Background
Due to observational inaccuracies, inaccuracies in the frame of reference stars, bias in the weighting of major observatories over smaller ones, and largely unknown non-gravitational forces on the asteroid, mainly the Yarkovsky effect, its position at the predicted time of encounter is uncertain in three dimensions. Typically, the region of probable positions is formed like a hair, thin and elongated, because visual observations yield 2-dimensional positions in the sky but no distances. If the region is not too extended, less than about one percent of the orbital radius, it may be represented as a 3-dimensional uncertainty ellipsoid and the orbits (ignoring the interaction) approximated as straight lines.
Now imagine a plane comoving with the planet and perpendicular to the incoming velocity of the asteroid (unperturbed by the interaction). This target plane is named b-plane after the collision parameter b, which is the distance of a point in the plane to the planet at its coordinate origin. Depending on a trajectory's position in the b-plane its post-encounter direction and kinetic energy is affected. The orbital energy is directly related to the length of the semi-major axis and also to the orbital period. If the post-encounter orbital period of the asteroid is a fractional multiple of the orbital period of the planet, there will be a close encounter at the same orbital position after the given numbers of orbits.
According to Ernst Öpik's theory of close encounters, the set of points in the b-plane leading to a given resonance ratio forms a circle. Lying on this circle are the planet and two gravitational keyholes, which are images of the planet in the b-plane of the future encounter (or rather of the slightly larger catchment area due to gravitational focusing). The form of the keyholes is a small circle elongated and bent along the circle for the given resonance ratio. The keyhole closest to the planet is smaller than the other, because the variation of deflection becomes steeper with decreasing collision parameter b.
High uncertainty affects calculation
Relevant keyholes are those close to the uncertainty ellipsoid projected onto the b-plane, where it becomes an elongated ellipse. The ellipse shrinks and jitters as new observations of the asteroid are added to the evaluation. If the probable path of the asteroid keeps close to a keyhole, the precise position of the keyhole itself would matter. It varies with the incoming direction and velocity of the asteroid and with the non-gravitational forces acting on it between the two encounters. Thus, “a miss is as good as a mile” does not apply to a keyhole of several hundred meters width. However, changing the path of an asteroid by a mile can be done with a relatively small impulse if the first encounter is still years away. Deflecting the asteroid after the fly-by would need a much stronger impulse.
For a rapidly rotating planet such as the Earth, calculation of trajectories passing close to it, less than a dozen radii, should include the oblateness of the planet—its gravitational field is not spherically symmetric. For even closer trajectories, gravity anomalies may be important.
For a large asteroid (or comet) passing close to the Roche limit, its size, which is inferred from its magnitude, affects not only the Roche limit but also the trajectory because the center of gravitational force on the body deviates from its center of mass resulting in a higher-order tidal force shifting the keyhole.
A near-Earth object (NEO) is any small Solar System body whose orbit brings it into proximity with Earth. By convention, a Solar System body is a NEO if its closest approach to the Sun (perihelion) is less than 1.3 astronomical units (AU). If a NEO's orbit crosses the Earth's orbit, and the object is larger than 140 meters (460 ft) across, it is considered a potentially hazardous object (PHO). Most known PHOs and NEOs are asteroids, but a small fraction are comets.
4179 Toutatis is an elongated, stony asteroid and slow rotator, classified as a near-Earth object and potentially hazardous asteroid of the Apollo asteroid and Alinda asteroid groups, approximately 2.5 kilometers in diameter. Discovered by French astronomer Christian Pollas at Caussols in 1989, the asteroid was named after Toutatis from Celtic mythology.
The Yarkovsky effect is a force acting on a rotating body in space caused by the anisotropic emission of thermal photons, which carry momentum. It is usually considered in relation to meteoroids or small asteroids, as its influence is most significant for these bodies.
A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.
(29075) 1950 DA, provisional designation 1950 DA, is a risk-listed asteroid, classified as a near-Earth object and potentially hazardous asteroid of the Apollo group, approximately 1.1 kilometers in diameter. It once had the highest known probability of impacting Earth. In 2002, it had the highest Palermo rating with a value of 0.17 for a possible collision in 2880. Since that time, the estimated risk has been updated several times. In December 2015, the odds of an Earth impact were revised to 1 in 8,300 (0.012%) with a Palermo rating of −1.42. As of 2022, It is listed on the Sentry Risk Table with the second highest cumulative Palermo rating of −2.05. 1950 DA is not assigned a Torino scale rating, because the 2880 date is over 100 years in the future.
Asteroid impact avoidance comprises the methods by which near-Earth objects (NEO) on a potential collision course with Earth could be diverted away, preventing destructive impact events. An impact by a sufficiently large asteroid or other NEOs would cause, depending on its impact location, massive tsunamis or multiple firestorms, and an impact winter caused by the sunlight-blocking effect of large quantities of pulverized rock dust and other debris placed into the stratosphere. A collision 66 million years ago between the Earth and an object approximately 10 kilometres wide is thought to have produced the Chicxulub crater and triggered the Cretaceous–Paleogene extinction event that is understood by the scientific community to have caused the extinction of all non-avian dinosaurs.
2002 AA29 (also written 2002 AA29) is a small near-Earth asteroid that was discovered on January 9, 2002 by the LINEAR (Lincoln Near Earth Asteroid Research) automatic sky survey. The diameter of the asteroid is only about 20–100 metres (70–300 ft). It revolves about the Sun on an almost circular orbit very similar to that of the Earth. This lies for the most part inside the Earth's orbit, which it crosses near the asteroid's furthest point from the Sun, the aphelion. Because of this orbit, the asteroid is classified as Aten type, named after the asteroid 2062 Aten.
99942 Apophis is a near-Earth asteroid and a potentially hazardous object with a diameter of 370 metres that caused a brief period of concern in December 2004 when initial observations indicated a probability up to 2.7% that it would hit Earth on April 13, 2029. Additional observations provided improved predictions that eliminated the possibility of an impact on Earth in 2029. Until 2006, a small probability nevertheless remained that, during its 2029 close encounter with Earth, Apophis would pass through a gravitational keyhole of no more than about 800 metres in diameter, which would have set up a future impact exactly seven years later on April 13, 2036. This possibility kept it at Level 1 on the Torino impact hazard scale until August 2006, when the probability that Apophis would pass through the keyhole was determined to be very small and Apophis' rating on the Torino scale was lowered to zero. By 2008, the keyhole had been determined to be less than 1 km wide. During the short time when it had been of greatest concern, Apophis set the record for highest rating ever on the Torino scale, reaching level 4 on December 27, 2004.
2006 RH120 is a tiny near-Earth asteroid and fast rotator with a diameter of approximately 2–3 meters that ordinarily orbits the Sun but makes close approaches to the Earth–Moon system around every twenty years, when it can temporarily enter Earth orbit through temporary satellite capture (TSC). Most recently, it was in Earth orbit from July 2006 to July 2007, during which time it was never more than 0.0116 AU (1.74 million km) from Earth. As a consequence of its temporary orbit around the Earth, it is currently the second smallest asteroid in the Solar System with a well-known orbit, after 2021 GM1. Until given a minor planet designation on 18 February 2008, the object was known as 6R10DB9, an internal identification number assigned by the Catalina Sky Survey.
2007 VK184 is a sub-kilometer asteroid, classified as a near-Earth object of the Apollo group, and estimated to be approximately 130 meters (430 ft) in diameter. It was listed on the Sentry Risk Table with a Torino Scale rating of 1 for a potential impactor in June 2048. It was removed from the Sentry Risk Table on 28 March 2014.
2007 WD5 is an Apollo asteroid some 50 m (160 ft) in diameter and a Mars-crosser asteroid first observed on 20 November 2007, by Andrea Boattini of the Catalina Sky Survey. Early observations of 2007 WD5 caused excitement amongst the scientific community when it was estimated as having as high as a 1 in 25 chance of colliding with Mars on 30 January 2008. However, by 9 January 2008, additional observations allowed NASA's Near Earth Object Program (NEOP) to reduce the uncertainty region resulting in only a 1-in-10,000 chance of impact. 2007 WD5 most likely passed Mars at a distance of 6.5 Mars radii. Due to this relatively small distance and the uncertainty level of the prior observations, the gravitational effects of Mars on its trajectory are unknown and, according to Steven Chesley of NASA's Jet Propulsion Laboratory Near-Earth Object program, 2007 WD5 is currently considered 'lost' (see lost asteroids).
A gravity tractor is a theoretical spacecraft that would deflect another object in space, typically a potentially hazardous asteroid that might impact Earth, without physically contacting it, using only its gravitational field to transmit the required impulse. The gravitational force of a nearby space vehicle, though small, is able to alter the path of a much larger asteroid if the vehicle spends enough time close to it; all that is required is that the vehicle thrust in a consistent direction relative to the asteroid's path, and that neither the vehicle nor its expelled reaction mass come in direct contact with the asteroid. The tractor spacecraft could either hover near the object being deflected, or orbit it, directing its exhaust perpendicular to the plane of the orbit.
The Nicemodel is a scenario for the dynamical evolution of the Solar System. It is named for the location of the Côte d'Azur Observatory—where it was initially developed in 2005—in Nice, France. It proposes the migration of the giant planets from an initial compact configuration into their present positions, long after the dissipation of the initial protoplanetary disk. In this way, it differs from earlier models of the Solar System's formation. This planetary migration is used in dynamical simulations of the Solar System to explain historical events including the Late Heavy Bombardment of the inner Solar System, the formation of the Oort cloud, and the existence of populations of small Solar System bodies such as the Kuiper belt, the Neptune and Jupiter trojans, and the numerous resonant trans-Neptunian objects dominated by Neptune.
D/1770 L1, popularly known as Lexell's Comet after its orbit computer Anders Johan Lexell, was a comet discovered by astronomer Charles Messier in June 1770. It is notable for having passed closer to Earth than any other comet in recorded history, approaching to a distance of only 0.015 astronomical units, or six times the distance from the Earth to the Moon. The comet has not been seen since 1770 and is considered a lost comet.
A minor planet is "lost" when today's observers cannot find it, because its location is too uncertain to target observations. This happens if the orbital elements of a minor planet are not known accurately enough, typically because the observation arc for the object is too short, or too few observations were made before the object became unobservable.
Minimum orbit intersection distance (MOID) is a measure used in astronomy to assess potential close approaches and collision risks between astronomical objects. It is defined as the distance between the closest points of the osculating orbits of two bodies. Of greatest interest is the risk of a collision with Earth. Earth MOID is often listed on comet and asteroid databases such as the JPL Small-Body Database. MOID values are also defined with respect to other bodies as well: Jupiter MOID, Venus MOID and so on.
367943 Duende (provisional designation 2012 DA14) is a micro-asteroid and a near-Earth object of the Aten and Atira group, approximately 30 meters (98 ft) in diameter. It was discovered by astronomers of the Astronomical Observatory of Mallorca at its robotic La Sagra Observatory in 2012, and named for the duende, a goblin-like creature from Iberian and Filipino mythology and folklore. Duende is likely an uncommon L-type asteroid and significantly elongated. For an asteroid of its size, it has a relatively long rotation period of 9.485 hours.
(410777) 2009 FD is a carbonaceous sub-kilometer asteroid and binary system, classified as near-Earth object and potentially hazardous asteroid of the Apollo group, discovered on 24 February 2009 by astronomers of the Spacewatch program at Kitt Peak National Observatory near Tucson, Arizona, in the United States.
Asteroid impact prediction is the prediction of the dates and times of asteroids impacting Earth, along with the locations and severities of the impacts.
