The Interplanetary Transport Network (ITN)
is a collection of
gravitation
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
ally determined pathways through the
Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
that require very little
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
for an object to follow. The ITN makes particular use of
Lagrange points
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of t ...
as locations where
trajectories
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete traj ...
through
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
can be redirected using little or no energy. These points have the peculiar property of allowing objects to
orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
around them, despite lacking an object to orbit. While it would use little energy, transport along the network would take a long time.
History
Interplanetary transfer orbits are solutions to the gravitational
three-body problem
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's ...
, which, for the general case, does not have analytical solutions, and is addressed by
numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...
approximations. However, a small number of exact solutions exist, most notably the five orbits referred to as "
Lagrange point
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of th ...
s", which are orbital solutions for circular orbits in the case when one body is significantly more massive.
The key to discovering the Interplanetary Transport Network was the investigation of the nature of the winding paths near the Earth-Sun and Earth-Moon Lagrange points. They were first investigated by
Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
in the 1890s. He noticed that the paths leading to and from any of those points would almost always settle, for a time, on an orbit about that point. There are in fact an
infinite
Infinite may refer to:
Mathematics
* Infinite set, a set that is not a finite set
*Infinity, an abstract concept describing something without any limit
Music
*Infinite (group), a South Korean boy band
*''Infinite'' (EP), debut EP of American m ...
number of paths taking one to the point and away from it, and all of which require nearly zero change in energy to reach. When plotted, they form a tube with the orbit about the Lagrange point at one end.
The derivation of these paths traces back to mathematicians
Charles C. Conley and
Richard P. McGehee in 1968.
''
Hiten Hiten may refer to:
* Hiten (name), Indian given name
* Hiten (spacecraft), Japanese lunar probe
*Tennin
, which may include , , and the specifically female version, the , are a divine kind of spiritual beings found in Japanese Buddhism, the ...
'', Japan's first lunar probe, was moved into lunar orbit using similar insight into the nature of paths between the
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
and the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
. Beginning in 1997,
Martin Lo
Martin Wen-Yu Lo is a spacecraft trajectory expert currently working at the NASA-owned Jet Propulsion Laboratory. Martin Lo is well known for discovering the Interplanetary Superhighway, also known as the Interplanetary Transport Network. The su ...
,
Shane D. Ross, and others wrote a series of papers identifying the mathematical basis that applied the technique to the
''Genesis'' solar wind sample return, and to lunar and
Jovian
Jovian is the adjectival form of Jupiter and may refer to:
* Jovian (emperor) (Flavius Iovianus Augustus), Roman emperor (363–364 AD)
* Jovians and Herculians, Roman imperial guard corps
* Jovian (lemur), a Coquerel's sifaka known for ''Zoboomafo ...
missions. They referred to it as an Interplanetary Superhighway (IPS).
Paths
As it turns out, it is very easy to transit from a path leading to the point to one leading back out. This makes sense, since the orbit is unstable, which implies one will eventually end up on one of the outbound paths after spending no energy at all.
Edward Belbruno
Edward Belbruno (born August 2, 1951, as a U.S. Citizen in Heidelberg, Germany) is an artist, mathematician and scientist whose interests are in celestial mechanics, dynamical systems, dynamical astronomy, and aerospace engineering. His artistic ...
coined the term "
weak stability boundary
Weak stability boundary (WSB), including Low-energy transfer, is a concept introduced by Edward Belbruno in 1987. The concept explained how a spacecraft could change orbits using very little fuel.
Weak stability boundary is defined for the thre ...
"
or "fuzzy boundary"
for this effect.
With careful calculation, one can pick ''which'' outbound path one wants. This turns out to be useful, as many of these paths lead to some interesting points in space, such as the Earth's Moon or between the
Galilean moons
The Galilean moons (), or Galilean satellites, are the four largest moons of Jupiter: Io, Europa, Ganymede, and Callisto. They were first seen by Galileo Galilei in December 1609 or January 1610, and recognized by him as satellites of Jupiter ...
of
Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...
, within a few months or years.
The transfers are so low-energy that they make travel to almost any point in the Solar System possible. On the downside, these transfers are very slow. For trips from Earth to other planets, they are not useful for crewed or uncrewed probes, as the trip would take many generations. Nevertheless, they have already been used to transfer spacecraft to the Earth–Sun point, a useful point for studying the Sun that was employed in a number of recent missions, including the
''Genesis'' mission, the first to return
solar wind
The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sola ...
samples to Earth. The network is also relevant to understanding Solar System dynamics;
Comet Shoemaker–Levy 9
Comet Shoemaker–Levy 9 ( formally designated D/1993 F2) broke apart in July 1992 and collided with Jupiter in July 1994, providing the first direct observation of an extraterrestrial collision of Solar System objects. This generated a l ...
followed such a trajectory on its collision path with Jupiter.
Further explanation
The ITN is based around a series of orbital paths predicted by
chaos theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...
and the
restricted three-body problem
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's ...
leading to and from the orbits around the Lagrange points – points in space where the
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
between various bodies balances with the centrifugal force of an object there. For any two bodies in which one body orbits around the other, such as a star/planet or planet/moon system, there are five such points, denoted through . For instance, the Earth–Moon point lies on a line between the two, where gravitational forces between them exactly balance with the centrifugal force of an object placed in orbit there. These five points have particularly low
delta-v
Delta-''v'' (more known as "change in velocity"), symbolized as ∆''v'' and pronounced ''delta-vee'', as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as ...
requirements, and appear to be the lowest-energy transfers possible, even lower than the common
Hohmann transfer orbit
In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and the Moon, or ano ...
that has dominated orbital navigation since the start of space travel.
Although the forces balance at these points, the first three points (the ones on the line between a certain large mass, e.g. a
star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
, and a smaller, orbiting mass, e.g. a
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
) are not stable
equilibrium points. If a
spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
placed at the Earth–Moon point is given even a slight nudge away from the equilibrium point, the spacecraft's trajectory will diverge away from the point. The entire system is in motion, so the spacecraft will not actually hit the Moon, but will travel in a winding path, off into space. There is, however, a semi-stable orbit around each of these points, called a
halo orbit
A halo orbit is a periodic, three-dimensional orbit near one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it ca ...
. The orbits for two of the points, and , are stable, but the halo orbits for through are stable only on the order of
months.
In addition to orbits around Lagrange points, the rich dynamics that arise from the gravitational pull of more than one mass yield interesting trajectories, also known as
low energy transfers
A low-energy transfer, or low-energy trajectory, is a route in space that allows spacecraft to change orbits using significantly less fuel than traditional transfers. These routes work in the Earth–Moon system and also in other systems, such as ...
.
For example, the gravity environment of the Sun–Earth–Moon system allows spacecraft to travel great distances on very little fuel, albeit on an often circuitous route.
Missions
Launched in 1978, the
ISEE-3
The International Cometary Explorer (ICE) spacecraft (designed and launched as the International Sun-Earth Explorer-3 (ISEE-3) satellite), was launched 12 August 1978, into a heliocentric orbit. It was one of three spacecraft, along with the mo ...
spacecraft was sent on a mission to orbit around one of the Lagrange points. The spacecraft was able to maneuver around the Earth's neighborhood using little fuel by taking advantage of the unique
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
environment. After the primary mission was completed, ISEE-3 went on to accomplish other goals, including a flight through the
geomagnetic
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic ...
tail and a comet flyby. The mission was subsequently renamed the
International Cometary Explorer
The International Cometary Explorer (ICE) spacecraft (designed and launched as the International Sun-Earth Explorer-3 (ISEE-3) satellite), was launched 12 August 1978, into a heliocentric orbit. It was one of three spacecraft, along with the mo ...
(ICE).
The first low energy transfer using what would later be called the ITN was the rescue of
Japan
Japan ( ja, 日本, or , and formally , ''Nihonkoku'') is an island country in East Asia. It is situated in the northwest Pacific Ocean, and is bordered on the west by the Sea of Japan, while extending from the Sea of Okhotsk in the north ...
's ''
Hiten Hiten may refer to:
* Hiten (name), Indian given name
* Hiten (spacecraft), Japanese lunar probe
*Tennin
, which may include , , and the specifically female version, the , are a divine kind of spiritual beings found in Japanese Buddhism, the ...
'' lunar mission in 1991.
Another example of the use of the ITN was
NASA
The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research.
NASA was established in 1958, succeeding t ...
's 2001–2003
Genesis mission, which orbited the Sun–Earth point for over two years collecting material, before being redirected to the Lagrange point, and finally redirected from there back to Earth.
[
The 2003–2006 '' SMART-1'' of the ]European Space Agency
, owners =
, headquarters = Paris, Île-de-France, France
, coordinates =
, spaceport = Guiana Space Centre
, seal = File:ESA emblem seal.png
, seal_size = 130px
, image = Views in the Main Control Room (1205 ...
used another low energy transfer from the ITN.
In a more recent example, the Chinese
Chinese can refer to:
* Something related to China
* Chinese people, people of Chinese nationality, citizenship, and/or ethnicity
**''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation
** List of ethnic groups in China, people of ...
spacecraft Chang'e 2
Chang'e 2 (; ) is a Chinese unmanned lunar probe that was launched on 1 October 2010. It was a follow-up to the Chang'e 1 lunar probe, which was launched in 2007. Chang'e 2 was part of the first phase of the Chinese Lunar Exploration Program, and ...
used the ITN to travel from lunar orbit to the Earth-Sun point, then on to fly by the asteroid 4179 Toutatis.
Asteroids
The asteroid 39P/Oterma's path from outside Jupiters orbit, to inside, and back to outside is said to use these low energy paths.[
]
See also
* Gravitational keyhole
* Gravity assist
In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver, or swing-by is the use of the relative movement (e.g. orbit around the Sun) and gravity of a planet or other astronomical object to alter the p ...
* Halo orbit
A halo orbit is a periodic, three-dimensional orbit near one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it ca ...
* Hill sphere
The Hill sphere of an astronomical body is the region in which it dominates the attraction of satellites. To be retained by a planet, a moon must have an orbit that lies within the planet's Hill sphere. That moon would, in turn, have a Hill sp ...
* Horseshoe orbit
In celestial mechanics, a horseshoe orbit is a type of co-orbital configuration, co-orbital motion of a small orbiting body relative to a larger orbiting body. The osculating orbit, osculating (instantaneous) orbital period of the smaller body re ...
* Interplanetary spaceflight
Interplanetary spaceflight or interplanetary travel is the crewed or uncrewed travel between stars and planets, usually within a single planetary system. In practice, spaceflights of this type are confined to travel between the planets of the ...
* Lunar cycler
* Mars cycler
A Mars cycler (or Earth–Mars cycler) is a kind of spacecraft trajectory that encounters Earth and Mars regularly. The term Mars cycler may also refer to a spacecraft on a Mars cycler trajectory. The Aldrin cycler is an example of a Mars cycler. ...
* Orbital mechanics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
Sources and notes
Further reading
''Dynamical Systems, the Three-Body Problem, and Space Mission Design''
, by Wang Sang Koon, Martin W. Lo
Martin Wen-Yu Lo is a spacecraft trajectory expert currently working at the NASA-owned Jet Propulsion Laboratory. Martin Lo is well known for discovering the Interplanetary Superhighway, also known as the Interplanetary Transport Network. The su ...
, Jerrold E. Marsden
Jerrold Eldon Marsden (August 17, 1942 – September 21, 2010) was a Canadian mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology.. Marsden is listed as an ISI ...
, Shane D. Ross (book available a
PDF
).
"Cylindrical manifolds and tube dynamics in the restricted three-body problem" - PhD dissertation
by Shane D. Ross
"The Interplanetary Transport Network"
by Shane D. Ross, ''American Scientist'', May–June 200
(Subscription)
"Tube Route" ''Science'', 18 November 2005
"Navigating Celestial Currents" ''Science News'', 18 April 2005
The Dynamical Mechanism of Ballistic Lunar Capture Transfers in the Four-Body Problem from the Perspective of Invariant Manifolds and Hill's Regions
by Edward Belbruno
Edward Belbruno (born August 2, 1951, as a U.S. Citizen in Heidelberg, Germany) is an artist, mathematician and scientist whose interests are in celestial mechanics, dynamical systems, dynamical astronomy, and aerospace engineering. His artistic ...
External links
"Next Exit 0.5 Million Kilometers" Engineering and Science, 2002
* ttp://focus.aps.org/story/v9/st31 "Asteroids Lost in Space" ''Physical Review Focus'', 14 June 2002
Interplanetary Transport Network lecture (YouTube)
by Shane D. Ross, 2004
''Capture Dynamics and Chaotic Motions in Celestial Mechanics: With the Construction of Low Energy Transfers''
- A mathematical analysis of aspects of the ITN, Edward Belbruno
Edward Belbruno (born August 2, 1951, as a U.S. Citizen in Heidelberg, Germany) is an artist, mathematician and scientist whose interests are in celestial mechanics, dynamical systems, dynamical astronomy, and aerospace engineering. His artistic ...
(2004)
2007-10-08 audio interview with Belbruno on low-energy transfer
{{Orbits
Astrodynamics
Dynamical systems
Orbits