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Asteroid impact avoidance

Asteroid impact avoidance encompasses 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 km 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.

While the chances of a major collision are low in the near term, it is a near-certainty that one will happen eventually unless defensive measures are taken. Astronomical events—such as the Shoemaker-Levy 9 impacts on Jupiter and the 2013 Chelyabinsk meteor, along with the growing number of near-Earth objects discovered and catalogued on the Sentry Risk Table—have drawn renewed attention to such threats. The popularity of the 2021 movie Don't Look Up helped to raise awareness of the possibility of avoiding NEOs.

In 2016, a NASA scientist warned that the Earth is unprepared for such an event. In April 2018, the B612 Foundation reported "It's 100 percent certain we'll be hit by a devastating asteroid, but we're not 100 percent sure when." Also in 2018, physicist Stephen Hawking, in his final book, Brief Answers to the Big Questions, considered an asteroid collision to be the biggest threat to the planet. Several ways of avoiding an asteroid impact have been described. Nonetheless, in March 2019, scientists reported that asteroids may be much more difficult to destroy than thought earlier. In addition, an asteroid may reassemble itself due to gravity after being disrupted. In May 2021, NASA astronomers reported that 5 to 10 years of preparation may be needed to avoid a virtual impactor based on a simulated exercise conducted by the 2021 Planetary Defense Conference.

In 2022, NASA spacecraft DART impacted Dimorphos, reducing the minor-planet moon's orbital period by 32 minutes. This mission constitutes the first successful attempt at asteroid deflection. In 2025, CNSA plans to launch another deflection mission to near-Earth object 2019 VL5, a 30-meter-wide (100 ft.) asteroid, which will include both an impactor and observer spacecraft.

Deflection efforts

According to expert testimony in the United States Congress in 2013, NASA would require at least five years of preparation before a mission to intercept an asteroid could be launched. In June 2018, the US National Science and Technology Council warned that the United States was unprepared for an asteroid impact event, and developed and released the "National Near-Earth Object Preparedness Strategy Action Plan" to better prepare.

Most deflection efforts for a large object require from a year to decades of warning, allowing time to prepare and carry out a collision avoidance project, as no known planetary defense hardware has yet been developed. It has been estimated that a velocity change of just .035 m/s ÷ t (where t is the number of years until potential impact) is needed to successfully deflect a body on a direct collision trajectory. Thus for a large number of years before impact, much smaller velocity changes are needed. For example, it was estimated there was a high chance of 99942 Apophis swinging by Earth in 2029 with a 10−4 probability of returning on an impact trajectory in 2035 or 2036. It was then determined that a deflection from this potential return trajectory, several years before the swing-by, could be achieved with a velocity change on the order of 10−6 m/s.

NASA's Double Asteroid Redirection Test (DART), the world's first full-scale mission to test technology for defending Earth against potential asteroid or comet hazards, launched on a SpaceX Falcon 9 rocket from Space Launch Complex 4 East at Vandenberg Space Force Base in California.

An impact by a 10 km asteroid on the Earth has historically caused an extinction-level event due to catastrophic damage to the biosphere. There is also the threat from comets entering the inner Solar System. The impact speed of a long-period comet would likely be several times greater than that of a near-Earth asteroid, making its impact much more destructive; in addition, the warning time is unlikely to be more than a few months. Impacts from objects as small as 50 m in diameter, which are far more common, are historically extremely destructive regionally (see Barringer crater).

Finding out the material composition of the object is also helpful before deciding which strategy is appropriate. Missions like the 2005 Deep Impact probe and the Rosetta spacecraft, have provided valuable information on what to expect. In October 2022, a method of mapping the insides of a potentially problematic asteroid in order to determine the best area for impact was proposed.

History of US government mandates
Efforts in asteroid impact prediction have concentrated on the survey method. The 1992 NASA-sponsored Near-Earth-Object Interception Workshop hosted by Los Alamos National Laboratory evaluated issues involved in intercepting celestial objects that could hit Earth. In a 1992 report to NASA, a coordinated Spaceguard Survey was recommended to discover, verify and provide follow-up observations for Earth-crossing asteroids. This survey was expected to discover 90% of these objects larger than one kilometer within 25 years. Three years later, another NASA report recommended search surveys that would discover 60–70% of short-period, near-Earth objects larger than one kilometer within ten years and obtain 90% completeness within five more years.

In 1998, NASA formally embraced the goal of finding and cataloging, by 2008, 90% of all near-Earth objects (NEOs) with diameters of 1 km or larger that could represent a collision risk to Earth. The 1 km diameter metric was chosen after considerable study indicated that an impact of an object smaller than 1 km could cause significant local or regional damage but is unlikely to cause a worldwide catastrophe. The impact of an object much larger than 1 km diameter could well result in worldwide damage up to, and potentially including, extinction of the human species. The NASA commitment has resulted in the funding of a number of NEO search efforts, which made considerable progress toward the 90% goal by 2008. However the 2009 discovery of several NEOs approximately 2 to 3 kilometers in diameter (e.g., , , and ) demonstrated there were still large objects to be detected.

United States Representative George E. Brown Jr. (D-CA) was quoted as voicing his support for planetary defense projects in Air & Space Power Chronicles, saying "If some day in the future we discover well in advance that an asteroid that is big enough to cause a mass extinction is going to hit the Earth, and then we alter the course of that asteroid so that it does not hit us, it will be one of the most important accomplishments in all of human history."

Because of Congressman Brown's long-standing commitment to planetary defense, a U.S. House of Representatives' bill, H.R. 1022, was named in his honor: The George E. Brown, Jr. Near-Earth Object Survey Act. This bill "to provide for a Near-Earth Object Survey program to detect, track, catalogue, and characterize certain near-Earth asteroids and comets" was introduced in March 2005 by Rep. Dana Rohrabacher (R-CA). It was eventually rolled into S.1281, the NASA Authorization Act of 2005, passed by Congress on December 22, 2005, subsequently signed by the President, and stating in part:

"The U.S. Congress has declared that the general welfare and security of the United States require that the unique competence of NASA be directed to detecting, tracking, cataloguing, and characterizing near-Earth asteroids and comets in order to provide warning and mitigation of the potential hazard of such near-Earth objects to the Earth. The NASA Administrator shall plan, develop, and implement a Near-Earth Object Survey program to detect, track, catalogue, and characterize the physical characteristics of near- Earth objects equal to or greater than 140 meters in diameter in order to assess the threat of such near-Earth objects to the Earth. It shall be the goal of the Survey program to achieve 90% completion of its near-Earth object catalogue (based on statistically predicted populations of near-Earth objects) within 15 years after the date of enactment of this Act. The NASA Administrator shall transmit to Congress not later than 1 year after the date of enactment of this Act an initial report that provides the following: (A) An analysis of possible alternatives that NASA may employ to carry out the Survey program, including ground-based and space-based alternatives with technical descriptions. (B) A recommended option and proposed budget to carry out the Survey program pursuant to the recommended option. (C) Analysis of possible alternatives that NASA could employ to divert an object on a likely collision course with Earth."

The result of this directive was a report presented to Congress in early March 2007. This was an Analysis of Alternatives (AoA) study led by NASA's Program Analysis and Evaluation (PA&E) office with support from outside consultants, the Aerospace Corporation, NASA Langley Research Center (LaRC), and SAIC (amongst others).

See also Improving impact prediction.

Ongoing projects
The Minor Planet Center in Cambridge, Massachusetts has been cataloging the orbits of asteroids and comets since 1947. It has recently been joined by surveys that specialize in locating the near-Earth objects (NEO), many (as of early 2007) funded by NASA's Near Earth Object program office as part of their Spaceguard program. One of the best-known is LINEAR that began in 1996. By 2004 LINEAR was discovering tens of thousands of objects each year and accounting for 65% of all new asteroid detections. LINEAR uses two one-meter telescopes and one half-meter telescope based in New Mexico.

The Catalina Sky Survey (CSS) is conducted at the Steward Observatory's Catalina Station, located near Tucson, Arizona, in the United States. It uses two telescopes, a 1.5 m f/2 telescope on the peak of Mount Lemmon, and a 68 cm f/1.7 Schmidt telescope near Mount Bigelow (both in the Tucson, Arizona area). In 2005, CSS became the most prolific NEO survey surpassing Lincoln Near-Earth Asteroid Research (LINEAR) in total number of NEOs and potentially hazardous asteroids discovered each year since. CSS discovered 310 NEOs in 2005, 396 in 2006, 466 in 2007, and in 2008 564 NEOs were found.

Spacewatch, which uses a 90 cm telescope sited at the Kitt Peak Observatory in Arizona, updated with automatic pointing, imaging, and analysis equipment to search the skies for intruders, was set up in 1980 by Tom Gehrels and Robert S. McMillan of the Lunar and Planetary Laboratory of the University of Arizona in Tucson, and is now being operated by McMillan. The Spacewatch project has acquired a 1.8 m telescope, also at Kitt Peak, to hunt for NEOs, and has provided the old 90-centimeter telescope with an improved electronic imaging system with much greater resolution, improving its search capability.

Other near-Earth object tracking programs include Near-Earth Asteroid Tracking (NEAT), Lowell Observatory Near-Earth-Object Search (LONEOS), Campo Imperatore Near-Earth Object Survey (CINEOS), Japanese Spaceguard Association, and Asiago-DLR Asteroid Survey. Pan-STARRS completed telescope construction in 2010, and it is now actively observing.

The Asteroid Terrestrial-impact Last Alert System, now in operation, conducts frequent scans of the sky with a view to later-stage detection on the collision stretch of the asteroid orbit. Those would be much too late for deflection, but still in time for evacuation and preparation of the affected Earth region.

Another project, supported by the European Union, is NEOShield, which analyses realistic options for preventing the collision of a NEO with Earth. Their aim is to provide test mission designs for feasible NEO mitigation concepts. The project particularly emphasises on two aspects.

 * 1) The first one is the focus on technological development on essential techniques and instruments needed for guidance, navigation and control (GNC) in close vicinity of asteroids and comets. This will, for example, allow hitting such bodies with a high-velocity kinetic impactor spacecraft and observing them before, during and after a mitigation attempt, e.g., for orbit determination and monitoring.
 * 2) The second one focuses on refining Near Earth Object (NEO) characterisation. Moreover, NEOShield-2 will carry out astronomical observations of NEOs, to improve the understanding of their physical properties, concentrating on the smaller sizes of most concern for mitigation purposes, and to identify further objects suitable for missions for physical characterisation and NEO deflection demonstration.

"Spaceguard" is the name for these loosely affiliated programs, some of which receive NASA funding to meet a U.S. Congressional requirement to detect 90% of near-Earth asteroids over 1 km diameter by 2008. A 2003 NASA study of a follow-on program suggests spending US$250–450 million to detect 90% of all near-Earth asteroids 140 m and larger by 2028.

NEODyS is an online database of known NEOs.

Sentinel mission
The B612 Foundation is a private nonprofit foundation with headquarters in the United States, dedicated to protecting the Earth from asteroid strikes. It is led mainly by scientists, former astronauts and engineers from the Institute for Advanced Study, Southwest Research Institute, Stanford University, NASA and the space industry.

As a non-governmental organization it has conducted two lines of related research to help detect NEOs that could one day strike the Earth, and find the technological means to divert their path to avoid such collisions. The foundation's goal had been to design and build a privately financed asteroid-finding space telescope, Sentinel, which was to be launched in 2017–2018. However the project was cancelled in 2015. Had the Sentinel's infrared telescope been parked in an orbit similar to that of Venus, it would have helped identify threatening NEOs by cataloging 90% of those with diameters larger than 140 m, as well as surveying smaller Solar System objects.

Data gathered by Sentinel would have helped identify asteroids and other NEOs that pose a risk of collision with Earth, by being forwarded to scientific data-sharing networks, including NASA and academic institutions such as the Minor Planet Center. The foundation also proposes asteroid deflection of potentially dangerous NEOs by the use of gravity tractors to divert their trajectories away from Earth, a concept co-invented by the organization's CEO, physicist and former NASA astronaut Ed Lu.

Prospective projects
Orbit@home intends to provide distributed computing resources to optimize search strategy. On February 16, 2013, the project was halted due to lack of grant funding. However, on July 23, 2013, the orbit@home project was selected for funding by NASA's Near Earth Object Observation program and was to resume operations sometime in early 2014. As of July 13, 2018, the project is offline according to its website.

The Large Synoptic Survey Telescope, currently under construction, is expected to perform a comprehensive, high-resolution survey starting in the early 2020s.

Detection from space
On November 8, 2007, the House Committee on Science and Technology's Subcommittee on Space and Aeronautics held a hearing to examine the status of NASA's Near-Earth Object survey program. The prospect of using the Wide-field Infrared Survey Explorer was proposed by NASA officials.

WISE surveyed the sky in the infrared band at a very high sensitivity. Asteroids that absorb solar radiation can be observed through the infrared band. It was used to detect NEOs, in addition to performing its science goals. It is projected that WISE could detect 400 NEOs (roughly two percent of the estimated NEO population of interest) within the one-year mission.

NEOSSat, the Near Earth Object Surveillance Satellite, is a microsatellite launched in February 2013 by the Canadian Space Agency (CSA) that will hunt for NEOs in space. Furthermore Near-Earth Object WISE (NEOWISE), an extension of the WISE mission, started in September 2013 (in its second mission extension) to hunt asteroids and comets close to the orbit of Earth.

Deep Impact
Research published in the March 26, 2009 issue of the journal Nature, describes how scientists were able to identify an asteroid in space before it entered Earth's atmosphere, enabling computers to determine its area of origin in the Solar System as well as predict the arrival time and location on Earth of its shattered surviving parts. The four-meter-diameter asteroid, called 2008 TC3, was initially sighted by the automated Catalina Sky Survey telescope, on October 6, 2008. Computations correctly predicted that it would impact 19 hours after discovery and in the Nubian Desert of northern Sudan.

A number of potential threats have been identified, such as 99942 Apophis (previously known by its provisional designation ), which in 2004 temporarily had an impact probability of about 3% for the year 2029. Additional observations revised this probability down to zero.

Double Asteroid Redirection Test
On September 26, 2022 DART impacted Dimorphos, reducing the minor-planet moon's orbital period by 32 minutes. This mission was the first successful attempt at asteroid deflection.

2019 VL5 Asteroid Deflection Mission
In 2025, China's CNSA intends to launch a deflection mission to near-Earth object 2019 VL5, a 30-meter wide asteroid. The mission will launch on a Long March 3B rocket and carry both an impactor and observer spacecraft.

Impact probability calculation pattern
The ellipses in the diagram on the right show the predicted position of an example asteroid at closest Earth approach. At first, with only a few asteroid observations, the error ellipse is very large and includes the Earth. Further observations shrink the error ellipse, but it still includes the Earth. This raises the predicted impact probability, since the Earth now covers a larger fraction of the error region. Finally, yet more observations (often radar observations, or discovery of a previous sighting of the same asteroid on archival images) shrink the ellipse revealing that the Earth is outside the error region, and the impact probability is near zero.

For asteroids that are actually on track to hit Earth the predicted probability of impact continues to increase as more observations are made. This similar pattern makes it difficult to differentiate between asteroids that will only come close to Earth and those that will actually hit it. This in turn makes it difficult to decide when to raise an alarm as gaining more certainty takes time, which reduces time available to react to a predicted impact. However, raising the alarm too soon has the danger of causing a false alarm and creating a Boy Who Cried Wolf effect if the asteroid in fact misses Earth.

Collision avoidance strategies
Various collision avoidance techniques have different trade-offs with respect to metrics such as overall performance, cost, failure risks, operations, and technology readiness. There are various methods for changing the course of an asteroid/comet. These can be differentiated by various types of attributes such as the type of mitigation (deflection or fragmentation), energy source (kinetic, electromagnetic, gravitational, solar/thermal, or nuclear), and approach strategy (interception, rendezvous, or remote station).

Strategies fall into two basic sets: Fragmentation and delay. Fragmentation concentrates on rendering the impactor harmless by fragmenting it and scattering the fragments so that they miss the Earth or are small enough to burn up in the atmosphere. Delay exploits the fact that both the Earth and the impactor are in orbit. An impact occurs when both reach the same point in space at the same time, or more correctly when some point on Earth's surface intersects the impactor's orbit when the impactor arrives. Since the Earth is approximately 12,750 km in diameter and moves at approximately 30 km/s in its orbit, it travels a distance of one planetary diameter in about 425 seconds, or slightly over seven minutes. Delaying, or advancing the impactor's arrival by times of this magnitude can, depending on the exact geometry of the impact, cause it to miss the Earth.

Collision avoidance strategies can also be seen as either direct, or indirect and in how rapidly they transfer energy to the object. The direct methods, such as nuclear explosives, or kinetic impactors, rapidly intercept the bolide's path. Direct methods are preferred because they are generally less costly in time and money. Their effects may be immediate, thus saving precious time. These methods would work for short-notice and long-notice threats, and are most effective against solid objects that can be directly pushed, but in the case of kinetic impactors, they are not very effective against large loosely aggregated rubble piles. Indirect methods, such as gravity tractors, attaching rockets or mass drivers, are much slower. They require traveling to the object, changing course up to 180 degrees for space rendezvous, and then taking much more time to change the asteroid's path just enough so it will miss Earth.

Many NEOs are thought to be "flying rubble piles" only loosely held together by gravity, and a typical spacecraft sized kinetic-impactor deflection attempt might just break up the object or fragment it without sufficiently adjusting its course. If an asteroid breaks into fragments, any fragment larger than 35 m across would not burn up in the atmosphere and itself could impact Earth. Tracking the thousands of buckshot-like fragments that could result from such an explosion would be a very daunting task, although fragmentation would be preferable to doing nothing and allowing the originally larger rubble body, which is analogous to a shot and wax slug, to impact the Earth.

In Cielo simulations conducted in 2011–2012, in which the rate and quantity of energy delivery were sufficiently high and matched to the size of the rubble pile, such as following a tailored nuclear explosion, results indicated that any asteroid fragments, created after the pulse of energy is delivered, would not pose a threat of re-coalescing (including for those with the shape of asteroid Itokawa) but instead would rapidly achieve escape velocity from their parent body (which for Itokawa is about 0.2 m/s) and therefore move out of an Earth-impact trajectory.

Nuclear explosive device

Initiating a nuclear explosive device above, on, or slightly beneath, the surface of a threatening celestial body is a potential deflection option, with the optimal detonation height dependent upon the composition and size of the object. It does not require the entire NEO to be vaporized to mitigate an impact threat. In the case of an inbound threat from a "rubble pile", the stand off, or detonation height above the surface configuration, has been put forth as a means to prevent the potential fracturing of the rubble pile. The energetic neutrons and soft X-rays released by the detonation, which do not appreciably penetrate matter, are converted into heat upon encountering the object's surface matter, ablatively vaporizing all line of sight exposed surface areas of the object to a shallow depth, turning the surface material it heats up into ejecta, and, analogous to the ejecta from a chemical rocket engine exhaust, changing the velocity, or "nudging", the object off course by the reaction, following Newton's third law, with ejecta going one way and the object being propelled in the other. Depending on the energy of the explosive device, the resulting rocket exhaust effect, created by the high velocity of the asteroid's vaporized mass ejecta, coupled with the object's small reduction in mass, would produce enough of a change in the object's orbit to make it miss the Earth.

A Hypervelocity Asteroid Mitigation Mission for Emergency Response (HAMMER) has been proposed. While there have been no updates as of 2023 regarding the HAMMER, NASA has published its regular Planetary Defense Strategy and Action Plan for 2023. In it, NASA acknowledges that it is crucial to continue studying the potential of nuclear energy in deflecting or destroying asteroids. This is because it is currently the only option for defense if scientists were not aware of the asteroid within a few months or years, depending on the asteroid's velocity. The report also notes there needs to be research done into the legal implications as well as policy implications on the topic.

Stand-off approach
If the object is very large but is still a loosely-held-together rubble pile, a solution is to detonate one or a series of nuclear explosive devices alongside the asteroid, at a 20 m or greater stand-off height above its surface, so as not to fracture the potentially loosely-held-together object. Providing that this stand-off strategy was done far enough in advance, the force from a sufficient number of nuclear blasts would alter the object's trajectory enough to avoid an impact, according to computer simulations and experimental evidence from meteorites exposed to the thermal X-ray pulses of the Z-machine.

In 1967, graduate students under Professor Paul Sandorff at the Massachusetts Institute of Technology were tasked with designing a method to prevent a hypothetical 18-month distant impact on Earth by the 1.4 km asteroid 1566 Icarus, an object that makes regular close approaches to Earth, sometimes as close as 16 lunar distances. To achieve the task within the timeframe and with limited material knowledge of the asteroid's composition, a variable stand-off system was conceived. This would have used a number of modified Saturn V rockets sent on interception courses and the creation of a handful of nuclear explosive devices in the 100-megaton energy range—coincidentally, the same as the maximum yield of the Soviets' Tsar Bomba would have been if a uranium tamper had been used—as each rocket vehicle's payload. The design study was later published as Project Icarus which served as the inspiration for the 1979 film Meteor.

A NASA analysis of deflection alternatives, conducted in 2007, stated:

"Nuclear standoff explosions are assessed to be 10–100 times more effective than the non-nuclear alternatives analyzed in this study. Other techniques involving the surface or subsurface use of nuclear explosives may be more efficient, but they run an increased risk of fracturing the target NEO. They also carry higher development and operations risks."

In the same year, NASA released a study where the asteroid Apophis (with a diameter of around 300 m) was assumed to have a much lower rubble pile density (1500 kg/m3) and therefore lower mass than it is now known to have, and in the study, it is assumed to be on an impact trajectory with Earth for the year 2029. Under these hypothetical conditions, the report determines that a "Cradle spacecraft" would be sufficient to deflect it from Earth impact. This conceptual spacecraft contains six B83 physics packages, each set for their maximum 1.2-megatonne yield, bundled together and lofted by an Ares V vehicle sometime in the 2020s, with each B83 being fuzed to detonate over the asteroid's surface at a height of 100 m ("1/3 of the objects diameter" as its stand-off), one after the other, with hour-long intervals between each detonation. The results of this study indicated that a single employment of this option "can deflect NEOs of [100-500 m diameter] two years before impact, and larger NEOs with at least five years warning". These effectiveness figures are considered to be "conservative" by its authors, and only the thermal X-ray output of the B83 devices was considered, while neutron heating was neglected for ease of calculation purposes.

Research published in 2021 pointed out the fact that for an effective deflection mission, there would need to be a significant amount of warning time, with the ideal being several years or more. The more warning time provided, the less energy will be necessary to divert the asteroid just enough to adjust the trajectory to avoid Earth. The study also emphasized that deflection, as opposed to destruction, can be a safer option, as there is a smaller likelihood of asteroid debris falling to Earth's surface. The researchers proposed the best way to divert an asteroid through deflection is adjusting the output of neutron energy in the nuclear explosion.

Surface and subsurface use

In 2011, the director of the Asteroid Deflection Research Center at Iowa State University, Dr. Bong Wie (who had published kinetic impactor deflection studies previously), began to study strategies that could deal with 50 to(-) objects when the time to Earth impact was less than one year. He concluded that to provide the required energy, a nuclear explosion or other event that could deliver the same power, are the only methods that can work against a very large asteroid within these time constraints.

This work resulted in the creation of a conceptual Hypervelocity Asteroid Intercept Vehicle (HAIV), which combines a kinetic impactor to create an initial crater for a follow-up subsurface nuclear detonation within that initial crater, which would generate a high degree of efficiency in the conversion of the nuclear energy that is released in the detonation into propulsion energy to the asteroid.

A similar proposal would use a surface-detonating nuclear device in place of the kinetic impactor to create the initial crater, then using the crater as a rocket nozzle to channel succeeding nuclear detonations.

Wie claimed the computer models he worked on showed the possibility for a 300-metre-wide (1,000 ft) asteroid to be destroyed using a single HAIV with a warning time of 30 days. Additionally, the models showed that less than 0.1% of debris from the asteroid would reach Earth's surface. However, there have been few substantial updates from Wie and his team since 2014 regarding the research.

As of 2015, Wie has collaborated with the Danish Emergency Asteroid Defence Project (EADP), which ultimately intends to crowdsource sufficient funds to design, build, and store a non-nuclear HAIV spacecraft as planetary insurance. For threatening asteroids too large and/or too close to Earth impact to effectively be deflected by the non-nuclear HAIV approach, nuclear explosive devices (with 5% of the explosive yield than those used for the stand-off strategy) are intended to be swapped in, under international oversight, when conditions arise that necessitate it.

A study published in 2020 pointed out that a non-nuclear kinetic impact becomes less effective the larger and closer the asteroid. However, researchers ran a model that suggested a nuclear detonation near the surface of an asteroid designed to cover one side of the asteroid with x-rays would be effective. When the x-rays cover one side of an asteroid in the program, they produce propulsion energy that would propel the asteroid in a preferred direction. The lead researcher with the study, Dave Dearborn, said a nuclear impact offered more flexibility than a non-nuclear approach, as the energy output can be adjusted specifically to the asteroid's size and location.

Comet deflection possibility

Following the 1994 Shoemaker-Levy 9 comet impacts with Jupiter, Edward Teller proposed, to a collective of U.S. and Russian ex-Cold War weapons designers in a 1995 planetary defense workshop meeting at Lawrence Livermore National Laboratory (LLNL), that they collaborate to design a one-gigaton nuclear explosive device, which would be equivalent to the kinetic energy of a 1 km asteroid. The theoretical one-gigaton device would weigh about 25–30 tons, light enough to be lifted on the Energia rocket. It could be used to instantaneously vaporize a one-kilometer asteroid, divert the paths of ELE-class asteroids (greater than 10 km in diameter) within short notice of a few months. With one year of notice, and at an interception location no closer than Jupiter, it could also deal with the even rarer short period comets that can come out of the Kuiper belt and transit past Earth orbit within two years. For comets of this class, with a maximum estimated diameter of 100 km, Chiron served as the hypothetical threat.

In 2013, the related National Laboratories of the US and Russia signed a deal that includes an intent to cooperate on defense from asteroids. The deal was meant to complement New START, but Russia suspended its participation in the treaty in 2023. As of April 2023, there has not been an official update from the White House or Moscow on how Russia's suspended participation will affect adjacent treaties.

Present capability
As of late 2022, the most likely and most effective method for asteroid deflection does not involve nuclear technology. Instead, it involves a kinetic impactor designed to redirect the asteroid, which showed promise in the NASA DART Mission. For nuclear technology, simulations have been run analyzing the possibility of using neutron energy put off by a nuclear device to redirect an asteroid. These simulations showed promise, with one study finding that increasing the neutron energy output had a notable effect on the angle of the asteroid's travel. However, there has not been a practical test studying the possibility as of April 2023.

Kinetic impact

The impact of a massive object, such as a spacecraft or even another near-Earth object, is another possible solution to a pending NEO impact. An object with a high mass close to the Earth could be sent out into a collision course with the asteroid, knocking it off course.

When the asteroid is still far from the Earth, a means of deflecting the asteroid is to directly alter its momentum by colliding a spacecraft with the asteroid. A NASA analysis of deflection alternatives, conducted in 2007, stated:

"Non-nuclear kinetic impactors are the most mature approach and could be used in some deflection/mitigation scenarios, especially for NEOs that consist of a single small, solid body."

This deviation method, which has been implemented by DART and, for a completely different purpose (analysis of the structure and composition of a comet), by NASA's Deep Impact space probe, involves launching a spacecraft against the near Earth object. The speed of the asteroid is modified due to the law of conservation of momentum:

M x V + M x V = (M + M) x V

with V velocity of the spacecraft, V velocity of the celestial body before impact, and V the velocity after impact. M and M respective mass of the spacecraft and of the celestial body. Velocities are vectors here.

The European Union's NEOShield-2 Mission is also primarily studying the Kinetic Impactor mitigation method. The principle of the kinetic impactor mitigation method is that the NEO or Asteroid is deflected following an impact from an impactor spacecraft. The principle of momentum transfer is used, as the impactor crashes into the NEO at a very high velocity of 10 km/s or more. The momentum of the impactor is transferred to the NEO, causing a change in velocity and therefore making it deviate from its course slightly.

As of mid-2021, the modified AIDA mission has been approved. The NASA Double Asteroid Redirection Test (DART) kinetic impactor spacecraft was launched in November 2021. The goal was to impact Dimorphos (nicknamed Didymoon), the 180 m minor-planet moon of near-Earth asteroid 65803 Didymos. The impact occurred in September 2022 when Didymos is relatively close to Earth, allowing Earth-based telescopes and planetary radar to observe the event. The result of the impact will be to change the orbital velocity and hence orbital period of Dimorphos, by a large enough amount that it can be measured from Earth. This will show for the first time that it is possible to change the orbit of a small 200 m asteroid, around the size most likely to require active mitigation in the future. The launch and use of the Double Asteroid Redirection Test system in March 2023 showed the world that asteroids could be safely redirected without the use of nuclear means. The success of this mission proved that kinetic methods of deflection are by far the best methods of asteroid deterrence.The second part of the AIDA mission–the ESA HERA spacecraft–has been approved by ESA member states in October 2019. It would reach the Didymos system in 2026 and measure both the mass of Dimorphos and the precise effect of the impact on that body, allowing much better extrapolation of the AIDA mission to other targets.

Asteroid gravity tractor
Another alternative to explosive deflection is to move the asteroid slowly over time. A small but constant amount of thrust accumulates to deviate an object sufficiently from its course. Edward T. Lu and Stanley G. Love have proposed using a massive uncrewed spacecraft hovering over an asteroid to gravitationally pull the asteroid into a non-threatening orbit. Though both objects are gravitationally pulled towards each other, the spacecraft can counter the force towards the asteroid by, for example, an ion thruster, so the net effect would be that the asteroid is accelerated towards the spacecraft and thus slightly deflected from its orbit. While slow, this method has the advantage of working irrespective of the asteroid's composition or spin rate; rubble pile asteroids would be difficult to deflect by means of nuclear detonations, while a pushing device would be difficult or inefficient to mount on a fast-rotating asteroid. A gravity tractor would likely have to spend several years beside the asteroid to be effective.

A NASA analysis of deflection alternatives, conducted in 2007, stated:

"'Slow push' mitigation techniques are the most expensive, have the lowest level of technical readiness, and their ability to both travel to and divert a threatening NEO would be limited unless mission durations of many years to decades are possible."

Ion beam shepherd
Another "contactless" asteroid deflection technique has been proposed by C. Bombardelli and J. Peláez from the Technical University of Madrid. The method involves the use of a low-divergence ion thruster pointed at the asteroid from a nearby hovering spacecraft. The momentum transmitted by the ions reaching the asteroid surface produces a slow but continuous force that can deflect the asteroid in a similar way as the gravity tractor, but with a lighter spacecraft.

Focused solar energy
H. J. Melosh with I. V. Nemchinov proposed deflecting an asteroid or comet by focusing solar energy onto its surface to create thrust from the resulting vaporization of material. This method would first require the construction of a space station with a system of large collecting, concave mirrors similar to those used in solar furnaces.

Orbit mitigation with highly concentrated sunlight is scalable to achieving the predetermined deflection within a year even for a global-threatening body without prolonged warning time.

Such a hastened strategy may become topical in the case of late detection of a potential hazard, and also, if required, in providing the possibility for some additional action. Conventional concave reflectors are practically inapplicable to the high-concentrating geometry in the case of a giant shadowing space target, which is located in front of the mirrored surface. This is primarily because of the dramatic spread of the mirrors' focal points on the target due to the optical aberration when the optical axis is not aligned with the Sun. On the other hand, the positioning of any collector at a distance to the target much larger than its size does not yield the required concentration level (and therefore temperature) due to the natural divergence of the sunrays. Such principal restrictions are inevitably at any location regarding the asteroid of one or many unshaded forward-reflecting collectors. Also, in the case of secondary mirrors use, similar to the ones found in Cassegrain telescopes, would be prone to heat damage by partially concentrated sunlight from primary mirror.

In order to remove the above restrictions, V.P. Vasylyev proposed to apply an alternative design of a mirrored collector – the ring-array concentrator. This type of collector has an underside lens-like position of its focal area that avoids shadowing of the collector by the target and minimizes the risk of its coating by ejected debris. Provided the sunlight concentration of approximately 5 × 103 times, a surface irradiance of around 4-5 MW/m2 leads to a thrusting effect of about 1000 N. Intensive ablation of the rotating asteroid surface under the focal spot will lead to the appearance of a deep "canyon", which can contribute to the formation of the escaping gas flow into a jet-like one. This may be sufficient to deflect a 0.5 km asteroid within several months and no addition warning period, only using ring-array collector size of about half of the asteroid's diameter. For such a prompt deflection of the larger NEOs, 1.3 to 2.2 km, the required collector sizes are comparable to the target diameter. In the case of a longer warning time, the required size of the collector may be significantly decreased.

Mass driver
A mass driver is an (automated) system on the asteroid to eject material into space, thus giving the object a slow steady push and decreasing its mass. A mass driver is designed to work as a very low specific impulse system, which in general uses a lot of propellant, but very little power. This essentially uses the asteroid against itself in order to divert a collision.

Modular Asteroid Deflection Mission Ejector Node, (MADMEN), is the idea of landing small unmanned vehicles such as space rovers to break up small portions of the asteroid. Using drills to break up small rocks and boulders from the surface, debris would eject from the surface very fast. Because there are no forces acting on the asteroid these rocks will push the asteroid off course at a very slow rate. This process takes time but could be very effective if implemented correctly. The idea is that when using local material as propellant, the amount of propellant is not as important as the amount of power, which is likely to be limited.

Conventional rocket engine
Attaching any spacecraft propulsion device would have a similar effect of giving a push, possibly forcing the asteroid onto a trajectory that takes it away from Earth. An in-space rocket engine that is capable of imparting an impulse of 106 N·s (E.g. adding 1 km/s to a 1000 kg vehicle), will have a relatively small effect on a relatively small asteroid that has a mass of roughly a million times more. Chapman, Durda, and Gold's white paper calculates deflections using existing chemical rockets delivered to the asteroid.

Such direct force rocket engines are typically proposed to use highly-efficient electrically powered spacecraft propulsion, such as ion thrusters or VASIMR.

Asteroid laser ablation
Similar to the effects of a nuclear device, it is thought possible to focus sufficient laser energy on the surface of an asteroid to cause flash vaporization / ablation to create either in impulse or to ablate away the asteroid mass. This concept, called asteroid laser ablation was articulated in the 1995 SpaceCast 2020 white paper "Preparing for Planetary Defense", and the 1996 Air Force 2025 white paper "Planetary Defense: Catastrophic Health Insurance for Planet Earth". Early publications include C. R. Phipps "ORION" concept from 1996, Colonel Jonathan W. Campbell's 2000 monograph "Using Lasers in Space: Laser Orbital Debris Removal and Asteroid Deflection", and NASA's 2005 concept Comet Asteroid Protection System (CAPS). Typically such systems require a significant amount of power, such as would be available from a Space-Based Solar Power Satellite.

Another proposal is the Phillip Lubin's DE-STAR proposal:

 * The DE-STAR project, proposed by researchers at the University of California, Santa Barbara, is a concept modular solar powered 1 μm, near infrared wavelength, laser array. The design calls for the array to eventually be approximately 1 km squared in size, with the modular design meaning that it could be launched in increments and assembled in space. In its early stages as a small array it could deal with smaller targets, assist solar sail probes and would also be useful in cleaning up space debris.

Other proposals

 * Wrapping the asteroid in a sheet of reflective plastic such as aluminized PET film as a solar sail
 * "Painting" or dusting the object with titanium dioxide (white) to alter its trajectory via increased reflected radiation pressure or with soot (black) to alter its trajectory via the Yarkovsky effect.
 * Planetary scientist Eugene Shoemaker in 1996 proposed deflecting a potential impactor by releasing a cloud of steam in the path of the object, hopefully gently slowing it. Nick Szabo in 1990 sketched a similar idea, "cometary aerobraking", the targeting of a comet or ice construct at an asteroid, then vaporizing the ice with nuclear explosives to form a temporary atmosphere in the path of the asteroid.
 * Coherent digger array multiple 1-ton flat tractors able to dig and expel asteroid soil mass as a coherent fountain array, coordinated fountain activity may propel and deflect over years.
 * Attaching a tether and ballast mass to the asteroid to alter its trajectory by changing its center of mass.
 * Magnetic flux compression to magnetically brake and or capture objects that contain a high percentage of meteoric iron by deploying a wide coil of wire in its orbital path and when it passes through, Inductance creates an electromagnet solenoid to be generated.

Deflection technology concerns
Carl Sagan, in his book Pale Blue Dot, expressed concern about deflection technology, noting that any method capable of deflecting impactors away from Earth could also be abused to divert non-threatening bodies toward the planet. Considering the history of genocidal political leaders and the possibility of the bureaucratic obscuring of any such project's true goals to most of its scientific participants, he judged the Earth at greater risk from a man-made impact than a natural one. Sagan instead suggested that deflection technology be developed only in an actual emergency situation.

All low-energy delivery deflection technologies have inherent fine control and steering capability, making it possible to add just the right amount of energy to steer an asteroid originally destined for a mere close approach toward a specific Earth target.

According to former NASA astronaut Rusty Schweickart, the gravitational tractor method is controversial because, during the process of changing an asteroid's trajectory, the point on the Earth where it could most likely hit would be slowly shifted across different countries. Thus, the threat for the entire planet would be minimized at the cost of some specific states' security. In Schweickart's opinion, choosing the way the asteroid should be "dragged" would be a tough diplomatic decision.

Analysis of the uncertainty involved in nuclear deflection shows that the ability to protect the planet does not imply the ability to target the planet. A nuclear explosion that changes an asteroid's velocity by 10 meters per second (plus or minus 20%) would be adequate to push it out of an Earth-impacting orbit. However, if the uncertainty of the velocity change was more than a few percent, there would be no chance of directing the asteroid to a particular target.

Additionally, there are legal concerns regarding the launch of nuclear technology into space. In 1992, the United Nations adopted a resolution that provides strict rules regarding sending nuclear technology to space, including preventing the contamination of space as well as protecting all citizens on Earth from potential fallout. As of 2022, the UN is still considering the safety and legal issues of launching nuclear powered items into outer space, particularly given the expanding field of space travel as more private organizations take part in the modern space race. The UN Committee on Peaceful Uses of Outer Space recently emphasized the point of the previous resolution, saying it is the responsibility of the member states to ensure the safety of everyone regarding nuclear power in space.

Planetary defense timeline

 * In their 1964 book, Islands in Space, Dandridge M. Cole and Donald W. Cox noted the dangers of planetoid impacts, both those occurring naturally and those that might be brought about with hostile intent. They argued for cataloging the minor planets and developing the technologies to land on, deflect, or even capture planetoids.
 * In 1967, students in the Aeronautics and Astronautics department at MIT did a design study, "Project Icarus", of a mission to prevent a hypothetical impact on Earth by asteroid 1566 Icarus. The design project was later published in a book by the MIT Press and received considerable publicity, for the first time bringing asteroid impact into the public eye.
 * In the 1980s NASA studied evidence of past strikes on planet Earth, and the risk of this happening at the current level of civilization. This led to a program that maps objects in the Solar System that both cross Earth's orbit and are large enough to cause serious damage if they hit.
 * In the 1990s, US Congress held hearings to consider the risks and what needed to be done about them. This led to a US$3 million annual budget for programs like Spaceguard and the near-Earth object program, as managed by NASA and USAF.
 * In 2005 a number of astronauts published an open letter through the Association of Space Explorers calling for a united push to develop strategies to protect Earth from the risk of a cosmic collision.
 * It is currently (as of late 2007) estimated that there are approximately 20,000 objects capable of crossing Earth's orbit and large enough (140 meters or larger) to warrant concern. On the average, one of these will collide with Earth every 5,000 years, unless preventive measures are undertaken. It was anticipated that by year 2008, 90% of such objects that are 1 km or more in diameter will have been identified and will be monitored. The further task of identifying and monitoring all such objects of 140m or greater was expected to be complete around 2020. By April 2018, astronomers have spotted more than 8,000 near-Earth asteroids that are at least 460 feet (140 meters) wide and it is estimated about 17,000 such near-Earth asteroids remain undetected. By 2019, the number of discovered near-Earth asteroids of all sizes totaled more than 19,000. An average of 30 new discoveries are added each week.
 * The Catalina Sky Survey (CSS) is one of NASA's four funded surveys to carry out a 1998 U.S. Congress mandate to find and catalog by the end of 2008, at least 90 percent of all near-Earth objects (NEOs) larger than 1 kilometer across. CSS discovered over 1150 NEOs in years 2005 to 2007. In doing this survey they discovered on November 20, 2007, an asteroid, designated 2007 WD5, which initially was estimated to have a chance of hitting Mars on January 30, 2008, but further observations during the following weeks allowed NASA to rule out an impact. NASA estimated a near miss by 26,000 km.
 * In January 2012, after a near pass-by of object 2012 BX34, a paper entitled "A Global Approach to Near-Earth Object Impact Threat Mitigation" was released by researchers from Russia, Germany, the United States, France, Britain, and Spain, which discusses the "NEOShield" project.
 * In November 2021, NASA launched a program with a different goal in terms of planetary defense. Many common methods previously in place were meant to completely destroy the asteroid. However, NASA and many others believed this method was far too unreliable so they funded the Double Asteroid Redirection Test or (DART) mission. This mission launched a small unmanned spacecraft to crash into the asteroid to break it up, or to deflect the rock away from Earth.
 * In January 2022, The NASA-funded Asteroid Terrestrial-impact Last Alert System (ATLAS)—a state-of-the-art asteroid detection system operated by the University of Hawaii (UH) Institute for Astronomy (IfA) for the agency's Planetary Defense Coordination Office (PDCO)—has reached a new milestone by becoming the first survey capable of searching the entire dark sky every 24 hours for near-Earth objects (NEOs) that could pose a future impact hazard to Earth. Now comprising four telescopes, ATLAS has expanded its reach to the southern hemisphere from the two existing northern-hemisphere telescopes on Haleakalā and Maunaloa in Hawai'i to include two additional observatories in South Africa and Chile.
 * As of March 1, 2023, we have proof from NASA that DART does indeed work. It was successful in both targeting and making contact with an asteroid moving at high speeds and, was successful in redirecting its course. This data showed that we can successfully move an asteroid with a diameter up to half a mile.

General bibliography

 * Luis Alvarez et al. 1980 paper in Science magazine on the great mass extinction 65 million years ago that led to the proliferation of mammal species such as the rise of the human race, thanks to asteroid-impact, a controversial theory in its day, now generally accepted.
 * Clark R. Chapman, Daniel D. Durda & Robert E. Gold (February 24, 2001) Impact Hazard, a Systems Approach, white paper on public policy issues associated with the impact hazard, at boulder.swri.edu
 * Donald W. Cox, and James H. Chestek. 1996. Doomsday Asteroid: Can We Survive? New York: Prometheus Books. ISBN 1-57392-066-5. (Note that despite its sensationalist title, this is a good treatment of the subject and includes a nice discussion of the collateral space development possibilities.)
 * Izzo, D., Bourdoux, A., Walker, R. and Ongaro, F.; "Optimal Trajectories for the Impulsive Deflection of NEOs"; Paper IAC-05-C1.5.06, 56th International Astronautical Congress, Fukuoka, Japan, (October 2005). Later published in Acta Astronautica, Vol. 59, No. 1-5, pp. 294–300, April 2006, available in esa.int – The first scientific paper proving that Apophis can be deflected by a small sized kinetic impactor.
 * David Morrison. "Is the Sky Falling?", Skeptical Inquirer 1997.
 * David Morrison, Alan W Harris, Geoff Summer, Clark R. Chapman, & Andrea Carusi Dealing with Impact Hazard, 2002 technical summary
 * Kunio M. Sayanagi. "How to Deflect an Asteroid". Ars Technica (April 2008).
 * Russell L. Schweickart, Edward T. Lu, Piet Hut and Clark R. Chapman; "The Asteroid Tugboat"; Scientific American (November 2003). Vol. 289, No. 5, pp. 54–61..
 * Russell L. Schweickart, Edward T. Lu, Piet Hut and Clark R. Chapman; "The Asteroid Tugboat"; Scientific American (November 2003). Vol. 289, No. 5, pp. 54–61..

 * Furfaro, Emily. NASA's DART Data Validates Kinetic Impact as Planetary Defense Method, NASA, 28 Feb. 2023,.

title: Asteroid impact avoidance


text:
Talk:Pigeonhole principle

Softball team section
The section points out that if you have 7 people who want to play softball, and there are only 4 teams, 1 team must have at least 2 of the 7 players. I don't understand the mathematics of the section, but it seems obvious that 5 people and 4 teams give the same result. Equivalently, if you have 7 players and 6 teams, one team must have 2 of the 7 players.

Perhaps I'm missing something here because of some ignorance about mathematics or softball, so I didn't feel competent to edit the page. TomClement (talk) 02:09, 8 March 2017 (UTC)

 * You aren't missing anything. The significance of this example lies in the fact that there is a formula which gives the correct conclusion. In the simpler cases that you mentioned, you don't need to rely on a formula since you can just reason it out and the answer is very obvious. With larger numbers you would need to put more effort into obtaining the correct conclusion. The 7-4 example is not as immediate as these others, but it is still small enough so that you can reason through the example and see why the formula is correct. --Bill Cherowitzo (talk) 05:11, 8 March 2017 (UTC)

 * If you don't need to rely on a formula for 5 players and 4 teams, then you certainly don't need a formula for 7 players and 4 teams, since it's trivial that 7 > 5. This section thoroughly confused me due the choice of 7/4.  Reading this talk page section, it seems as though the only purpose was to give a formula for a less trivial case.  If that's true, then perhaps it would be better to say it's true for 5, present the formula (even though it's obvious) and then extend the formula to 7 (even though it's obvious that 7 > 5).  Or perhaps, to show how the formula is derived for arbitrary numbers, and then using 7/4 as an example.  But as it stands, it's a real head-scratcher and detracts from the article rather than contributing to it. Learjeff (talk) 20:19, 6 August 2018 (UTC)

 * I think you are missing the point here. It is also true that 9 > 5 and 101 > 5 so you are claiming that you don't need a formula for these cases? The answers for 9 players and 4 teams is that some team must have at least 3 players, and in the other example some team must have at least 25 players. These results are not in any way related to the number 5. Actually, you don't need a formula for this in the same way that you don't need a formula to solve quadratic equations. You can always work it out. A formula is just a way of codifying this process, so that when the numbers change you don't have to go through all the steps again (those steps, if carried out with general rather than specific numbers, form the proof of the formula). The 7/4 example was chosen to illustrate that the formula works correctly. Smaller numbers would present no challenge to the formula's ability. --Bill Cherowitzo (talk) 21:22, 6 August 2018 (UTC)

On the evitability of hash table collisions
The pigeonhole principle arises in computer science. For example, collisions are inevitable in a hash table because the number of possible keys exceeds the number of indices in the array. A hashing algorithm, no matter how clever, cannot avoid these collisions. If the number of items stored in the hash table is less than the number of buckets, there need not be any collisions. If a perfect hash function is used (an algorithm that is exactly as clever as it needs to be), there are guaranteed to be no collisions. The number of possible keys is irrelevant; what matters is the actual number of items stored vs. the actual number of buckets -- and even that's assuming a hash table that does not dynamically resize.

I'd remove this example altogether because the caveats make it not very insightful. I hope someone with a name agrees. 82.95.254.249 (talk) 21:06, 2 November 2017 (UTC)

 * I agree and I have removed it. I think it was a good example, but it was worded incorrectly and unsourced.  If another editor wants to reinsert it, it should be reworded and cited.—Anita5192 (talk) 21:23, 2 November 2017 (UTC)

The way strong form of the pigeonhole principle is stated is unnecessarily complicated
I propose rewriting it as follows:

Let $q_{1}, q_{2}, ..., q_{n}$ be positive integers. If more than
 * $$q_1 + q_2 + \cdots + q_n$$

objects are distributed into $n$ boxes, then there exists a box $i$ that has more than $q_{i}$ objects. The simple form is obtained from this by taking $q_{i} = 1$ for $i = 1$ to $n$.

Misleading image
If you want yer actual pigeons, Trafalgar Square used to be full of them.

Those Columbidae in the article pic are doves. MinorProphet (talk) 17:31, 17 January 2021 (UTC)

Applications to Computer Engineering
I think it makes sense to discuss applications of the Pigeonhole principle to Computer Engineering because it comes up so often in memory management and allocation, but some editors disagree. CessnaMan1989 (talk) 16:54, 13 September 2021 (UTC)

Quantum mechanics section citation dates don't make sense
The article says that someone proposed that quantum mechanics violates the pigeonhole principle but that 'later' research has shown this might not be the case, but the citation on the proposal is 2016, and the two refutation sources are from 2014 and 2015 respectively. (Also, all of this is now six years out of date at the least, which is relatively large for a rapidly moving field like QM.) Seems like this needs revision? --Nerd1a4i (talk) 07:45, 7 April 2022 (UTC)

 * Yes! How about that article:
 * Photons suggest the weird quantum pigeonhole paradox is real | Science News
 * ?? :) 80.215.65.208 (talk) 11:21, 20 July 2022 (UTC)
 * https://www.sciencenews.org/article/quantum-pigeonhole-paradox-photons
 * Sorry.
 * It links to a more "scientific" article on pnas.org where one can read:
 * "In summary, we have implemented the quantum pigeonhole paradox by transmitting three single photons through two polarization channels, which demonstrates the pigeonhole paradox definitely at the level of individual quantum particles (31). The experiments show that in addition to the condition of well-defined pre- and postselected subensemble, noninvasive weak measurement is also required to observe the counting paradox. We implement the desired measurement indirectly by analyzing the measurement effects order by order and reveal the paradox will not survive under high-order measurement."
 * Creds to Ming-Cheng Chen, Chang Liu, Yi-Han Luo and Jian-Wei Pan (dating from end 2018, start 2019). 80.215.65.208 (talk) 11:54, 20 July 2022 (UTC)

\lfloor(n - 1)/m \rfloor + 1 = \lceil n/m\rceil is not true when n/m is integer
Second paragraph states "For arbitrary n and m this generalizes to k + 1 = \lfloor(n - 1)/m \rfloor + 1 = \lceil n/m\rceil ..." This is not true when n/m is integer. My sugestion is to replace by "For arbitrary n and m this generalizes to k + 1 = \lceil n/m\rceil ..."

Renato.carmo (talk) 15:58, 8 April 2022 (UTC)

In answer to both the Computer Engineering & Quantum mechanics topics above... and with some of txt of the topic "Why m > 0 is appropriate in the first line" in mind
Well when you think of it, real life violates the pigeonhole principle. Let's say I am blind and have a drawer with 50 thousand blue socks and 50 thousands black socks: do you really believe I will need to pull out only 3 to have a guaranteed pair of either black or blue socks? Assuming a uniform repartition of the 2 types in the drawer and that the color is the only difference between all those socks here. It's like saying in a class of 366 students (367 if taking leap years into account) it is guaranteed to find a pair with the same birthday: true for computer, false for real life unless some divinity has forcedly distributed all possible birthday dates without exception! Let us be careful with generalization and thus the examples we present. In clear text I strongly agree with the 2 first mentioned topics above. The third one about m>0 is interesting because it talks about what is implicit in the pigeonhole principle and those implicit rules are enough to understand that this principle is rarely usable in real life, outside of computer science. I am no expert in QR so will not judge the validity of the above statement but can intuitively imagine that it's not hard in physics to violate this principle as soon as someone fails to realize the implicit rules are not met. In a way I'm not talking about violation but misuse of the pigeonhole principle. 80.215.65.208 (talk) 11:16, 20 July 2022 (UTC)
 * Sorry, but your comment shows you don't really understand what the article is talking about. Referring to the sock example: if you pull three socks from the drawer, you will either have 3 blue socks, or 2 blue and 1 black, or 1 blue and 2 black, or 3 black; in any case, you will have a pair of two socks of the same color (although you can't know in advance if it'll be black or blue). I also don't know why do you think that the birthday example is "false for real life" -- unless you can somehow show us how 367 people can all have 367 different birthdays if there are only 366 possible birthdays. JudgeDeadd (talk) 12:25, 31 August 2022 (UTC)

Hairs and London.
Could someone explain the London example and the hair ? I feel like this makes sense from a syntactic sense and when you replace pigeonholes and pigeons with population and hairs, but in real life, I don’t think this would actually work like that, since you don’t put humans in pigeons, metaphors or not. Could somebody explain ? Kwikygoat (talk) 17:44, 28 April 2023 (UTC)

Edit : here’s what I struggle with and don’t really understand. If we assign a person to the pigeon hole corresponding to the numbers of hairs on its head, what tells me on the 1 000 000 than there won’t be 100 000 with 12 hairs in the column 12 and 900 000 with 100 hairs in the column 100 ? Still, there would be way more than 10 Londoners with the same amount of hairs (here 900 000). So why would we suppose there is supposed to be the same amount of people for every hair, that is 9 people have 1 hair, 9 have 2, 9 have 3, etc… — Preceding unsigned comment added by Kwikygoat (talk • contribs) 19:08, 28 April 2023 (UTC)

 * London currenly has a population of about 8,799,800 (and increasing). The number of hairs on a human head is not likely to exceed 150,000. Hence if the 8,799,800 people (pigeons) in London are "placed" (categorized) in 150,000 "pigeonholes" (categories), they cannot all be in separate categories. There must be at least one pigeonhole (category) with at least two people (in fact, many) placed in it. That is, there must be at least two people in London who have the same number of hairs on their heads.—Anita5192 (talk) 19:10, 30 April 2023 (UTC)

three gloves analogy
I don't like the three gloves analogy makes things more confusing if anything, the pigeonhole idea is already an analogy, i don't see the reason for an analogy ontop of another analogy. 2407:7000:986C:1300:A421:58E0:3174:9124 (talk) 01:25, 9 April 2024 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Pigeonhole principle


text:
Action figure

An action figure is a poseable character model figure made most commonly of plastic, and often based upon characters from a film, comic book, military, video game or television program; fictional or historical. These figures are usually marketed toward boys and adult collectors. The term was coined by Hasbro in 1964 to market G.I. Joe to boys (while competitors called similar offerings boy's dolls).

According to a 2005 study in Sweden, action figures which display traditional masculine traits primarily target boys. While most commonly marketed as a child's toy, the action figure has gained widespread acceptance as collector item for adults. In such a case, the item may be produced and designed on the assumption it will be bought solely for display as a collectible and not played with like a child's toy.

Precursors
Articulated dolls go back to at least 200 BCE, with articulated clay and wooden dolls of ancient Greece and Rome. Many types of articulated figures date to the early modern period, including the artists' mannequin and the Japanese ichimatsu doll. The modern ball-jointed doll was first created in Western Europe in the late 19th century. From the late 19th century through the early 20th century French and German manufacturers made bisque dolls with strung bodies articulated with ball-joints made of composition: a mix of pulp, sawdust, glue and similar materials. These dolls could measure between 15 and 100 cm and are now collectible antiques.

Besides the articulated doll, another important precursor to the action figure is the toy soldier. Military figures have been found in ancient Egyptian tombs, and have appeared in many cultures and eras. Tin soldiers were produced in Germany as early as the 1730s, by molding the metal between two pieces of slate. As industry and demand advanced, so did production methods, with hollow casting first being utilized in the 1890s and polyethylene figures becoming common by the 1950s. The toy soldier market, ubiquitous thanks to its history and mass-production methods, would therefore become a natural home for the military-themed action figure.

One of the earliest toys to bear resemblance to modern action figures is Albert Schoenhut's "Humpy Dumpty Circus", released in 1904, which featured articulated wooden figures interacting with various devices.

1960s–1970s
The term "action figure" was coined by Hasbro in 1964, to market their G.I. Joe figure to boys who refused to play with "dolls", a term primarily associated as a girl's toy. (A similar toy named Johnny Hero was introduced by Rosko Industries for Sears in 1965, but was known as a "Boy's Doll" since the term action figure had not gained widespread usage at that point.) G.I. Joe was initially a military-themed 11.5-inch figure proposed by marketing and toy idea-man Stan Weston. It featured changeable clothes with various uniforms to suit different purposes.

In a move that would create global popularity for this type of toy, Hasbro also licensed the product to companies in other markets. These different licensees had a combination of uniforms and accessories that were usually identical to the ones manufactured for the US market by Hasbro, along with some sets that were unique to the local market. The Japanese had at least two examples where a Hasbro licensee also issued sublicenses for related products. For example, Palitoy (in the UK) issued a sublicense to Tsukuda, a company in Japan, to manufacture and sell Palitoy's Action Man accessories in the Japanese market. Takara also issued a sublicense to Medicom for the manufacture of action figures.

Takara, still under license by Hasbro to make and sell G.I. Joe toys in Japan, also manufactured an action figure incorporating the licensed GI Joe torso for Henshin Cyborg-1, using transparent plastic revealing cyborg innards, and a chrome head and cyborg feet. During the oil supply crisis of the 1970s, like many other manufacturers of action figures, Takara was struggling with the costs associated with making the large $11 1/2$-inch figures, So, a smaller version of the cyborg toy was developed, standing at 3+3/4 in high, and was first sold in 1974 as Microman. The Microman line was also novel in its use of interchangeable parts. This laid the foundation for both the smaller action figure size and the transforming robot toy. Takara began producing characters in the Microman line with increasingly robotic features, including Robotman, a 12 in robot with room for a Microman pilot, and Mini-Robotman, a 3+3/4 in version of Robotman. These toys also featured interchangeable parts, with emphasis placed on the transformation and combination of the characters.

In 1971, Mego began licensing and making American Marvel and DC comic book superhero figures, which had highly successful sales and are considered highly collectible by many adults today. They eventually brought the Microman toy line to the United States as the Micronauts, but Mego eventually lost control of the market after losing the license to produce Star Wars toys to Kenner in 1976. The widespread success of Kenner's Star Wars 3+3/4 in toy line made the newer, smaller size figure with molded-on clothing the industry standard. Instead of a single character with outfits that changed for different applications, toy lines included teams of characters with special functions. Led by Star Wars-themed sales, collectible action figures quickly became a multimillion-dollar secondary business for movie studios.

From 1972 to 1986 there was a famous line of Big Jim action figures produced by Mattel.

1980s–1990s
The 1980s spawned all sorts of popular action figure lines, many based on cartoon series, which were one of the largest marketing tools for toy companies. Some of the most successful to come about were Masters of the Universe, G.I. Joe, Thundercats, The Real Ghostbusters and Super Powers Collection, to name just a few. Early in the decade, the burgeoning popularity of Japanese robot anime such as Gundam also encouraged Takara to reinvent the Microman line as the Micro Robots, moving from the cyborg action figure concept to the concept of the living robot. This led to the Micro Change line of toys: objects that could "transform" into robots. In 1984, Hasbro licensed Micro Change and another Takara line, the Diaclone transforming cars, and combined them in the US as the Transformers, spawning a still-continuing family of animated cartoons.

As the '80s were ending, more and more collectors started to surface, buying up the toys to keep in their original packaging for display purposes and for future collectability. This led to flooding of the action figure toy market. One of the most popular action figure lines of the late 1980s and early 1990s, Teenage Mutant Ninja Turtles action figures were produced in such high quantities that the value for most figures would never be higher than a few dollars. In the mid-1990s, a new Star Wars figure line had surfaced and Spawn figures flooded the toy store shelves, proving action figures were not just for kids anymore. Corinthian Figures of association football players were popular in England during this time. Beginning in 1997, ToyFare magazine would become a popular read for mature collectors in providing news and embracing nostalgia with a comedic twist. And with the gaining popularity of the Internet, websites such as Toy News International would soon offer information on upcoming collectible figures and merchandise.

It was during this time that popular characters were increasingly getting specialized costume and variant figures. Batman quickly became most notorious for this (i.e. Arctic Batman, Piranha Blade Batman, Neon Armor Batman). Rather than individual characters, these variants would make up the bulk of many action figure lines and often make use of the old figure and accessory molds. Glow-in-the-dark figures and accessories also became popular in the early '90s with lines like Toxic Crusaders and Swamp Thing.

A 1999 study found that "the figures have grown much more muscular over time, with many contemporary figures far exceeding the muscularity of even the largest human bodybuilders" and that the changing cultural expectations reflected by those changes may contribute to body image disorders in both sexes.

2000s onwards
The adult collector market for action figures expanded with companies such as McFarlane Toys, Palisades, and NECA. These companies have given numerous movie characters, musicians, and athletes their very first highly detailed figures. The Cinema of Fear action figures were sold together with plush dolls, "screen grab" dioramas, and limited edition toys based on New Line Cinema's horror franchise. These kinds of action figure are mainly intended as statuesque display pieces rather than toys. Child-oriented lines such as the Masters of the Universe revival and Justice League Unlimited, however, still evoke adult collector followings as well. Comic book firms are also able to get figures of their characters produced, regardless of whether or not they appeared in movies or animated cartoons. Examples of companies that produce comic figures and merchandise almost exclusively include Toy Biz and DC Direct.

Adult-oriented figure lines are often exclusive to specific chain stores rather than mass retail. Popular lines often have figures available exclusively through mail-in offers and comic conventions, which raises their value significantly. Ploys such as packaging "errors" and "short-packed" figures have also been used by toy companies to increase collector interest.

Raw materials
Modelling clay and various sculpting tools are used to create the prototype. The actual figure is molded from a harder plastic resin such as acrylonitrile butadiene styrene (ABS). Softer plastics and nylon may be used for costume components including body suits, capes, and face masks. Acrylic paints of various colors may be used to decorate the figure. More elaborate toys may contain miniature electronic components that provide light and sound effects.

Designs
Once the character has been selected, the actual design process begins with sketches of the proposed figure. The next step is the creation of a clay prototype, but other materials such as wax can also be used for the prototype. This model is made by bending aluminum wires to form the backbone of the figure, known as an armature. The wire form includes the outline of the arms and legs posed in the general stance that the figure will assume. The sculptor then adds clay to the armature to give the basic weight and shape that is desired. The clay may be baked slightly during the prototyping process to harden it. Then, the sculptor uses various tools, such as a wire loop, to carve the clay and shape details on the figure.

After creating the basic form, the sculptor may choose to remove the arms and work on them separately for later attachment. This gives the sculptor more control and allows him to produce finer details on the prototype. Working with blunt tools, the sculptor shapes the body with as much detail as is desired. During this process, photo and sketch references are used to ensure the figure is as realistic as possible. Some sculptors may even use human models to guide their design work.

After the general body shape is complete, the sculptor adds the finer details, paying close attention to the eyes, nose, and mouth that give the figure its lifelike expression. The designer may attach a rough lump of clay on the main figure as a temporary head while the real head is sculpted on a separate armature. This allows the sculptor to finish the figure's facial expressions independently of the body. At this point, the finished head can be attached to the main armature and joined to the body with additional clay. Once the head is attached, the neck and hair are sculpted to properly fit to the figure. Then, depending on the design of the figure, the costume may be sculpted directly onto the body. However, if a cloth costume or uniform will be added later, the prototype is sculpted without any costume details. During this process, parts of the clay may be covered with aluminum foil to keep it from prematurely drying out. Once everything is completed, the entire figure is baked to harden the clay.

The sculpted prototype is then sent for approval to the manufacturer. Once all design details have been finalized, the prototype is used to make the molds that will form the plastic pieces for the mass-produced figure. The entire sculpting process may take about two weeks, depending on the skill and speed of the sculptor. This process may be repeated several times if revisions must be made to the figure. Several months are typically allowed for this design phase.

Scale
Action Figures come in fixed scales to allow compatibility within (and sometimes between) toy ranges.

Articulation
A common feature among action figures is body articulation, often referred to as points of articulation (POA) or joints. The most basic forms of articulation include one neck joint, two shoulder joints, and two hip joints. Beyond these, rotating wrists, bending knees, and a swiveling waist are also common. Various terms have come into practice such as a "cut" joint, frequently used to allow a basic head rotation at the neck or arm rotation at the shoulder. The "T" joint at a figure's hips commonly allows up to 180° of front-to-back leg rotation; although, this may vary. Ball joints often allow more liberal movement than a cut, such as the figure's head being able to tilt in addition to a cut's strict vertical rotation. Basic knee articulation often relies on what is considered a pin joint.

The amount and style of figure articulation used by toy designers have varied over the years. Two of the most popular figure lines of the 1980s, G.I. Joe: A Real American Hero and Masters of the Universe, contrasted one another greatly in articulation; the former included several points in their small, 3+3/4 in scale while the bulkier latter remained minimal. Both, however, used methods involving rubber cords at the hips that are little used today. In the 2000s, Toy Biz's popular Marvel Legends line became known for its high rate of articulation, even boasting points at the abdomen, toes, and fingers.

Accessories
While not all action figures include accessories, the additional items often prove essential to characters and their effectiveness as interactive toys. Typical 3+3/4 in scale G.I. Joe figures include several intricately sculpted guns or hand weapons that can be fastened inside the figures' hands. Missile launchers are also commonplace in military and comic book figure lines and usually involve a spring-loaded mechanism. However, possibly due to safety concerns, this method saw a decline in the mid-1990s. Some figures, particularly of the Joker, have incorporated water-squirting weapons.

More recently, Marvel Legends has popularized the "build-a-figure" concept. Each figure of a particular series includes a body part to a larger-scaled figure. This encourages the consumer to purchase every figure of the given series, in order to complete the larger figure. The concept has spread into Mattel's DC Universe Classics. Figures intended to appeal to the collector market commonly include a display base and/or pack-in comic book. In such cases accessories may be designed more for display than play.

Types of packaging
Manufacturers have packaged their action figures in a number of ways.

Window Box packaging Window box packages consist of a sturdy, but somewhat thin cardboard box that allows for easy stacking. The box has colorful artwork to draw one's attention. The front of the box will have an area of the cardboard that is cut out and a thin piece of soft plastic then fills the cutout area. This ensures easy visibility of the action figure inside of the box. This type of packaging was used by companies such as Mego Corporation in the early 1970s until they switched to the Carded Bubble style of packaging in the mid to late 1970s. Window Box packaging is still used today, often for figures that measure 10" or taller in height.

Carded Bubble packaging This type of packaging consists of a sturdy piece of thin cardboard backing known as a "Card." The card is decorated with colorful artwork to draw consumer attention. The action figure is placed on the card and a bubble of clear plastic is then laid over the top of the action figure and attached to the card. The figure is then clearly visible to consumers. Often the bubble will have several small, fitted compartments to hold the figure and its accessories in place. Kenner and Hasbro's packaging of Star Wars action figures since 1977 are an example.

PVC packaging A more recent type of packaging that is common as of the 2000s decade is PVC packaging. With this type of packaging, the cardboard card is replaced by a clear PVC plastic backing. The front of the package is a different piece of PVC plastic that is molded to include a bubble that will house the action figure and all of its accessories. Any colorful artwork designed to help draw attention to the package will be printed on a thin piece of paper that is placed between these two pieces of PVC, or will be affixed in sticker form to the front piece of PVC. This type of packaging is popular today and can be seen being used by McFarlane Toys for their Movie Maniacs line of action figures beginning with Series V. Other companies that utilize this type of packaging are NECA/Reel Toys (National Entertainment Collectibles Association) with their Cult Classics and Pirates of the Caribbean line of figures, and Toy Biz with its Marvel Legends action figures, which included a comic book placed between the two PVC segments.

Tube packaging Another recent type of PVC packaging is a tube-shaped piece of PVC plastic surrounding the action figure. The tube may be cylindrical or oval in shape. Artwork on the package is often in the form of a sticker affixed to the outside of the PVC tube. This type of packaging has been used by Hasbro for their Star Wars Galactic Heroes line of figures.

Action features
Figures of the original Masters of the Universe line included many unique "action features": Battle Armor He-Man and Skeletor had rotating chest plates to represent varying degrees of damage; Leech featured suction cup limbs; Mantenna's eyes would pop out using a lever on his back; and Thunder Punch He-Man would thrust a punch and emit a loud bang from the ring cap in his backpack. Other features emphasized aesthetic rather than action, such as the flocked bodies of Grizzlor and Moss Man as well as the unique scents of the latter and Stinkor.

The success of the many Transformers lines has relied heavily on their signature feature of shifting from vehicle to robot. The popularity of this carried into Teenage Mutant Ninja Turtles' Mutatin' series among others.

In 1987, Mattel introduced figures for the television series Captain Power and the Soldiers of the Future. The line boasted an interactive game where children could shoot at the TV screen. However, while an ambitious concept, it was not a long-term success.

Glow-in-the-dark paint and plastic have been utilized in various figure collections, particularly those of the early '90s including Ninja Turtles, Swamp Thing, and Toxic Crusaders. Similarly, a color-changing feature has been demonstrated on some figures throughout the years. This concept involves dipping the character's head into cold water and revealing a temperature-sensitive paint. Examples include Kenner's Sky Escape Joker and Camouflage Swamp Thing, as well as Hasbro's Desert-Camo Sgt. Savage.

The majority of figures in Kenner's Super Powers Collection toted a punching action upon the squeezing together of their legs. In a more technically advanced method, the Ninja Turtles' Wacky Action series involved a wind-up gear that caused the motorized performance of certain actions like swimming legs or a rotating wrist. Two years prior also saw the release of Tyco's Dino-Riders, which featured battery powered, motorized dinosaurs.

title: Action figure


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Talk:C-47

There's probably no point in changing the redirect, but in filmmaking jargon a C-47 is a clothespin. --Brion 00:11 Jan 25, 2003 (UTC)

OK, you got me. I am dying of curiosity now! Please elucidate. Tannin

 * Well, they're used mainly for holding filters in place on lights, as general handy clips that, being made of wood, don't conduct heat and thus don't burn your hand off quite so much. ;) Why they're called C-47's is something of a mystery; that's the way of industry jargon. --Brion 00:49 Jan 25, 2003 (UTC)

 * I've edited the article to reflect the filmmaking jargon, eliminating the redirect, creating a disambiguation page and copying an article on the film equipment from http://wikifilmschool.com HamillianActor 14:03, 30 June 2006 (UTC)

 * The use in filmmaking is included in clothes-pin. I think it's more than reasonable that someone looking for C47 is looking for the Skytrain as much as they're looking for a clothes pin.  If the clothes-pin article gets so large that it seems inappropriate to include the filmmaking portion, then perhaps a C-47 article would be warranted... kmccoy (talk) 17:34, 30 June 2006 (UTC)
 * I didn't see the filmmaking section included in clothes-pin, so I suppose a separate article would be extraneous. However, I think I'm beginning to discover that I'm an inclusionist. =) HamillianActor 00:26, 2 July 2006 (UTC)

The clothespin got the nickname C-47 because, according to the legend, a film producer looking over a proposed budget for a film disallowed clothespins because he didn't think the crew needed them. The lighting crew resubmitted their budget with an entry for C-47. C-47 was the item number for clothespins in a catalog. —Preceding unsigned comment added by 24.20.77.198 (talk) 01:18, 15 November 2008 (UTC)

title: Talk:C-47