Scientists discover more than 600 new periodic orbits of the famous three body problemOctober 12, 2017
The famous three-body problem can be traced back to Isaac Newton in 1680s, thereafter Lagrange, Euler, Poincare and so on. Studies on the three-body problem leaded to the discovery of the so-called sensitivity dependence of initial condition (SDIC) of chaotic dynamic system. Nowadays, the chaotic dynamics is widely regarded as the third great scientific revolution in physics in 20th century, comparable to the relativity and the quantum mechanics. Thus, the studies on three-body problem have very important scientific meanings.
Poincare in 1890 revealed that trajectories of three-body systems are commonly non-periodic, i.e. not repeating. This can explain why it is so hard to gain periodic orbits of three-body system. In the 300 years since three-body problem was first recognized, only three families of periodic orbits had been found, until 2013 when Suvakov and Dmitrasinovic [Phys. Rev. Lett. 110, 114301 (2013)] made a breakthrough to numerically find 13 new distinct periodic orbits, which belong to 11 new families of Newtonian planar three-body problem with equal mass and zero angular momentum (see http://www.sciencemag.org/news/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem). Currently, two scientists, XiaoMing Li and ShiJun Liao at Shanghai Jiaotong University, China, successfully gained 695 families of periodic orbits of the above-mentioned Newtonian planar three-body system by means of national supercomputer TH-2 at Guangzhou, China, which are published online via SCIENCE CHINA-Physics Mechanics Astronomy, 2017, Vol. 60, No. 12: 129511. The movies of these orbits are given on the website http://numericaltank.sjtu.edu.cn/three-body/three-body.htm
These 695 periodic orbits include the well-known figure-eight family found by Moore in 1993, the 11 families found by Suvakov and Dmitrasinovic in 2013, and especially more than 600 new families that have never been reported. The two scientists used the so-called "Clean Numerical Simulation (CNS)", a new numerical strategy for reliable simulations of chaotic dynamic systems proposed by the second author in 2009, which is based on high enough order of Taylor series and multiple precision data with many enough significant digits, plus a convergence/reliability check. The CNS can reduce truncation error and round-off error so greatly that numerical noises are negligible in a long enough interval of time, thus more periodic orbits of the three-body system can be gained.
As pointed out by Montgomery in 1998, each periodic orbit in real space of the three-body system corresponds to a closed curve on the so-called "shape sphere", which is characterized by its topology using the so-called "free group element". The averaged period of an orbit is equal to the period of the orbit divided by the length of the corresponding free group element. These 695 families suggest that there should exist the quasi Kepler's third law: the square of the average period times the cube of the total kinetic and potential energy approximately equals to a constant. The generalized Kepler's third law reveals that the three-body system has something in common, which might deepen our understandings and enrich our knowledges about three-body system.
"The discovery of the more than 600 new periodic orbits is mainly due to the advance in computer science and the use of the new strategy of numerical simulation for chaotic dynamic systems, namely the CNS", spoke the two scientists. It should be emphasized that 243 more new periodic orbits of the three-body system are found by means of the CNS. In other words, if traditional algorithms in double precision were used, about 40% new periodic orbits would be lost. This indicates the novelty and originality of the Clean Numerical Simulation (CNS), since any new methods must bring something completely new/different.
As shown in Figure 1, many pictures of these newly-found periodic orbits of the three-body system are beautiful and elegant, like modern paintings. "We are shocked and captivated by the perfect of them", spoke the two scientists.
XiaoMing Li, and ShiJun Liao, More than six hundred new families of Newtonian periodic planar collisionless three-body orbits, Sci. China-Phys. Mech. Astron. 60, 129511 (2017), doi: 10.1007/s11433-017-9078-5 https://link.springer.com/article/10.1007%2Fs11433-017-9078-5
Science China Press
Related Orbit Articles:
Recently, a paper published in SCIENCE CHINA Information Sciences reviews the status and development of soft robotics and a conceptual design of configuration and manipulation of space soft robot is proposed.
An international team of astronomers has observed evidence of a star that whips around a black hole at a rate of nearly twice an hour.
Astronomers have found evidence of a star that whips around a likely black hole twice an hour.
Astronomers have found evidence for a star that whips around a black hole about twice an hour.
A Southwest Research Institute team successfully opened a 'failsafe' door on the Lyman-Alpha Mapping Project (LAMP) instrument in lunar orbit, improving the quality of ultraviolet (UV) data it collects.
A new research paper suggests that the impact that formed the moon also sent the Earth spinning much faster, and at a much steeper tilt, than it does today.
A joint team of the University of Science and Technology of China and the Peking University made breakthrough in quantum simulation of ultracold atoms.
Astronomers have directly detected a planet in a triple star system using imaging techniques.
Today, April 28, 5:01 Moscow time, the first launch from the Vostochny Cosmodrome took place.
New images from ALMA reveal never-before-seen details in the planet-forming disk around a nearby Sun-like star, including a tantalizing gap at the same distance from the star as the Earth is from the Sun.
Related Orbit Reading:
Orbit: A Novel
by John J. Nance (Author)
The year is 2009. For Kip Dawson, winning a passenger seat on American Space Adventure's spacecraft is a dream come true. One grand shot of insanity and he can return to earth fulfilled. But the thrill of the successful launch turns to terror when a micrometeorite penetrates the capsule, leaving the radios as dead as the pilot. Reality hits: Kip isn't going home. With nothing to do but wait for his doomed fate, Kip writes his epitaph on the ship's laptop computer, unaware that an audience of millions has discovered it and is tracking his every word on the Internet. As a massive struggle gets... View Details
Eccentric Orbits: The Iridium Story
by John Bloom (Author)
In the early 1990s, Motorola, the legendary American technology company developed a revolutionary satellite system called Iridium that promised to be its crowning achievement. Light years ahead of anything previously put into space, and built on technology developed for Ronald Reagan’s “Star Wars,” Iridium’s constellation of 66 satellites in polar orbit meant that no matter where you were on Earth, at least one satellite was always overhead, and you could call Tibet from Fiji without a delay and without your call ever touching a wire.
Iridium the satellite system was a... View Details
A Closed and Common Orbit (Wayfarers)
by Becky Chambers (Author)
A Publishers Weekly "Best Books of 2017" pick!
Nominated for the 2017 Hugo Award for Best Novel!
Shortlisted for the 2017 Arthur C. Clarke Award!
Winner of the Prix Julia-Verlanger!
Embark on an exciting, adventurous, and dangerous journey through the galaxy with the motley crew of the spaceship Wayfarer in this fun and heart-warming space opera—the sequel to the acclaimed The Long Way to a Small, Angry Planet.
Lovelace was once merely a ship’s artificial... View Details
Aliens: Dead Orbit
by James Stokoe (Author), James Stokoe (Illustrator)
After a horrific accident strikes a space station, an engineering officer must use all available tools--a timer, utility kit, and his wits--to survive an attack from the deadliest creature known to man. Collects issues #1-#4 of the thrilling and claustrophobic Aliens story: Dead Orbit, penned by Orc Stain creator James Stokoe! View Details
Modern Orbit Determination: Second Edition
by William E. Wiesel (Author)
Modern Orbit Determination is an introduction to the applications of estimation theory to orbit determination. Beginning with the deterministic point of view, the author moves towards the more modern stochastic viewpoint. The fact that the degree of determinism present is an engineering decision is emphasized. View Details
Leaving Orbit: Notes from the Last Days of American Spaceflight
by Margaret Lazarus Dean (Author)
Winner of the Graywolf Press Nonfiction Prize, a breathtaking elegy to the waning days of human spaceflight as we have known it
In the 1960s, humans took their first steps away from Earth, and for a time our possibilities in space seemed endless. But in a time of austerity and in the wake of high-profile disasters like Challenger, that dream has ended. In early 2011, Margaret Lazarus Dean traveled to Cape Canaveral for NASA's last three space shuttle launches in order to bear witness to the end of an era. With Dean as our guide to Florida's Space Coast and to... View Details
Orbit: NASA Astronauts Photograph The Earth
by Jay Apt (Author), Michael Helfert (Author), Justin Wilkinson (Author), Roger Ressmeyer (Editor)
More than 170 spectacular full-color photographs of the Earth taken from space capture the natural forces that have shaped the planet, the vast and fragile beauty of the planet's ecosystems, and human impact on Earth. 35,000 first printing. View Details
Statistical Orbit Determination
by Bob Schutz (Author), Byron Tapley (Author), George H. Born (Author)
Statistical Orbit Determination presents fundmentals of orbit determination--from weighted least squares approaches (Gauss) to today's high-speed computer algorithms that provide accuracy within a few centimeters. Numerous examples and problems are provided to enhance readers' understanding of the material.Covers such topics as coordinate and time systems, square root filters, process noise techniques, and the use of fictitious parameters for absorbing un-modeled and incorrectly modeled forces acting on a satellite.Examples and exercises serve to illustrate the principles throughout... View Details
by Megeen R. Mulholland (Author)
In her first published book of poetry titled Orbit, Megeen R. Mulholland has written a collection of work that poignantly explores motherhood. This poetry has been inspired by her large Irish family’s oral narrative and snapshot photography. The author creates dialogues between past and present family history as she visually and thematically arranges words and images on the page. She does so with the awareness that she carries a valuable emotional investment like that other inter-arts writers bring to their material. She is inspired when she discovers details like her father’s... View Details
Crowded Orbits: Conflict and Cooperation in Space
by James Clay Moltz (Author)
Space has become increasingly crowded since the end of the Cold War, with new countries, companies, and even private citizens operating satellites and becoming spacefarers. This book offers general readers a valuable primer on space policy from an international perspective. It examines the competing themes of space competition and cooperation while providing readers with an understanding of the basics of space technology, diplomacy, commerce, science, and military applications.
The recent expansion of human space activity poses new challenges to existing treaties and other governance... View Details