Lissajous orbit
Encyclopedia
In orbital mechanics, a Lissajous orbit, li.sa.ʒu, named after Jules Antoine Lissajous
, is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point
of a three-body system without requiring any propulsion. Lyapunov orbits
around a libration point are curved paths that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits include components in this plane and perpendicular to it, and follow a Lissajous curve
. Halo orbit
s also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not.
In practice, any orbit around Lagrangian point
s , , or is dynamically unstable, meaning small departures from equilibrium grow exponentially over time. As a result, spacecraft in libration point orbits must use their propulsion systems to perform orbital station-keeping. Orbits about Lagrangian point
s and are dynamically stable in theory, meaning the natural dynamics (without the use of a spacecraft's propulsion system) keep the spacecraft in the vicinity of the Lagrangian point
even when slightly perturbed from equilibrium. In the case of the Earth–Moon system the effect of the eccentricity
of the Moon's orbit and the effect of solar perturbation cause these Lagrange points to be unstable as well.
Several missions have used Lissajous trajectories: ACE
at Sun–Earth and WMAP
at Sun–Earth and also the Genesis
mission collecting solar particles at .
On 14 May 2009, the European Space Agency
(ESA) launched into space the Herschel
and Planck observatories, both of which use Lissajous orbits at Sun–Earth .
ESA's future Gaia mission will also use a Lissajous orbit at Sun–Earth .
China's lunar orbiter Chang'e 2
will leave lunar orbit on June 16, 2011 and fly to .
In the science fiction
novel Sunstorm
by Arthur C. Clarke
and Stephen Baxter, a huge shield is constructed in space to protect the Earth from a deadly solar superstorm which would have been in a Lissajous orbit as would a group of other wealthy and powerful people who sheltered opposite it at – in line with both Earth and Moon as well as the shield with a Lunar eclipse
taking place at the time.
Jules Antoine Lissajous
Jules Antoine Lissajous was a French mathematician, after whom Lissajous figures are named. Among other innovations, Lissajous invented the Lissajous apparatus, a device that creates the figures that bear his name...
, is a quasi-periodic orbital trajectory that an object can follow around a Lagrangian point
Lagrangian point
The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects...
of a three-body system without requiring any propulsion. Lyapunov orbits
Lyapunov exponent
In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories...
around a libration point are curved paths that lie entirely in the plane of the two primary bodies. In contrast, Lissajous orbits include components in this plane and perpendicular to it, and follow a Lissajous curve
Lissajous curve
In mathematics, a Lissajous curve , also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equationswhich describe complex harmonic motion...
. Halo orbit
Halo orbit
A halo orbit is a periodic, three-dimensional orbit near the , , or Lagrange points in the three-body problem of orbital mechanics. A spacecraft in a halo orbit does not technically orbit the Lagrange point itself , but travels in a closed, repeating path near the Lagrange point...
s also include components perpendicular to the plane, but they are periodic, while Lissajous orbits are not.
In practice, any orbit around Lagrangian point
Lagrangian point
The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects...
s , , or is dynamically unstable, meaning small departures from equilibrium grow exponentially over time. As a result, spacecraft in libration point orbits must use their propulsion systems to perform orbital station-keeping. Orbits about Lagrangian point
Lagrangian point
The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects...
s and are dynamically stable in theory, meaning the natural dynamics (without the use of a spacecraft's propulsion system) keep the spacecraft in the vicinity of the Lagrangian point
Lagrangian point
The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects...
even when slightly perturbed from equilibrium. In the case of the Earth–Moon system the effect of the eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...
of the Moon's orbit and the effect of solar perturbation cause these Lagrange points to be unstable as well.
Several missions have used Lissajous trajectories: ACE
Advanced Composition Explorer
Advanced Composition Explorer is a NASA space exploration mission being conducted as part of the Explorer program to study matter in situ, comprising energetic particles from the solar wind, the interplanetary medium, and other sources. Real-time data from ACE is used by the Space Weather...
at Sun–Earth and WMAP
Wilkinson Microwave Anisotropy Probe
The Wilkinson Microwave Anisotropy Probe — also known as the Microwave Anisotropy Probe , and Explorer 80 — is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat — the Cosmic Microwave Background Radiation — across the full sky. Headed by Professor...
at Sun–Earth and also the Genesis
Genesis (spacecraft)
The Genesis spacecraft was a NASA sample return probe which collected a sample of solar wind and returned it to Earth for analysis. It was the first NASA sample return mission to return material since the Apollo Program, and the first to return material from beyond the orbit of the Moon...
mission collecting solar particles at .
On 14 May 2009, the European Space Agency
European Space Agency
The European Space Agency , established in 1975, is an intergovernmental organisation dedicated to the exploration of space, currently with 18 member states...
(ESA) launched into space the Herschel
Herschel Space Observatory
The Herschel Space Observatory is a European Space Agency space observatory sensitive to the far infrared and submillimetre wavebands. It is the largest space telescope ever launched, carrying a single mirror of in diameter....
and Planck observatories, both of which use Lissajous orbits at Sun–Earth .
ESA's future Gaia mission will also use a Lissajous orbit at Sun–Earth .
China's lunar orbiter Chang'e 2
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 conducted research from a 100-kilometer-high lunar orbit...
will leave lunar orbit on June 16, 2011 and fly to .
In the science fiction
Science fiction
Science fiction is a genre of fiction dealing with imaginary but more or less plausible content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities...
novel Sunstorm
Sunstorm (novel)
Sunstorm is a 2005 science fiction novel co-written by Arthur C. Clarke and Stephen Baxter. It is the second book in the series A Time Odyssey. The books in this series are often likened to the Space Odyssey series, although the Time Odyssey novels ostensibly deal with time where the...
by Arthur C. Clarke
Arthur C. Clarke
Sir Arthur Charles Clarke, CBE, FRAS was a British science fiction author, inventor, and futurist, famous for his short stories and novels, among them 2001: A Space Odyssey, and as a host and commentator in the British television series Mysterious World. For many years, Robert A. Heinlein,...
and Stephen Baxter, a huge shield is constructed in space to protect the Earth from a deadly solar superstorm which would have been in a Lissajous orbit as would a group of other wealthy and powerful people who sheltered opposite it at – in line with both Earth and Moon as well as the shield with a Lunar eclipse
Lunar eclipse
A lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
taking place at the time.