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On 14 March 2023, one of two intercepting Russian Su-27 fighters collided with an MQ-9 Reaper flying in international airspace over the Black Sea.US Air Force Gen. James Hecker, commander of the United States Air Forces in Europe – Air Forces Africa, stated, "At approximately 7:03 am (CET), one of the Russian Su-27 aircraft struck the propeller of the MQ-9, causing U.S. forces to have to ...
The 828-metre (2,717 ft) tall Burj Khalifa in Dubai has been the tallest building since 2010. The Burj Khalifa has been classified as megatall. A diagram showing the tallest buildings as of 2024 This is a list of the tallest buildings.Tall buildings, such as skyscrapers, are intended here as enclosed structures with continuously occupiable floors and a height of at least 340 metres (1,120 ft).
- Mathematical Description
- Solutions
- History
- Other Problems Involving Three Bodies
- N-Body Problem
- External Links
The mathematical statement of the three-body problem can be given in terms of the Newtonian equations of motion for vector positions r i = ( x i , y i , z i ) {\displaystyle \mathbf {r_{i}} =(x_{i},y_{i},z_{i})} of three gravitationally interacting bodies with masses m i {\displaystyle m_{i}} : where H {\displaystyle {\mathcal {H}}} is the Hamilton...
General solution
There is no general closed-form solution to the three-body problem.In other words, it does not have a general solution that can be expressed in terms of a finite number of standard mathematical operations. Moreover, the motion of three bodies is generally non-repeating, except in special cases. However, in 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists an analytic solution to the three-body problem in the form of a Puiseux series, specifically a power series in t...
Special-case solutions
In 1767, Leonhard Euler found three families of periodic solutions in which the three masses are collinear at each instant. See Euler's three-body problem. In 1772, Lagrange found a family of solutions in which the three masses form an equilateral triangle at each instant. Together with Euler's collinear solutions, these solutions form the central configurations for the three-body problem. These solutions are valid for any mass ratios, and the masses move on Keplerian ellipses. These four fam...
Numerical approaches
Using a computer, the problem may be solved to arbitrarily high precision using numerical integration although high precision requires a large amount of CPU time. There have been attempts of creating computer programs that numerically solve the three-body problem (and by extension, the n-body problem) involving both electromagnetic and gravitational interactions, and incorporating modern theories of physics such as special relativity. In addition, using the theory of random walks, an approxim...
The gravitational problem of three bodies in its traditional sense dates in substance from 1687, when Isaac Newton published his Philosophiæ Naturalis Principia Mathematica, when Newton was trying to figure out if any long term stability is possible, especially the system of our Earth, the Moon, and the Sun. He was guided under the major Renaissanc...
The term "three-body problem" is sometimes used in the more general sense to refer to any physical problem involving the interaction of three bodies. A quantum-mechanical analogue of the gravitational three-body problem in classical mechanics is the helium atom,in which a helium nucleus and two electrons interact according to the inverse-square Cou...
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details). Ho...
Chenciner, Alain (2007). "Three body problem". Scholarpedia. 2 (10): 2111. Bibcode:2007SchpJ...2.2111C. doi:10.4249/scholarpedia.2111.Lockheed Martin FB-22. The Lockheed Martin/Boeing F-22 Raptor is an American twin-engine all-weather stealth fighter aircraft developed and produced for the United States Air Force (USAF). As a product of the USAF's Advanced Tactical Fighter (ATF) program the aircraft was designed as an air superiority fighter, but also incorporates ground ...
The Internet of things (IoT) describes devices with sensors, processing ability, software and other technologies that connect and exchange data with other devices and systems over the Internet or other communications networks.[1][2][3][4][5] The Internet of things encompasses electronics, communication, and computer science engineering ...
The Maldives is the smallest country in Asia. Including the sea, the territory spans roughly 90,000 square kilometres (35,000 sq mi), and a land area of 298 square kilometres (115 sq mi). The Maldives is one of the world's most geographically dispersed sovereign states, and the smallest Muslim-majority country by land area.
The crucifixion of Jesus was the execution by crucifixion of Jesus of Nazareth in 1st-century Judaea, most likely in AD 30 or AD 33.It is described in the four canonical gospels, referred to in the New Testament epistles, attested to by other ancient sources, and is broadly accepted as one of the events most likely to have occurred during his life.
