The Hill sphere is a common model for the calculation of a gravitational sphere of influence . It is the most commonly used model to calculate the spatial extent of gravitational influence of an astronomical body ( m ) in which it dominates over the gravitational influence of other bodies, particularly a primary ( M ). It is sometimes confused with other models of gravitational influence, such as the Laplace sphere or being named the Roche sphere , the latter causing confusion with the Roche limit . It was defined by the American astronomer George William Hill , based on the work of the French astronomer Édouard Roche .
62-632: Wide-field Infrared Survey Explorer ( WISE , observatory code C51, Explorer 92 and MIDEX-6 ) was a NASA infrared astronomy space telescope in the Explorers Program launched in December 2009. WISE discovered thousands of minor planets and numerous star clusters . Its observations also supported the discovery of the first Y-type brown dwarf and Earth trojan asteroid . WISE performed an all-sky astronomical survey with images in 3.4, 4.6, 12 and 22 μm wavelength range bands, over ten months using
124-454: A {\displaystyle a} , and an eccentricity of e {\displaystyle e} , then the Hill radius or sphere, R H {\displaystyle R_{\mathrm {H} }} of the less massive body, calculated at the pericenter , is approximately: When eccentricity is negligible (the most favourable case for orbital stability), this expression reduces to
186-585: A Mercury-crossing asteroid that has a moon (named Squannit), measures 22 km in radius. A typical extrasolar " hot Jupiter ", HD 209458 b , has a Hill sphere radius of 593,000 km, about eight times its physical radius of approx 71,000 km. Even the smallest close-in extrasolar planet, CoRoT-7b , still has a Hill sphere radius (61,000 km), six times its physical radius (approx 10,000 km). Therefore, these planets could have small moons close in, although not within their respective Roche limits . The following table and logarithmic plot show
248-481: A zero-velocity surface in space which cannot be passed, the contour of the Jacobi integral . When the object's energy is low, the zero-velocity surface completely surrounds the less massive body (of this restricted three-body system ), which means the third object cannot escape; at higher energy, there will be one or more gaps or bottlenecks by which the third object may escape the less massive body and go into orbit around
310-425: A "two-body problem"—are "completely integrable ([meaning]...there exists one independent integral or constraint per degree of freedom)" and thus an exact, analytic solution, the interactions of three (or more) such bodies "cannot be deduced analytically", requiring instead solutions by numerical integration, when possible. This is the case, unless the negligible mass of one of the three bodies allows approximation of
372-605: A 40 cm (16 in) diameter infrared telescope in Earth orbit . After its solid hydrogen coolant depleted, it was placed in hibernation mode in February 2011. In 2013, NASA reactivated the WISE telescope to search for near-Earth objects (NEO), such as comets and asteroids , that could collide with Earth. The reactivation mission was called Near-Earth Object Wide-field Infrared Survey Explorer ( NEOWISE ). As of August 2023, NEOWISE
434-499: A binomial expansion to leading order in r H / r {\displaystyle r_{\mathrm {H} }/r} , can be written as Hence, the relation stated above If the orbit of the secondary about the primary is elliptical, the Hill radius is maximum at the apocenter , where r {\displaystyle r} is largest, and minimum at the pericenter of the orbit. Therefore, for purposes of stability of test particles (for example, of small satellites),
496-410: A few light years from the solar system; the first Earth trojan ; and the most luminous galaxies in the universe. Nearby stars discovered using WISE within 30 light years: The nearest brown dwarfs discovered by WISE within 20 light-years include: Before the discovery of Luhman 16 in 2013, WISE 1506+7027 at a distance of 11.1 +2.3 −1.3 light-years was suspected to be closest brown dwarf on
558-520: A full-sky survey, then an additional three months of survey until cryogenic coolant (which kept the instruments at 17 K) ran out. The partial second survey pass facilitated the study of changes (e.g. orbital movement) in observed objects. On 8 November 2007, the House Committee on Science and Technology 's Subcommittee on Space and Aeronautics held a hearing to examine the status of NASA's Near-Earth Object (NEO) survey program. The prospect of using WISE
620-486: A long history under Wright's efforts and was first funded by NASA in 1999 as a candidate for a NASA Medium-class Explorer (MIDEX) mission under the name Next Generation Sky Survey (NGSS). The history of the program from 1999 to date is briefly summarized as follows: Hibernation Reactivation The launch of the Delta II launch vehicle carrying the WISE spacecraft was originally scheduled for 11 December 2009. This attempt
682-703: A mission would have allowed use of the 3.4 and 4.6 μm detectors after the last of cryo-coolant had been exhausted, with the goal of completing a second sky survey to detect additional objects and obtain parallax data on putative brown dwarf stars. NASA extended the mission in October 2010 to search for near-Earth objects (NEO). By October 2010, over 33,500 new asteroids and comets were discovered, and over 154,000 Solar System objects were observed by WISE. While active it found dozens of previously unknown asteroids every day. In total, it captured more than 2.7 million images during its primary mission. In October 2010, NASA extended
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#1733085029603744-415: A revised version was subsequently published. The same year, an analysis of 100 asteroids by an independent group of astronomers gave results consistent with the original WISE analysis. The Allwise co-added images were intentionally blurred, which is optimal for detecting isolated point sources. This has the disadvantage that many sources are not detected in crowded regions. The unofficial, unblurred coadds of
806-552: A robotic spacecraft could intercept and redirect to orbit the Moon. The extended mission would be for three years at a cost of US$ 5 million per year, and was brought about in part due to calls for NASA to step up asteroid detection after the Chelyabinsk meteor exploded over Russia in February 2013. NEOWISE was successfully taken out of hibernation in September 2013. With its coolant depleted,
868-538: A total of 399 near-Earth objects (NEOs), including 2016 WF 9 and C/2016 U 1 , discovered by the spacecraft: Of the 365 near-Earth asteroids (NEAs), 66 of them are considered potentially hazardous asteroids (PHAs), a subset of the much larger family of NEOs, but particularly more likely to hit Earth and cause significant destruction. NEOs can be divided into NECs (comets only) and NEAs (asteroids only), and further into subcategories such as Atira asteroids , Aten asteroids , Apollo asteroids , Amor asteroids and
930-459: Is 0.14. The telescope was turned on again in 2013, and by December 2013 the telescope had cooled down sufficiently to be able to resume observations. Between then and May 2017, the telescope made almost 640,000 detections of over 26,000 previously known objects including asteroids and comets. In addition, it discovered 416 new objects and about a quarter of those were near-Earth objects classification. As of July 2024, WISE / NEOWISE statistics lists
992-540: Is 40% through the 20th coverage of the full sky since the start of the Reactivation mission." On 13 December 2023, the Jet Propulsion Laboratory (JPL), announced that the satellite would enter a low orbit causing it to be unusable by early 2025. Increased solar activity as the sun approaches solar maximum during Solar cycle 25 is expected to increase atmospheric drag causing orbital decay . The satellite
1054-483: Is a list of observatory codes ( IAU codes or MPC codes ) published by the Minor Planet Center . For a detailed description, see observations of small Solar System bodies . bla de Vallbona Hill sphere To be retained by a more gravitationally attracting astrophysical object—a planet by a more massive star, a moon by a more massive planet—the less massive body must have an orbit that lies within
1116-399: Is expected to subsequently reenter the earth's atmosphere. On 8 August 2024, the Jet Propulsion Laboratory updated its estimate of orbital decay to sometime in late 2024 and announced that NEOWISE's science survey had ended on 31 July. NEOWISE entered and burnt up in the earth's atmosphere on 1 November 2024. On 14 April 2011, a preliminary release of WISE data was made public, covering 57% of
1178-460: Is represented mathematically as follows: where, in this representation, major axis "a" can be understood as the "instantaneous heliocentric distance" between the two masses (elsewhere abbreviated r p ). More generally, if the less massive body, m 2 {\displaystyle m2} , orbits a more massive body (m1, e.g., as a planet orbiting around the Sun) and has a semi-major axis
1240-457: Is therefore not at risk of being pulled into an independent orbit around the Sun. The earlier eccentricity-ignoring formula can be re-stated as follows: where M is the sum of the interacting masses. The expression for the Hill radius can be found by equating gravitational and centrifugal forces acting on a test particle (of mass much smaller than m {\displaystyle m} ) orbiting
1302-494: The Carina constellation showing infrared light in false color from three of WISE's four wavelength bands: Blue, green and red corresponding to 3.4, 4.6, and 12 μm, respectively. On 14 January 2010, the WISE mission started its official sky survey. The WISE group's bid for continued funding for an extended "warm mission" scored low by a NASA review board, in part because of a lack of outside groups publishing on WISE data. Such
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#17330850296031364-500: The galactic nucleus or other more massive stars). A more complex example is the one at right, the Earth's Hill sphere, which extends between the Lagrange points L 1 and L 2 , which lie along the line of centers of the Earth and the more massive Sun. The gravitational influence of the less massive body is least in that direction, and so it acts as the limiting factor for the size of
1426-522: The list of nearest stars (also see § Map with nearby WISE stars ) . Directly imaged exoplanets first detected with WISE. See Definition of exoplanets : IAU working definition as of 2018 requires M planet ≤ 13 M J and M planet /M central < 0.04006. M min and M max are the lower and upper mass limit of the planet in Jupiter masses. M max =7.8<13 M max /M central =0.02<0.04 List of observatory codes This
1488-509: The terminator , its telescope pointing always to the opposite direction to the Earth, except for pointing towards the Moon , which was avoided, and its solar cells towards the Sun . Each image covers a 47 arcminute field of view (FoV), which means a 6 arcsecond resolution . Each area of the sky was scanned at least 10 times at the equator ; the poles were scanned at theoretically every revolution due to
1550-529: The 104 ton Space Shuttle at an orbit 300 km above the Earth, because a 104-ton object at that altitude has a Hill sphere of only 120 cm in radius, much smaller than a Space Shuttle. A sphere of this size and mass would be denser than lead , and indeed, in low Earth orbit , a spherical body must be more dense than lead in order to fit inside its own Hill sphere, or else it will be incapable of supporting an orbit. Satellites further out in geostationary orbit , however, would only need to be more than 6% of
1612-547: The Hill radius at the pericenter distance needs to be considered. To leading order in r H / r {\displaystyle r_{\mathrm {H} }/r} , the Hill radius above also represents the distance of the Lagrangian point L 1 from the secondary. The Hill sphere is only an approximation, and other forces (such as radiation pressure or the Yarkovsky effect ) can eventually perturb an object out of
1674-430: The Hill sphere; beyond that distance, a third object in orbit around the Earth would spend at least part of its orbit outside the Hill sphere, and would be progressively perturbed by the tidal forces of the more massive body, the Sun, eventually ending up orbiting the latter. For two massive bodies with gravitational potentials and any given energy of a third object of negligible mass interacting with them, one can define
1736-730: The Solar System, including twenty comets. During its primary and extended missions, the spacecraft delivered characterizations of 158,000 minor planets, including more than 35,000 newly discovered objects. After completing a full scan of the asteroid belt for the NEOWISE mission, the spacecraft was put into hibernation on 1 February 2011. The spacecraft was briefly contacted to check its status on 20 September 2012. On 21 August 2013, NASA announced it would recommission NEOWISE to continue its search for near-Earth objects (NEO) and potentially dangerous asteroids. It would additionally search for asteroids that
1798-629: The WISE All-Sky data release. This is a factor of 1,000 times better sensitivity than the survey completed in 1983 by the IRAS satellite in the 12 and 23 μm bands, and a factor of 500,000 times better than the 1990s survey by the Cosmic Background Explorer (COBE) satellite at 3.3 and 4.7 μm. On the other hand, IRAS could also observe 60 and 100 μm wavelengths. The primary mission lasted 10 months: one month for checkout, six months for
1860-438: The WISE imaging (unWISE) creates sharp images and masks defects and transients. unWISE coadded images can be searched by coordinates on the unWISE website. unWISE images are used for the citizen science projects Disk Detective and Backyard Worlds . In 2019, a preliminary catalog was released. The catalog is called CatWISE. This catalog combines the WISE and NEOWISE data and provides photometry at 3.4 and 4.6 μm. It uses
1922-520: The WISE telescope was divided between Ball Aerospace & Technologies (spacecraft, operations support), SSG Precision Optronics, Inc. (telescope, optics, scan mirror), DRS Technologies and Rockwell International (focal planes), Lockheed Martin ( cryostat , cooling for the telescope), and Space Dynamics Laboratory (instruments, electronics, and testing). The program was managed through the Jet Propulsion Laboratory . The WISE instrument
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1984-418: The combination of reflected light and thermal infrared emission, using a thermal model of the asteroid to estimate both its diameter and its albedo. In May 2016, technologist Nathan Myhrvold questioned the precision of the diameters and claimed systemic errors arising from the spacecraft's design. The original version of his criticism itself faced criticism for its methodology and did not pass peer review , but
2046-554: The density of water to fit inside their own Hill sphere. Within the Solar System , the planet with the largest Hill radius is Neptune , with 116 million km, or 0.775 au; its great distance from the Sun amply compensates for its small mass relative to Jupiter (whose own Hill radius measures 53 million km). An asteroid from the asteroid belt will have a Hill sphere that can reach 220,000 km (for 1 Ceres ), diminishing rapidly with decreasing mass. The Hill sphere of 66391 Moshup ,
2108-399: The dust. Infrared measurements from the WISE astronomical survey have been particularly effective at unveiling previously undiscovered star clusters . Examples of such embedded star clusters are Camargo 18, Camargo 440, Majaess 101, and Majaess 116. In addition, galaxies of the young Universe and interacting galaxies, where star formation is intensive, are bright in infrared. On this wavelength
2170-462: The former radius ) has been described as "the region around a planetary body where its own gravity (compared to that of the Sun or other nearby bodies) is the dominant force in attracting satellites," both natural and artificial. As described by de Pater and Lissauer, all bodies within a system such as the Sun's Solar System "feel the gravitational force of one another", and while the motions of just two gravitationally interacting bodies—constituting
2232-404: The gravitational potential represented by the more massive body's Hill sphere. That moon would, in turn, have a Hill sphere of its own, and any object within that distance would tend to become a satellite of the moon, rather than of the planet itself. One simple view of the extent of the Solar System is that it is bounded by the Hill sphere of the Sun (engendered by the Sun's interaction with
2294-571: The interstellar gas clouds are also detectable, as well as proto-planetary discs. WISE satellite was expected to find at least 1,000 of those proto-planetary discs. The WISE satellite bus was built by Ball Aerospace & Technologies in Boulder, Colorado . The spacecraft is derived from the Ball Aerospace & Technologies RS-300 spacecraft architecture, particularly the NEXTSat spacecraft built for
2356-415: The mission by one month with a program called Near-Earth Object WISE ( NEOWISE ). Due to its success, the program was extended a further three months. The focus was to look for asteroids and comets close to Earth orbit, using the remaining post-cryogenic detection capability (two of four detectors on WISE work without cryogenic). In February 2011, NASA announced that NEOWISE had discovered many new objects in
2418-465: The more massive one. If the energy is at the border between these two cases, then the third object cannot escape, but the zero-velocity surface confining it touches a larger zero-velocity surface around the less massive body at one of the nearby Lagrange points, forming a cone-like point there. At the opposite side of the less massive body, the zero-velocity surface gets close to the other Lagrange point. The Hill radius or sphere (the latter defined by
2480-464: The one presented above. In the Earth-Sun example, the Earth ( 5.97 × 10 kg ) orbits the Sun ( 1.99 × 10 kg ) at a distance of 149.6 million km, or one astronomical unit (AU). The Hill sphere for Earth thus extends out to about 1.5 million km (0.01 AU). The Moon's orbit, at a distance of 0.384 million km from Earth, is comfortably within the gravitational sphere of influence of Earth and it
2542-470: The overlapping of the images. The produced image library contains data on the local Solar System , the Milky Way , and the more distant Universe . Among the objects WISE studied are asteroids, cool and dim stars such as brown dwarfs , and the most luminous infrared galaxies . WISE was not able to detect Kuiper belt objects , because their temperatures are too low. Pluto is the only Kuiper belt object that
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2604-430: The potentially hazardous asteroids (PHAs). NEOWISE has provided an estimate of the size of over 1,850 near-Earth objects. NEOWISE mission was extended for two more years (1 July 2021 – 30 June 2023). As of June 2021 NEOWISE's replacement, the next-generation NEO Surveyor , is scheduled to launch in 2028, and will greatly expand on what humans have learned, and continue to learn, from NEOWISE. "As of August 2023 NEOWISE
2666-510: The primary and the secondary body, the force balance requires that where G {\displaystyle G} is the gravitational constant and Ω = G M r 3 {\displaystyle \Omega ={\sqrt {\frac {GM}{r^{3}}}}} is the ( Keplerian ) angular velocity of the secondary about the primary (assuming that m ≪ M {\displaystyle m\ll M} ). The above equation can also be written as which, through
2728-439: The primary is larger than the region for prograde orbits at a large distance from the primary. This was thought to explain the preponderance of retrograde moons around Jupiter; however, Saturn has a more even mix of retrograde/prograde moons so the reasons are more complicated. It is possible for a Hill sphere to be so small that it is impossible to maintain an orbit around a body. For example, an astronaut could not have orbited
2790-405: The secondary body. Assume that the distance between masses M {\displaystyle M} and m {\displaystyle m} is r {\displaystyle r} , and that the test particle is orbiting at a distance r H {\displaystyle r_{\mathrm {H} }} from the secondary. When the test particle is on the line connecting
2852-526: The sky observed by the spacecraft. On 14 March 2012, a new atlas and catalog of the entire infrared sky as imaged by WISE was released to the astronomic community. On 31 July 2012, NEOWISE Post-Cryo Preliminary Data was released. A release called AllWISE, combining all data, was released on 13 November 2013. NEOWISE data is released annually. The WISE data include diameter estimates of intermediate precision, better than from an assumed albedo but not nearly as precise as good direct measurements, can be obtained from
2914-423: The spacecraft's temperature was reduced from 200 K (−73 °C; −100 °F) — a relatively high temperature resulting from its hibernation — to an operating temperature of 75 K (−198.2 °C; −324.7 °F) by having the telescope stare into deep space. Its instruments were then re-calibrated, and the first post-hibernation photograph was taken on 19 December 2013. The post-hibernation NEOWISE mission
2976-399: The sphere. As stated, the satellite (third mass) should be small enough that its gravity contributes negligibly. Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term; it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. The region of stability for retrograde orbits at a large distance from
3038-553: The successful Orbital Express mission launched on 9 March 2007. The flight system has an estimated mass of 560 kg (1,230 lb). The spacecraft is three-axis stabilized , with body-fixed solar arrays . It uses a high-gain antenna in the Ku-band to transmit to the ground through the Tracking and Data Relay Satellite System (TDRSS) geostationary system . Ball also performed the testing and flight system integration. Construction of
3100-449: The system as a two-body problem, known formally as a "restricted three-body problem". For such two- or restricted three-body problems as its simplest examples—e.g., one more massive primary astrophysical body, mass of m1, and a less massive secondary body, mass of m2—the concept of a Hill radius or sphere is of the approximate limit to the secondary mass's "gravitational dominance", a limit defined by "the extent" of its Hill sphere, which
3162-667: The unWISE images and the Allwise pipeline to detect sources. CatWISE includes fainter sources and far more accurate measurement of the motion of objects. The catalog is used to extend the number of discovered brown dwarfs, especially the cold and faint Y dwarfs. CatWISE is led by Jet Propulsion Laboratory (JPL), California Institute of Technology , with funding from NASA's Astrophysics Data Analysis Program. The CatWISE preliminary catalog can be accessed through Infrared Science Archive (IRSA). In addition to numerous comets and minor planets, WISE and NEOWISE discovered many brown dwarfs , some just
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#17330850296033224-419: Was 1,000 times more sensitive than prior surveys such as IRAS , AKARI , and COBE 's DIRBE . A month-long checkout after launch found all spacecraft systems functioning normally and both the low- and high-rate data links to the operations center working properly. The instrument cover was successfully jettisoned on 29 December 2009. A first light image was released on 6 January 2010: an eight-second exposure in
3286-690: Was 40% through the 20th coverage of the full sky. Science operations and data processing for WISE and NEOWISE take place at the Infrared Processing and Analysis Center at the California Institute of Technology in Pasadena, California . The WISE All-Sky (WISEA) data, including processed images, source catalogs and raw data, was released to the public on 14 March 2012, and is available at the Infrared Science Archive . The NEOWISE mission
3348-481: Was announced in late 2010 based on early data. In July 2011, it was announced that WISE had discovered the first Earth trojan asteroid , 2010 TK 7 . Also, the third-closest star system, Luhman 16 . As of May 2018, WISE / NEOWISE had also discovered 290 near-Earth objects and comets (see section below) . The WISE mission is led by Edward L. Wright of the University of California, Los Angeles . The mission has
3410-553: Was anticipated to discover 150 previously unknown near-Earth objects and to learn more about the characteristics of 2,000 known asteroids. Few objects smaller than 100 m (330 ft) in diameter were detected by NEOWISE's automated detection software, known as the WISE Moving Object Processing Software (WMOPS), because it requires five or more detections to be reported. The average albedo of asteroids larger than 100 m (330 ft) discovered by NEOWISE
3472-589: Was built by the Space Dynamics Laboratory in Logan, Utah . WISE surveyed the sky in four wavelengths of the infrared band, at a very high sensitivity. Its design specified as goals that the full sky atlas of stacked images it produced have 5-sigma sensitivity limits of 120, 160, 650, and 2600 microjanskies (μJy) at 3.3, 4.7, 12, and 23 μm (aka microns ). WISE achieved at least 68, 98, 860, and 5400 μJy; 5 sigma sensitivity at 3.4, 4.6, 12, and 22 μm for
3534-414: Was detected. It was able to detect any objects warmer than 70–100 K . A Neptune -sized object would be detectable out to 700 Astronomical unit (AU), a Jupiter mass object out to 1 light year (63,000 AU), where it would still be within the Sun's zone of gravitational control . A larger object of 2–3 Jupiter masses would be visible at a distance of up to 7–10 light years. At the time of planning, it
3596-608: Was estimated that WISE would detect about 300,000 main-belt asteroids , of which approximately 100,000 will be new, and some 700 Near-Earth objects (NEO) including about 300 undiscovered. That translates to about 1000 new main-belt asteroids per day, and 1–3 NEOs per day. The peak of magnitude distribution for NEOs will be about 21–22 V . WISE would detect each typical Solar System object 10–12 times over about 36 hours in intervals of 3 hours. Star formation , which are covered by interstellar dust , are detectable in infrared , since at this wavelength electromagnetic radiation can penetrate
3658-459: Was originally expected to end in early 2025 with the satellite reentering the atmosphere some time after. However, the NEOWISE mission concluded its science survey on 31 July 2024 with the satellite expected to reenter Earth's atmosphere later the same year (2 November 2024). This decision was made due to increased solar activity hastening the decay of its orbit and the lack of an onboard propulsion system for orbital maintenance. The onboard transmitter
3720-563: Was proposed by NASA officials. NASA officials told Committee staff that NASA plans to use WISE to detect [near-Earth objects in addition to performing its science goals. It was projected that WISE could detect 400 NEOs (or roughly 2% of the estimated NEO population of interest) within its one-year mission. By October 2010, over 33,500 new asteroids and comets were discovered, and nearly 154,000 Solar System objects had been observed by WISE. Discovery of an ultra-cool brown dwarf, WISEPC J045853.90+643451.9 , about 10~30 light years away from Earth,
3782-636: Was scrubbed to correct a problem with a booster rocket steering engine. The launch was then rescheduled for 14 December 2009. The second attempt launched on time at 14:09:33 UTC from Vandenberg Air Force Base in California . The launch vehicle successfully placed the WISE spacecraft into the planned polar orbit at an altitude of 525 km (326 mi) above the Earth. WISE avoided the problem that affected Wide Field Infrared Explorer (WIRE), which failed within hours of reaching orbit in March 1999. In addition, WISE
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#17330850296033844-465: Was turned off on 8 August, marking the formal decommissioning of the spacecraft. The mission was planned to create infrared images of 99% of the sky, with at least eight images made of each position on the sky in order to increase accuracy. The spacecraft was placed in a 525 km (326 mi), circular, polar, Sun-synchronous orbit for its ten-month mission, during which it has taken 1.5 million images, one every 11 seconds. The satellite orbited above
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