In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.
A flyby (/ˈflaɪbaɪ/) is a spaceflight operation in which a spacecraft passes in proximity to another body, usually a target of its space exploration mission and/or a source of a gravity assist (also called swing-by) to impel it towards another target. Spacecraft which are specifically designed for this purpose are known as flyby spacecraft, although the term has also been used in regard to asteroid flybys of Earth for example. Important parameters are the time and distance of closest approach.
The Space Race (Russian: космическая гонка, romanized: kosmicheskaya gonka, IPA: [kɐsˈmʲitɕɪskəjə ˈɡonkə]) was a 20th-century competition between the Cold War rivals, the United States and the Soviet Union, to achieve superior spaceflight capability. It had its origins in the ballistic missile-based nuclear arms race between the two nations following World War II and the onset of the Cold War. The technological advantage demonstrated by spaceflight achievement was seen as necessary for national security, particularly in regard to intercontinental ballistic missile and satellite reconnaissance capability, but also became part of the cultural symbolism and ideology of the time. The Space Race brought pioneering launches of artificial satellites, robotic landers to the Moon, Venus, and Mars, and human spaceflight in low Earth orbit and ultimately to the Moon.
Public interest in space travel originated in the 1951 publication of a Soviet youth magazine and was promptly picked up by US magazines. The competition began on July 29, 1955, when the United States announced its intent to launch artificial satellites for the International Geophysical Year. Five days later, the Soviet Union responded by declaring they would also launch a satellite "in the near future". The launching of satellites was enabled by developments in ballistic missile capabilities since the end of World War II. The competition gained Western public attention with the "Sputnik crisis", when the USSR achieved the first successful satellite launch, Sputnik 1, on October 4, 1957. It gained momentum when the USSR sent the first human, Yuri Gagarin, into space with the orbital flight of Vostok 1 on April 12, 1961. These were followed by a string of other firsts achieved by the Soviets over the next few years.
Flight or flying is the motion of an object through an atmosphere or through the vacuum of space, in this case also called spaceflight, without contacting any planetary surface. This can be achieved by generating aerodynamic lift associated with gliding or propulsive thrust, aerostatically using buoyancy, or by ballistic movement.
Many things can fly, from animal aviators such as birds, bats and insects, to natural gliders/parachuters such as patagial animals, anemochorous seeds and ballistospores, to human inventions like aircraft (airplanes, helicopters, airships, balloons, etc.) and rockets which may propel spacecraft and spaceplanes.
Astronautics (or cosmonautics) is the practice of sending spacecraft beyond Earth's atmosphere into outer space. Spaceflight is one of its main applications and space science is its overarching field.
The term astronautics (originally astronautique in French) was coined in the 1920s by J.-H. Rosny, president of the Goncourt academy, in analogy with aeronautics. Because there is a degree of technical overlap between the two fields, the term aerospace is often used to describe both at once. In 1930, Robert Esnault-Pelterie published the first book on the new research field.
Human spaceflight (also referred to as crewed spaceflight, or more historically manned spaceflight) is spaceflight with a crew or passengers aboard a spacecraft, often with the spacecraft being operated directly by the onboard human crew. Spacecraft can also be remotely operated from ground stations on Earth, or autonomously, without any direct human involvement. People trained for spaceflight are called astronauts (American or other), cosmonauts (Russian), or taikonauts (Chinese); and non-professionals are referred to as spaceflight participants or spacefarers.
The first human in space was Soviet cosmonaut Yuri Gagarin, who launched as part of the Soviet Union's Vostok program on 12 April 1961 at the beginning of the Space Race. On 5 May 1961, Alan Shepard became the first American in space, as part of Project Mercury. Humans traveled to the Moon nine times between 1968 and 1972 as part of the United States' Apollo program, and have had a continuous presence in space for 25 years and 30 days on the International Space Station (ISS). On 15 October 2003, the first Chinese taikonaut, Yang Liwei, went to space as part of Shenzhou 5, the first Chinese human spaceflight. As of December 2025, humans have not traveled beyond low Earth orbit since the Apollo 17 lunar mission in December 1972.
Interplanetary spaceflight or interplanetary travel is spaceflight (crewed or uncrewed) between bodies within a single planetary system. Spaceflights become interplanetary by accelerating spacecrafts beyond orbital speed, reaching escape velocity relative to Earth at 11.2 km/s, entering heliocentric orbit, possibly accelerating further, often by performing gravity assist flybys at Earth and other planets. Most of today's spaceflight remains Earth bound, with much less being interplanetary, all of which performed by uncrewed spacecrafts, and only just a few spaceflights having accelerated beyond, to system escape velocity, eventually performing interstellar spaceflight.
Uncrewed space probes have flown to all the observed planets in the Solar System as well as to dwarf planets Pluto and Ceres, and several asteroids. Orbiters and landers return more information than fly-by missions. Crewed flights have landed on the Moon and have been planned, from time to time, for Mars, Venus and Mercury. While many scientists appreciate the knowledge value that uncrewed flights provide, the value of crewed missions is more controversial. Science fiction writers propose a number of benefits, including the mining of asteroids, access to solar power, and room for colonization in the event of an Earth catastrophe.
A spaceplane is a vehicle that can fly and glide as an aircraft in Earth's atmosphere and function as a spacecraft in outer space. To do so, spaceplanes must incorporate features of both aircraft and spacecraft. Orbital spaceplanes tend to be more similar to conventional spacecraft, while sub-orbital spaceplanes tend to be more similar to fixed-wing aircraft. All spaceplanes as of 2024 have been rocket-powered for takeoff and climb, but have then landed as unpowered gliders.
Four examples of spaceplanes have successfully launched to orbit, reentered Earth's atmosphere, and landed: the U.S. Space Shuttle, Russian Buran, U.S. X-37, and the Chinese Shenlong. Another, Dream Chaser, is under development in the U.S. As of 2024 all past and current orbital spaceplanes launch vertically; some are carried as a payload in a conventional fairing, while the Space Shuttle used its own engines with the assistance of boosters and an external tank. Orbital spaceflight takes place at high velocities, with orbital kinetic energies typically greater than suborbital trajectories. This kinetic energy is shed as heat during re-entry. Many more spaceplanes have been proposed.
A sub-orbital spaceflight is a spaceflight in which the spacecraft reaches outer space, but its trajectory intersects the surface of the gravitating body from which it was launched. Hence, it will not complete one orbital revolution, will not become an artificial satellite nor will it reach escape velocity.
For example, the path of an object launched from Earth that reaches the Kármán line (about 83 km [52 mi] – 100 km [62 mi] above sea level), and then falls back to Earth, is considered a sub-orbital spaceflight. Some sub-orbital flights have been undertaken to test spacecraft and launch vehicles later intended for orbital spaceflight. Other vehicles are specifically designed only for sub-orbital flight; examples include crewed vehicles, such as the X-15 and SpaceShipTwo, and uncrewed ones, such as ICBMs and sounding rockets.
An orbital spaceflight (or orbital flight) is a spaceflight in which a spacecraft is placed on a trajectory where it could remain in space for at least one orbit. To do this around the Earth, it must be on a free trajectory which has an altitude at perigee (altitude at closest approach) around 80 kilometers (50 mi); this is the boundary of space as defined by NASA, the US Air Force and the FAA. To remain in orbit at this altitude requires an orbital speed of ~7.8 km/s. Orbital speed is slower for higher orbits, but attaining them requires greater delta-v. The Fédération Aéronautique Internationale has established the Kármán line at an altitude of 100 km (62 mi) as a working definition for the boundary between aeronautics and astronautics. This is used because at an altitude of about 100 km (62 mi), as Theodore von Kármán calculated, a vehicle would have to travel faster than orbital velocity to derive sufficient aerodynamic lift from the atmosphere to support itself.
Due to atmospheric drag, the lowest altitude at which an object in a circular orbit can complete at least one full revolution without propulsion is approximately 150 kilometres (93 mi).