In celestial mechanics, the Lagrange points are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. Mathematically, this involves the solution of the restricted three-body problem.
The Jupiter trojans, commonly called trojan asteroids or simply trojans, are a large group of asteroids that share the planet Jupiter's orbit around the Sun. Relative to Jupiter, each trojan librates around one of Jupiter's stable Lagrange points: either L4, existing 60° ahead of the planet in its orbit, or L5, 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average semi-major axis of about 5.2 AU.
The Interplanetary Transport Network (ITN) is a collection of gravitationally determined pathways through the Solar System that require very little energy for an object to follow. The ITN makes particular use of Lagrange points as locations where trajectories through space can be redirected using little or no energy. These points have the peculiar property of allowing objects to orbit around them, despite lacking an object to orbit, as these points exist where gravitational forces between two celestial bodies are equal. While it would use little energy, transport along the network would take a long time.
In astrodynamics, orbital station-keeping is keeping a spacecraft at a fixed distance from another spacecraft or celestial body. It requires a series of orbital maneuvers made with thruster burns to keep the active craft in the same orbit as its target. For many low Earth orbit satellites, the effects of non-Keplerian forces, i.e. the deviations of the gravitational force of the Earth from that of a homogeneous sphere, gravitational forces from Sun/Moon, solar radiation pressure and air drag, must be counteracted. For spacecraft in a halo orbit around a Lagrange point, station-keeping is even more fundamental, as such an orbit is unstable; without an active control with thruster burns, the smallest deviation in position or velocity would result in the spacecraft leaving orbit completely.
The International Cometary Explorer (ICE) spacecraft, designed and launched as the International Sun-Earth Explorer-3 (ISEE-3) satellite, was launched on 12 August 1978 into a heliocentric orbit. It was one of three spacecraft, along with the mother/daughter pair of ISEE-1 and ISEE-2, built for the International Sun-Earth Explorer (ISEE) program, a joint effort by NASA and ESRO/ESA to study the interaction between the Earth's magnetic field and the solar wind.
The following outline is provided as an overview of and topical guide to space exploration.
In orbital mechanics, a Lissajous orbit, named after Jules Antoine Lissajous, is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point of a three-body system with minimal propulsion. Lyapunov orbits around a Lagrangian point are curved paths that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits include components in this plane and perpendicular to it, and follow a Lissajous curve. Halo orbits also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are usually not.
A halo orbit is a periodic, three-dimensional orbit associated with one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited by a Lissajous orbit or by a halo orbit. These can be thought of as resulting from an interaction between the gravitational pull of the two planetary bodies and the Coriolis and centrifugal force on a spacecraft. Halo orbits exist in any three-body system, e.g., a Sun–Earth–orbiting satellite system or an Earth–Moon–orbiting satellite system. Continuous "families" of both northern and southern halo orbits exist at each Lagrange point. Because halo orbits tend to be unstable, station-keeping using thrusters may be required to keep a satellite on the orbit.
An Earth trojan is an asteroid that orbits the Sun in the vicinity of the Earth–Sun Lagrange points L4 (leading 60°) or L5 (trailing 60°), thus having an orbit similar to Earth's. Only two Earth trojans have so far been discovered. The name "trojan" was first used in 1906 for the Jupiter trojans, the asteroids that were observed near the Lagrangian points of Jupiter's orbit.
Aditya-L1 is a coronagraphy spacecraft for studying the solar atmosphere, designed and developed by the Indian Space Research Organisation (ISRO) and various other Indian Space Research Institutes. It is orbiting at about 1.5 million km from Earth in a halo orbit around the Lagrange point 1 (L1) between the Earth and the Sun, where it will study the solar atmosphere, solar magnetic storms, and their impact on the environment around the Earth.
Chang'e 2 is a Chinese uncrewed lunar probe that was launched on 1 October 2010. It was a follow-up to the Chang'e 1 lunar probe, which was launched in 2007. Chang'e 2 was part of the first phase of the Chinese Lunar Exploration Program, and conducted research from a 100-km-high lunar orbit in preparation for the December 2013 soft landing by the Chang'e 3 lander and rover. Chang'e 2 was similar in design to Chang'e 1, although it featured some technical improvements, including a more advanced onboard camera. Like its predecessor, the probe was named after Chang'e, an ancient Chinese moon goddess.
(706765) 2010 TK7 (provisional designation 2010 TK7) is a sub-kilometer Near-Earth asteroid and the first Earth trojan discovered; it precedes Earth in its orbit around the Sun. Trojan objects are most easily conceived as orbiting at a Lagrangian point, a dynamically stable location (where the combined gravitational force acts through the Sun's and Earth's barycenter) 60 degrees ahead of or behind a massive orbiting body, in a type of 1:1 orbital resonance. In reality, they oscillate around such a point. Such objects had previously been observed in the orbits of Mars, Jupiter, Neptune, and the Saturnian moons Tethys and Dione.
A distant retrograde orbit (DRO), as most commonly conceived, is a spacecraft orbit around a moon that is highly stable because of its interactions with two Lagrange points (L1 and L2) of the planet–moon system.
EQUULEUS is a nanosatellite of the 6U CubeSat format that will measure the distribution of plasma that surrounds the Earth (plasmasphere) to help scientists understand the radiation environment in that region. It will also demonstrate low-thrust trajectory control techniques, such as multiple lunar flybys, within the Earth-Moon region using water steam as propellant. The spacecraft was designed and developed jointly by the Japan Aerospace Exploration Agency (JAXA) and the University of Tokyo.
In the year 2024, for the fourth year in a row, new world records in spaceflight were set for both orbital launch attempts and successful orbital launches. The year featured the successful maiden launches of Vulcan Centaur, Gravity-1, Long March 12, Ariane 6, and also more developmental launches of SpaceX's Starship, including its first ever landing on Flight 5. Additionally, the final launch of a Delta family rocket occurred in April with a IV Heavy variant. In May, the CNSA launched the Chang'e 6, which successfully completed the first sample return from the far side of the Moon. The Polaris Dawn mission conducted the first ever commercial spacewalk in September upon a Crew Dragon during an elliptic orbit.
Vigil, formerly known as Lagrange, is a space weather mission developed by the European Space Agency. The mission will provide the ESA Space Weather Office with instruments able to monitor the Sun, its solar corona and interplanetary medium between the Sun and Earth, to provide early warnings of increased solar activity, to identify and mitigate potential threats to society and ground, airborne and space based infrastructure as well as to allow 4 to 5 days space weather forecasts. To this purpose the Vigil mission will place for the first time a spacecraft at Sun-Earth Lagrange point 5 (L5) from where it would get a 'side' view of the Sun, observing regions of solar activity on the solar surface before they turn and face Earth.
