Nav: Home

Scientists discover more than 600 new periodic orbits of the famous three body problem

October 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 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

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.
See the article:

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

Science China Press

Related Orbit Articles:

Configuration and manipulation of soft robotics for on-orbit servicing
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.
Researchers discover star in closest known orbit around black hole
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.
Star in closest orbit ever seen around black hole
Astronomers have found evidence of a star that whips around a likely black hole twice an hour.
Star discovered in closest known orbit around black hole
Astronomers have found evidence for a star that whips around a black hole about twice an hour.
SwRI flips switch on LAMP in lunar orbit
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.
New model explains the moon's weird orbit
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.
Two-dimensional spin-orbit coupling for Bose-Einstein condensates realized
A joint team of the University of Science and Technology of China and the Peking University made breakthrough in quantum simulation of ultracold atoms.
Unusual planet within a triple star system imaged
Astronomers have directly detected a planet in a triple star system using imaging techniques.
'Lomonosov' embarks to the orbit
Today, April 28, 5:01 Moscow time, the first launch from the Vostochny Cosmodrome took place.
Planet formation in Earth-like orbit around a young star
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

A Closed and Common Orbit (Wayfarers)
by Becky Chambers (Author)

Nominated for the 2017 Hugo Award for Best Novel!

Shortlisted for the 2017 Arthur C. Clarke Award!

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 intelligence. When she wakes up in a new body, following a total system shut-down and reboot, she has no memory of what came before. As Lovelace learns to... 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

Orbit: NASA Astronauts Photograph The Earth
by Jay Apt (Author), Michael Helfert (Author), Justin Wilkinson (Author), Roger Ressmeyer (Editor)

Photographs taken from space capture the natural forces that have shaped the planet, and human impact on Earth. View Details

ORBIT: Observation of Rapport Based Interview Techniques: Coding Manual

The ORBIT has been designed to capture the interpersonal dynamics which evolve over the course of an investigative police interview between the interviewer and the detainee. The ORBIT adopts a holistic or global approach to collecting observations on the development of rapport and communication styles expressed during the interview. The ORBIT coding manual is the first book in the ORBIT series. View Details

Orbit (Pitt Poetry Series)
by Arthur Vogelsang (Author)

Orbit connects the intimate with what is farthest from us, mixing what we can imagine with what is daily and near. Landscapes stretch from stable and fulfilling domestic interiors to the destiny of our sun as an exploding red giant. That dilemma of human fertility and love facing ultimate destruction is orchestrated by the author’s provocative voice and coiled lines, which fondle and handle the reader’s heart and mind in a bright light. The book insists on connecting the three eras of human experience – Then, Now, and When – at every turn. Orbit continues the unique... View Details

Orbit: Life with My People
by Orbit (Author)

"Orbit is not just a dog; he's a spiritual being..." Yakov Smirnoff Orbit was a Great Pyrenees who touched many people all over the world. He was born in a log cabin in the Ozarks and was adopted by a self-sufficient community. Within the community, he adopted Bettine and Peter, whose property, Alpha Meadows, became his kingdom. His life was filled with a lot of happiness in an idyllic setting, but set against a back story of fear and pain. His ability to sing to Bettine's flutes, took him in film around the world on concert tours where his spirit moved international audiences. His... 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

Planet Kindergarten: 100 Days in Orbit
by Sue Ganz-Schmitt (Author), Shane Prigmore (Illustrator)

Star Log: Day 100. Base camp is lively. I greet my crewmates and admire their work. We have mastered many skills on our journey, but today brings a new milestone. There have been: 100 roll calls. 100 songs. 100 pledges. 100 challenging days full of exploration and triumph! Little ones will be over the moon as they celebrate school's 100th Day with this clever, dynamically illustrated book, and eager to suit up for another daring adventure exploring and conquering Planet Kindergarten. View Details

The Orbit Magazine Anthology: Re-Entry (Painted Turtle)
by Robert St Mary (Author), Ben Blackwell (Afterword), Jerry Vile (Afterword)

With a mischievous globe-headed mascot that appeared in every issue and even on Quentin Tarantino's T-shirt in Pulp Fiction, Orbit was an instantly recognizable arbiter of 1990s Detroit culture. But its irreverent tone and unique editorial features could be traced to two earlier local publications from creator Jerry Peterson, a.k.a. Jerry Vile-White Noise (1978-1980) and Fun: The Magazine for Swinging Intelectuals [sic] (1986-1990). In The Orbit Magazine Anthology: Re-Entry, author Rob St. Mary details the full run of White Noise, Fun,... View Details

Best Science Podcasts 2017

We have hand picked the best science podcasts for 2017. Sit back and enjoy new science podcasts updated daily from your favorite science news services and scientists.
Now Playing: TED Radio Hour

We think we're the ones who control what we see, read, think and remember. But is that true? Who decides? And who should decide? This hour, TED speakers reveal just how easily we can be manipulated. Guests include design ethicist Tristan Harris, MSNBC host Ali Velshi, psychologist Elizabeth Loftus, and neuroscientist Steve Ramirez.
Now Playing: Science for the People

#443 Batteries
This week on Science for the People we take a deep dive into modern batteries: how they work now and how they might work in the future. We speak with Gerbrand Ceder from UC Berkeley, about the most commonly used batteries today, how they work, and how they could work better. And we talk with Kathryn Toghill, electrochemist from Lancaster University, about redox flow batteries and how they could help make our power grids more sustainable.