinos, dust and cosmic rays. The baseline temperature, as set by the background radiation from the Big Bang, is 2.7 kelvins (K) (−270.45 °C; −454.81 °F). Plasma with a number density of less than one hydrogen atom per cubic metre and a temperature of millions of kelvins in the space between galaxies accounts for most of the baryonic (ordinary) matter in outer space; local concentrations have condensed into stars and galaxies. In most galaxies, observations provide evidence that 90% of the mass is in an unknown form, called dark matter, which interacts with other matter through gravitational but not electromagnetic forces. Data indicates that the majority of the mass-energy in the observable universe is a poorly understood vacuum energy of space which astronomers label dark energy. Intergalactic space takes up most of the volume of the Universe, but even galaxies and star systems consist almost entirely of empty space.

Out(Fn)

In mathematics, Out(F_n) is the outer automorphism group of a free group on n generators. These groups play an important role in geometric group theory.

Outer space

Out(F_n) acts geometrically on a cell complex known as Culler–Vogtmann Outer space, which can be thought of as the Teichmüller space for a bouquet of circles.

Definition

A point of the outer space is essentially an R-graph X homotopy equivalent to a bouquet of n circles together with a certain choice of a free homotopy class of a homotopy equivalence from X to the Bouquet of n circles. An R-graph is just a weighted Graph with weights in R. The sum of all weights should be 1 and all weights should be positive. To avoid ambiguity (and to get a finite dimensional space) it is furthermore required that the valency of each vertex should be at least 2.

A more descriptive view avoiding the homotopy equivalence f is the following. We may fix an identification of the fundamental group of the bouquet of n circles with the free group F_n in n variables. Furthermore we may choose a maximal tree in X and choose for each remaining edge a direction. We will now assign to each remaining edge e a word in F_n in the following way. Consider the closed path starting with e and then going back to the origin of e in the maximal tree. Composing this path with f we get a closed path in a bouquet of n circles and hence an element in its fundamental group F_n. This element is not well defined; if we change f by a free homotopy we obtain another element. It turns out, that those two elements are conjugate to each other, and hence we can choose the unique cyclically reduced element in this conjugacy class. It is possible to reconstruct the free homotopy type of f from these data. This view has the advantage, that it avoids the extra choice of f and has the disadvantage that additional ambiguity arises, because one has to choose a maximal tree and an orientation of the remaining edges.

Outer space (disambiguation)

Outer space comprises the relatively empty regions of the universe outside the atmospheres of celestial bodies.

Outer space may also refer to:

See also