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''Planck'' was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013. It was an ambitious project that aimed to map the anisotropies of the
cosmic microwave background The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dar ...
(CMB) at microwave and infrared frequencies, with high sensitivity and angular resolution. The mission was highly successful and substantially improved upon observations made by the NASA
Wilkinson Microwave Anisotropy Probe The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic mic ...
(WMAP). The Planck observatory was a major source of information relevant to several cosmological and astrophysical issues. One of its key objectives was to test theories of the early Universe and the origin of cosmic structure. The mission provided significant insights into the composition and evolution of the Universe, shedding light on the fundamental physics that governs the cosmos. Planck was initially called COBRAS/SAMBA, which stands for the Cosmic Background Radiation Anisotropy Satellite/Satellite for Measurement of Background Anisotropies. The project started in 1996, and it was later renamed in honor of the German physicist
Max Planck Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
(1858–1947), who is widely regarded as the originator of quantum theory by deriving the formula for
black-body radiation Black-body radiation is the thermal radiation, thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific ...
. Built at the
Cannes Mandelieu Space Center The Cannes Mandelieu Space Center is an industrial plant dedicated to spacecraft manufacturing, located in both the towns of Cannes and Mandelieu in France. After a long history in aircraft manufacturing, starting in 1929, the center became incr ...
by
Thales Alenia Space Thales Alenia Space () is a joint venture between the French technology corporation Thales Group (67%) and Italian defense conglomerate Leonardo (company), Leonardo (33%). The company is headquartered in Cannes, France. It provides space-based ...
, Planck was created as a medium-sized mission for ESA's Horizon 2000 long-term scientific program. The observatory was launched in May 2009 and reached the Earth/Sun L2 point by July 2009. By February 2010, it had successfully started a second all-sky survey. On 21 March 2013, the Planck team released its first all-sky map of the cosmic microwave background. The map was of exceptional quality and allowed researchers to measure temperature variations in the CMB with unprecedented accuracy. In February 2015, an expanded release was published, which included polarization data. The final papers by the Planck team were released in July 2018, marking the end of the mission. At the end of its mission, Planck was put into a
heliocentric Heliocentrism (also known as the heliocentric model) is a Superseded theories in science#Astronomy and cosmology, superseded astronomical model in which the Earth and Solar System, planets orbit around the Sun at the center of the universe. His ...
graveyard orbit A graveyard orbit, also called a junk orbit or disposal orbit, is an Orbit (physics), orbit that lies away from common operational orbits. One significant graveyard orbit is a supersynchronous orbit well beyond geosynchronous orbit. Some satellit ...
and passivated to prevent it from endangering any future missions. The final deactivation command was sent to Planck in October 2013. The mission was a remarkable success and provided the most precise measurements of several key cosmological parameters. Planck's observations helped determine the age of the universe, the average density of ordinary matter and
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
in the Universe, and other important characteristics of the cosmos.


Objectives

The mission had a wide variety of scientific aims, including: * high resolution detections of both the total intensity and polarization of primordial CMB anisotropies, * creation of a catalogue of
galaxy clusters A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. Clusters consist of galax ...
through the Sunyaev–Zel'dovich effect, * observations of the
gravitational lens A gravitational lens is matter, such as a galaxy cluster, cluster of galaxies or a point particle, that bends light from a distant source as it travels toward an observer. The amount of gravitational lensing is described by Albert Einstein's Ge ...
ing of the CMB, as well as the integrated
Sachs–Wolfe effect The Sachs–Wolfe effect, named after Rainer K. Sachs and Arthur M. Wolfe, is a property of the cosmic microwave background radiation (CMB), in which photons from the CMB are gravitationally redshifted, causing the CMB spectrum to appear uneven ...
, * observations of bright extragalactic radio (
active galactic nuclei An active galactic nucleus (AGN) is a compact region at the center of a galaxy that emits a significant amount of energy across the electromagnetic spectrum, with characteristics indicating that this luminosity is not produced by the stars. Such e ...
) and infrared (dusty galaxy) sources, * observations of the
Milky Way The Milky Way or Milky Way Galaxy is the galaxy that includes the Solar System, with the name describing the #Appearance, galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars in other arms of the galax ...
, including the
interstellar medium The interstellar medium (ISM) is the matter and radiation that exists in the outer space, space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as cosmic dust, dust and cosmic rays. It f ...
, distributed
synchrotron A synchrotron is a particular type of cyclic particle accelerator, descended from the cyclotron, in which the accelerating particle beam travels around a fixed closed-loop path. The strength of the magnetic field which bends the particle beam i ...
emission and measurements of the Galactic
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
, and * studies of 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 "Sola ...
, including
planet A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...
s,
asteroid An asteroid is a minor planet—an object larger than a meteoroid that is neither a planet nor an identified comet—that orbits within the Solar System#Inner Solar System, inner Solar System or is co-orbital with Jupiter (Trojan asteroids). As ...
s,
comet A comet is an icy, small Solar System body that warms and begins to release gases when passing close to the Sun, a process called outgassing. This produces an extended, gravitationally unbound atmosphere or Coma (cometary), coma surrounding ...
s and the
zodiacal light The zodiacal light (also called false dawn when seen before sunrise) is a faint glow of diffuse sunlight scattered by interplanetary dust. Brighter around the Sun, it appears in a particularly dark night sky to extend from the Sun's direct ...
. ''Planck'' had a higher resolution and sensitivity than WMAP, allowing it to probe the power spectrum of the CMB to much smaller scales (×3). It also observed in nine
frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
bands rather than WMAP's five, with the goal of improving the astrophysical foreground models. It is expected that most ''Planck'' measurements have been limited by how well foregrounds can be subtracted, rather than by the detector performance or length of the mission, a particularly important factor for the polarization measurements. The dominant foreground radiation depends on frequency, but could include synchrotron radiation from the Milky Way at low frequencies, and dust at high frequencies.


Instruments

The spacecraft carries two instruments: the Low Frequency Instrument (LFI) and the High Frequency Instrument (HFI). Both instruments can detect both the total intensity and polarization of photons, and together cover a frequency range of nearly 830 GHz (from 30 to 857 GHz). The cosmic microwave background spectrum peaks at a frequency of 160.2 GHz. ''Planck'' passive and active cooling systems allow its instruments to maintain a temperature of , or 0.1 °C above
absolute zero Absolute zero is the lowest possible temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The absolute zero is defined as 0 K on the Kelvin scale, equivalent to −273.15 ° ...
. From August 2009, ''Planck'' was the coldest known object in space, until its active coolant supply was exhausted in January 2012. NASA played a role in the development of this mission and contributes to the analysis of scientific data. Its
Jet Propulsion Laboratory The Jet Propulsion Laboratory (JPL) is a Federally funded research and development centers, federally funded research and development center (FFRDC) in La Cañada Flintridge, California, Crescenta Valley, United States. Founded in 1936 by Cali ...
built components of the science instruments, including
bolometer A bolometer is a device for measuring radiant heat by means of a material having a temperature-dependent electrical resistance. It was invented in 1878 by the American astronomer Samuel Pierpont Langley. Principle of operation A bolometer ...
s for the high-frequency instrument, a 20-kelvin
cryocooler A cryocooler is a refrigerator designed to reach cryogenic temperatures (below 120 K, -153 °C, -243.4 °F). The term is most often used for smaller systems, typically table-top size, with input powers less than about 20 kW. Some can have inpu ...
for both the low- and high-frequency instruments, and amplifier technology for the low-frequency instrument.


Low Frequency Instrument

The LFI has three frequency bands, covering the range of 30–70 GHz, covering the microwave to infrared regions of the electromagnetic spectrum. The detectors use
high-electron-mobility transistor A high-electron-mobility transistor (HEMT or HEM FET), also known as heterostructure FET (HFET) or modulation-doped FET (MODFET), is a field-effect transistor incorporating a junction between two materials with different band gaps (i.e. a heter ...
s.


High Frequency Instrument

The HFI was sensitive between 100 and 857 GHz, using 52 bolometric detectors, manufactured by JPL/Caltech, optically coupled to the telescope through cold optics, manufactured by Cardiff University's School of Physics and Astronomy, consisting of a triple horn configuration and optical filters, a similar concept to that used in the Archeops balloon-borne experiment. These detection assemblies are divided into 6 frequency bands (centred at 100, 143, 217, 353, 545 and 857 GHz), each with a bandwidth of 33%. Of these six bands, only the lower four have the capability to measure the polarisation of incoming radiation; the two higher bands do not. On 13 January 2012, it was reported that the on-board supply of
helium-3 Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron. (In contrast, the most common isotope, helium-4, has two protons and two neutrons.) Helium-3 and hydrogen-1 are the only stable nuclides with ...
used in ''Planck''
dilution refrigerator A 3He/4He dilution refrigerator is a cryogenics, cryogenic device that provides continuous cooling to temperatures as low as 2 Kelvin, mK, with no moving parts in the low-temperature region. The cooling power is provided by the heat o ...
had been exhausted, and that the HFI would become unusable within a few days. By this date, ''Planck'' had completed five full scans of the CMB, exceeding its target of two. The LFI (cooled by
helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consi ...
) was expected to remain operational for another six to nine months.


Service module

A common
service module A service module (also known as an equipment module or instrument compartment) is a component of a crewed space capsule containing a variety of support systems used for spacecraft operations. Usually located in the uninhabited area of the spacec ...
(SVM) was designed and built by Thales Alenia Space in its
Turin Turin ( , ; ; , then ) is a city and an important business and cultural centre in northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. The city is main ...
plant, for both the ''
Herschel Space Observatory The Herschel Space Observatory was a space observatory built and operated by the European Space Agency (ESA). It was active from 2009 to 2013, and was the largest infrared telescope ever launched until the launch of the James Webb Space Telesco ...
'' and ''Planck'' missions, combined into one single program. The overall cost is estimated to be for the ''Planck'' and for the ''Herschel'' mission. Both figures include their mission's spacecraft and payload, (shared) launch and mission expenses, and science operations. Structurally, the ''Herschel'' and ''Planck'' SVMs are very similar. Both SVMs are octagonal in shape and each panel is dedicated to accommodate a designated set of warm units, while taking into account the dissipation requirements of the different warm units, of the instruments, as well as the spacecraft. On both spacecraft, a common design was used for the
avionics Avionics (a portmanteau of ''aviation'' and ''electronics'') are the Electronics, electronic systems used on aircraft. Avionic systems include communications, Air navigation, navigation, the display and management of multiple systems, and the ...
, attitude control and measurement (ACMS), command and data management (CDMS), power, and tracking, telemetry and command (TT&C) subsystems. All units on the SVM are redundant.


Power Subsystem

On each spacecraft, the power subsystem consists of a
solar array A photovoltaic system, also called a PV system or solar power system, is an electric power system designed to supply usable solar power by means of photovoltaics. It consists of an arrangement of several components, including solar panels to abs ...
, employing triple-junction
solar cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.
s, a battery and the power control unit (PCU). The PCU is designed to interface with the 30 sections of each solar array, to provide a regulated 28 volt bus, to distribute this power via protected outputs, and to handle the battery charging and discharging. For ''Planck'', the circular solar array is fixed on the bottom of the satellite, always facing the Sun as the satellite rotates on its vertical axis.


Attitude and Orbit Control

This function is performed by the attitude control computer (ACC), which is the platform for the attitude control and measurement subsystem (ACMS). It was designed to fulfil the pointing and slewing requirements of the ''Herschel'' and ''Planck'' payloads. The ''Planck'' satellite rotates at one revolution per minute, with an aim of an absolute pointing error less than 37 arc-minutes. As ''Planck'' is also a survey platform, there is the additional requirement for pointing reproducibility error less than 2.5 arc-minutes over 20 days. The main line-of-sight sensor in both ''Herschel'' and ''Planck'' is the
star tracker A star tracker is an optical device that measures the positions of stars using photocells or a camera. As the positions of many stars have been measured by astronomers to a high degree of accuracy, a star tracker on a satellite or spacecraft may ...
.


Launch and orbit

The satellite was successfully launched, along with the ''
Herschel Space Observatory The Herschel Space Observatory was a space observatory built and operated by the European Space Agency (ESA). It was active from 2009 to 2013, and was the largest infrared telescope ever launched until the launch of the James Webb Space Telesco ...
'', at 13:12:02 UTC on 14 May 2009 aboard an
Ariane 5 ECA Ariane 5 is a retired European Heavy-lift launch vehicle, heavy-lift space launch vehicle operated by Arianespace for the European Space Agency (ESA). It was launched from the Guiana Space Centre (CSG) in French Guiana. It was used to deliver p ...
heavy launch vehicle from the
Guiana Space Centre The Guiana Space Centre (; CSG), also called Europe's Spaceport, is a spaceport to the northwest of Kourou in French Guiana, an Overseas departments and regions of France, overseas region of France in South America. Kourou is located approxim ...
. The launch placed the craft into a very elliptical orbit (
perigee An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...
: ,
apogee An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...
: more than ), bringing it near the Lagrangian point of the Earth-Sun system, from the Earth. The manoeuvre to inject ''Planck'' into its final orbit around was successfully completed on 3 July 2009, when it entered a Lissajous orbit with a radius around the Lagrangian point. The temperature of the High Frequency Instrument reached just a tenth of a degree above absolute zero (0.1 K) on 3 July 2009, placing both the Low Frequency and High Frequency Instruments within their cryogenic operational parameters, making ''Planck'' fully operational.


Decommissioning

In January 2012 the HFI exhausted its supply of liquid helium, causing the detector temperature to rise and rendering the HFI unusable. The LFI continued to be used until science operations ended on 3 October 2013. The spacecraft performed a manoeuvre on 9 October to move it away from Earth and its , placing it into a
heliocentric orbit A heliocentric orbit (also called circumsolar orbit) is an orbit around the barycenter of the Solar System, which is usually located within or very near the surface of the Sun. All planets, comets, and asteroids in the Solar System, and the Sun ...
, while payload deactivation occurred on 19 October. ''Planck'' was commanded on 21 October to exhaust its remaining fuel supply; passivation activities were conducted later, including battery disconnection and the disabling of protection mechanisms. The final deactivation command, which switched off the spacecraft's transmitter, was sent to ''Planck'' on 23 October 2013 at 12:10:27 UTC.


Results

''Planck'' started its First All-Sky Survey on 13 August 2009. In September 2009, the
European Space Agency The European Space Agency (ESA) is a 23-member International organization, international organization devoted to space exploration. With its headquarters in Paris and a staff of around 2,547 people globally as of 2023, ESA was founded in 1975 ...
announced the preliminary results from the ''Planck First Light Survey'', which was performed to demonstrate the stability of the instruments and the ability to calibrate them over long periods. The results indicated that the data quality is excellent. On 15 January 2010 the mission was extended by 12 months, with observation continuing until at least the end of 2011. After the successful conclusion of the First Survey, the spacecraft started its Second All Sky Survey on 14 February 2010. The last observations for the Second All Sky Survey were made on 28 May 2010. Some planned pointing list data from 2009 has been released publicly, along with a video visualization of the surveyed sky. On 17 March 2010, the first ''Planck'' photos were published, showing dust concentration within 500 light years from the Sun. On 5 July 2010, the ''Planck'' mission delivered its first all-sky image. The first public scientific result of ''Planck'' is the Early-Release Compact-Source Catalogue, released during the January 2011 ''Planck conference'' in Paris. On 5 May 2014 a map of the galaxy's magnetic field created using ''Planck'' was published. The Planck team and principal investigators Nazzareno Mandolesi and Jean-Loup Puget shared the 2018 Gruber Prize in Cosmology. Puget was also awarded the 2018 Shaw Prize in Astronomy.


2013 data release

On 21 March 2013, the European-led research team behind the ''Planck'' cosmology probe released the mission's all-sky map of the cosmic microwave background. This map suggests the Universe is slightly older than thought: according to the map, subtle fluctuations in temperature were imprinted on the deep sky when the Universe was about 370,000 years old. The imprint reflects ripples that arose as early in the existence of the Universe as the first nonillionth (10−30) of a second. It is theorised that these ripples gave rise to the present vast cosmic web of galactic clusters and
dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...
. The 2013 release found an asymmetry in the statistics of the CMB with respect to viewing angle in the sky, determining that "deviations from isotropy have been found and demonstrated to be robust against component separation algorithm, mask choice and frequency dependence", more commonly known as the
Axis of evil (cosmology) The "axis of evil" is a name given to a purported correlation between the plane of the Solar System and aspects of the cosmic microwave background (CMB). Such a correlation would give the plane of the Solar System and hence the location of Earth a ...
. According to the team, the Universe is billion-years-old, and contains ordinary matter, dark matter and
dark energy In physical cosmology and astronomy, dark energy is a proposed form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. It also slows the rate of structure format ...
.See Table 9 in The
Hubble constant Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther a galaxy is from the Earth, the faste ...
was also measured to be .


2015 data release

Results from an analysis of ''Planck'' full mission were made public on 1 December 2014 at a conference in
Ferrara Ferrara (; ; ) is a city and ''comune'' (municipality) in Emilia-Romagna, Northern Italy, capital of the province of Ferrara. it had 132,009 inhabitants. It is situated northeast of Bologna, on the Po di Volano, a branch channel of the main ...
, Italy. A full set of papers detailing the mission results were released in February 2015. Some of the results include: * More agreement with previous WMAP results on parameters such as the density and distribution of matter in the Universe, as well as more accurate results with less margin of error. * Confirmation of the Universe having a 26% content of dark matter. These results also raise related questions about the
positron The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatt ...
excess over
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
s detected by the Alpha Magnetic Spectrometer, an experiment on the
International Space Station The International Space Station (ISS) is a large space station that was Assembly of the International Space Station, assembled and is maintained in low Earth orbit by a collaboration of five space agencies and their contractors: NASA (United ...
. Previous research suggested that positrons could be created by the collision of dark matter particles, which could only occur if the probability of dark matter collisions is significantly higher now than in the early Universe. ''Planck'' data suggests that the probability of such collisions must remain constant over time to account for the structure of the Universe, negating the previous theory. * Validation of the simplest models of
inflation In economics, inflation is an increase in the average price of goods and services in terms of money. This increase is measured using a price index, typically a consumer price index (CPI). When the general price level rises, each unit of curre ...
, thus giving the
Lambda-CDM model The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components: # a cosmological constant, denoted by lambda (Λ), associated with dark energy; # the postulated cold dark mat ...
stronger support. * That there are likely only three types of
neutrino A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...
s, with a fourth proposed
sterile neutrino Sterile neutrinos (or inert neutrinos) are hypothetical particles (neutral leptons – neutrinos) that interact only via gravity and not via any of the other fundamental interactions of the Standard Model. The term ''sterile neutrino'' is used to ...
unlikely to exist. Project scientists worked too with BICEP2 scientists to release joint research in 2015 answering whether a signal detected by BICEP2 was evidence of primordial
gravitational wave Gravitational waves are oscillations of the gravitational field that Wave propagation, travel through space at the speed of light; they are generated by the relative motion of gravity, gravitating masses. They were proposed by Oliver Heaviside i ...
s, or was simple
background noise Background noise or ambient noise is any sound other than the sound being monitored (primary sound). Background noise is a form of noise pollution or interference. Background noise is an important concept in setting noise levels. Background no ...
from dust in the Milky Way galaxy. Their results suggest the latter.


2018 final data release


See also

* DustPedia *
Lambda-CDM model The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components: # a cosmological constant, denoted by lambda (Λ), associated with dark energy; # the postulated cold dark mat ...
* List of cosmological computation software *
Observational cosmology Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. Early observations The science of physical cosmology as it is ...
*
Physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fu ...
*
Terahertz radiation Terahertz radiation – also known as submillimeter radiation, terahertz waves, tremendously high frequency (THF), T-rays, T-waves, T-light, T-lux or THz – consists of electromagnetic waves within the International Telecommunicat ...


References


Further reading

*


External links

* ESA *
''Planck'' mission website
*
''Planck'' science website
*
''Planck'' operations website
*
''Planck'' science results website
* NASA *
''Planck'' mission website
*

{{Authority control European Space Agency space probes Cosmic microwave background experiments Space telescopes Infrared telescopes Submillimetre telescopes Derelict satellites in heliocentric orbit Spacecraft using Lissajous orbits Space probes launched in 2009 2013 disestablishments Max Planck