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130-525: Stars do exist in the Hertzsprung gap region, but because they move through this section of the Hertzsprung–Russell diagram very quickly in comparison to the lifetime of the star (thousands of years, compared to millions or billions of years for the lifetime of the star), that portion of the diagram is less densely populated. Full Hertzsprung–Russell diagrams of the 11,000 Hipparcos mission targets show

260-495: A cyclic quadrilateral , today called Ptolemy's theorem because its earliest extant source is a proof in the Almagest (I.10). The stereographic projection was ambiguously attributed to Hipparchus by Synesius (c. 400 AD), and on that basis Hipparchus is often credited with inventing it or at least knowing of it. However, some scholars believe this conclusion to be unjustified by available evidence. The oldest extant description of

390-435: A 7-parameter, or even 9-parameter model fit (compared to the standard 5-parameter model), and typically such models could be enhanced in complexity until suitable fits were obtained. A complete orbit, requiring 7 elements, was determined for 45 systems. Orbital periods close to one year can become degenerate with the parallax, resulting in unreliable solutions for both. Triple or higher-order systems provided further challenges to

520-448: A comprehensive system of cross-checking and validation, and is described in detail in the published catalogue. A detailed optical calibration model was included to map the transformation from sky to instrumental coordinates. Its adequacy could be verified by the detailed measurement residuals. The Earth's orbit, and the satellite's orbit with respect to the Earth , were essential for describing

650-672: A corruption of another value attributed to a Babylonian source: 365 + ⁠ 1 / 4 ⁠ + ⁠ 1 / 144 ⁠ days (= 365.25694... days = 365 days 6 hours 10 min). It is not clear whether Hipparchus got the value from Babylonian astronomers or calculated by himself. Before Hipparchus, astronomers knew that the lengths of the seasons are not equal. Hipparchus made observations of equinox and solstice, and according to Ptolemy ( Almagest III.4) determined that spring (from spring equinox to summer solstice) lasted 94 1 ⁄ 2 days, and summer (from summer solstice to autumn equinox) 92 + 1 ⁄ 2 days. This

780-460: A difference of approximately one day in approximately 300 years. So he set the length of the tropical year to 365 + 1 ⁄ 4 − 1 ⁄ 300 days (= 365.24666... days = 365 days 5 hours 55 min, which differs from the modern estimate of the value (including earth spin acceleration), in his time of approximately 365.2425 days, an error of approximately 6 min per year, an hour per decade, and ten hours per century. Between

910-514: A handful of stars in that region. Well-known stars inside of or towards the end of the Hertzsprung gap include: Canopus , Iota Carinae , and Upsilon Carinae are also starting to enter the gap. This article about stellar evolution is a stub . You can help Misplaced Pages by expanding it . Hipparcos Hipparcos was a scientific satellite of the European Space Agency (ESA), launched in 1989 and operated until 1993. It

1040-413: A long orbital period such that non-linear motions of the photocentre were insignificant over the short (3-year) measurement duration, the binary nature of the star would pass unrecognised by Hipparcos , but could show as a Hipparcos proper motion discrepant compared to those established from long temporal baseline proper motion programmes on ground. Higher-order photocentric motions could be represented by

1170-718: A mean number of 110 observations per star, and a median photometric precision (Hp<9 magnitude) of 0.0015 magnitude, with 11,597 entries were identified as variable or possibly-variable. For the star mapper results, the data analysis was carried out by the Tycho Data Analysis Consortium (TDAC). The Tycho Catalogue comprises more than one million stars with 20–30 milliarc-sec astrometry and two-colour (B and V band) photometry. The final Hipparcos and Tycho Catalogues were completed in August 1996. The catalogues were published by European Space Agency (ESA) on behalf of

1300-502: A more detailed discussion. Pliny ( Naturalis Historia II.X) tells us that Hipparchus demonstrated that lunar eclipses can occur five months apart, and solar eclipses seven months (instead of the usual six months); and the Sun can be hidden twice in thirty days, but as seen by different nations. Ptolemy discussed this a century later at length in Almagest VI.6. The geometry, and the limits of

1430-414: A more secure empirical basis. Observationally, the objective was to provide the positions, parallaxes , and annual proper motions for some 100,000 stars with an unprecedented accuracy of 0.002  arcseconds , a target in practice eventually surpassed by a factor of two. The name of the space telescope, "Hipparcos", was an acronym for High Precision Parallax Collecting Satellite , and it also reflected

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1560-450: A multinational context. Its acceptance within the European Space Agency 's scientific programme, in 1980, was the result of a lengthy process of study and lobbying . The underlying scientific motivation was to determine the physical properties of the stars through the measurement of their distances and space motions, and thus to place theoretical studies of stellar structure and evolution, and studies of galactic structure and kinematics, on

1690-439: A popular poem by Aratus based on the work by Eudoxus . Hipparchus also made a list of his major works that apparently mentioned about fourteen books, but which is only known from references by later authors. His famous star catalog was incorporated into the one by Ptolemy and may be almost perfectly reconstructed by subtraction of two and two-thirds degrees from the longitudes of Ptolemy's stars . The first trigonometric table

1820-420: A sensitive field of view of about 38-arc-sec diameter converted the modulated light into a sequence of photon counts (with a sampling frequency of 1200 Hz ) from which the phase of the entire pulse train from a star could be derived. The apparent angle between two stars in the combined fields of view, modulo the grid period, was obtained from the phase difference of the two star pulse trains. Originally targeting

1950-499: A simpler sexagesimal system dividing a circle into 60 parts. Hipparchus also adopted the Babylonian astronomical cubit unit ( Akkadian ammatu , Greek πῆχυς pēchys ) that was equivalent to 2° or 2.5° ('large cubit'). Hipparchus probably compiled a list of Babylonian astronomical observations; Gerald J. Toomer , a historian of astronomy, has suggested that Ptolemy's knowledge of eclipse records and other Babylonian observations in

2080-532: A table giving the daily motion of the Moon according to the date within a long period. However, the Greeks preferred to think in geometrical models of the sky. At the end of the third century BC, Apollonius of Perga had proposed two models for lunar and planetary motion: Apollonius demonstrated that these two models were in fact mathematically equivalent. However, all this was theory and had not been put to practice. Hipparchus

2210-525: A tight range of only approximately ± 1 ⁄ 2 hour, guaranteeing (after division by 4,267) an estimate of the synodic month correct to one part in order of magnitude 10 million. Hipparchus could confirm his computations by comparing eclipses from his own time (presumably 27 January 141 BC and 26 November 139 BC according to Toomer ) with eclipses from Babylonian records 345 years earlier ( Almagest IV.2 ). Later al-Biruni ( Qanun VII.2.II) and Copernicus ( de revolutionibus IV.4) noted that

2340-449: A triangle formed by the two places and the Moon, and from simple geometry was able to establish a distance of the Moon, expressed in Earth radii. Because the eclipse occurred in the morning, the Moon was not in the meridian , and it has been proposed that as a consequence the distance found by Hipparchus was a lower limit. In any case, according to Pappus, Hipparchus found that the least distance

2470-485: Is 71 (from this eclipse), and the greatest 83 Earth radii. In the second book, Hipparchus starts from the opposite extreme assumption: he assigns a (minimum) distance to the Sun of 490 Earth radii. This would correspond to a parallax of 7′, which is apparently the greatest parallax that Hipparchus thought would not be noticed (for comparison: the typical resolution of the human eye is about 2′; Tycho Brahe made naked eye observation with an accuracy down to 1′). In this case,

2600-417: Is a function of time. The resulting effect of secular or perspective acceleration is the interpretation of a transverse acceleration actually arising from a purely linear space velocity with a significant radial component, with the positional effect proportional to the product of the parallax, the proper motion, and the radial velocity. At the accuracy levels of Hipparcos it is of (marginal) importance only for

2730-400: Is also close to an integer number of years (4,267 moons : 4,573 anomalistic periods : 4,630.53 nodal periods : 4,611.98 lunar orbits : 344.996 years : 344.982 solar orbits : 126,007.003 days : 126,351.985 rotations). What was so exceptional and useful about the cycle was that all 345-year-interval eclipse pairs occur slightly more than 126,007 days apart within

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2860-534: Is an acronym for HIgh Precision PARallax COllecting Satellite and also a reference to the ancient Greek astronomer Hipparchus of Nicaea, who is noted for applications of trigonometry to astronomy and his discovery of the precession of the equinoxes . By the second half of the 20th century, the accurate measurement of star positions from the ground was running into essentially insurmountable barriers to improvements in accuracy, especially for large-angle measurements and systematic terms. Problems were dominated by

2990-401: Is consistent with 94 + 1 ⁄ 4 and 92 + 1 ⁄ 2 days, an improvement on the results ( 94 + 1 ⁄ 2 and 92 + 1 ⁄ 2 days) attributed to Hipparchus by Ptolemy. Ptolemy made no change three centuries later, and expressed lengths for the autumn and winter seasons which were already implicit (as shown, e.g., by A. Aaboe ). Hipparchus also undertook to find

3120-467: Is generally imperceptible to astrometric measurements (in the plane of the sky), and therefore it is generally ignored in large-scale astrometric surveys. In practice, it can be measured as a Doppler shift of the spectral lines. More strictly, however, the radial velocity does enter a rigorous astrometric formulation. Specifically, a space velocity along the line-of-sight means that the transformation from tangential linear velocity to (angular) proper motion

3250-512: Is inconsistent with a premise of the Sun moving around the Earth in a circle at uniform speed. Hipparchus's solution was to place the Earth not at the center of the Sun's motion, but at some distance from the center. This model described the apparent motion of the Sun fairly well. It is known today that the planets , including the Earth, move in approximate ellipses around the Sun, but this was not discovered until Johannes Kepler published his first two laws of planetary motion in 1609. The value for

3380-411: Is post-Hipparchus so the direction of transmission is not settled by the tablets. Hipparchus was recognized as the first mathematician known to have possessed a trigonometric table , which he needed when computing the eccentricity of the orbits of the Moon and Sun. He tabulated values for the chord function, which for a central angle in a circle gives the length of the straight line segment between

3510-646: Is sometimes called the "father of astronomy", a title conferred on him by Jean Baptiste Joseph Delambre in 1817. Hipparchus was born in Nicaea ( Ancient Greek : Νίκαια ), in Bithynia . The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him in the period from 147 to 127 BC, and some of these are stated as made in Rhodes ; earlier observations since 162 BC might also have been made by him. His birth date ( c.  190  BC)

3640-408: Is sometimes used to study other long-period exoplanets , such as HR 5183 b . Hipparchus Hipparchus ( / h ɪ ˈ p ɑːr k ə s / ; Greek : Ἵππαρχος , Hípparkhos ; c.  190  – c.  120  BC) was a Greek astronomer , geographer , and mathematician . He is considered the founder of trigonometry , but is most famous for his incidental discovery of

3770-512: Is the Galactic latitude). Stars constituting this survey are flagged in the Hipparcos Catalogue . The second component comprised additional stars selected according to their scientific interest, with none fainter than about magnitude V=13 mag. These were selected from around 200 scientific proposals submitted on the basis of an Invitation for Proposals issued by ESA in 1982, and prioritised by

3900-526: Is the first astronomer known to attempt to determine the relative proportions and actual sizes of these orbits. Hipparchus devised a geometrical method to find the parameters from three positions of the Moon at particular phases of its anomaly. In fact, he did this separately for the eccentric and the epicycle model. Ptolemy describes the details in the Almagest IV.11. Hipparchus used two sets of three lunar eclipse observations that he carefully selected to satisfy

4030-485: Is visible simultaneously on half of the Earth, and the difference in longitude between places can be computed from the difference in local time when the eclipse is observed. His approach would give accurate results if it were correctly carried out but the limitations of timekeeping accuracy in his era made this method impractical. Late in his career (possibly about 135 BC) Hipparchus compiled his star catalog. Scholars have been searching for it for centuries. In 2022, it

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4160-474: The Almagest came from a list made by Hipparchus. Hipparchus's use of Babylonian sources has always been known in a general way, because of Ptolemy's statements, but the only text by Hipparchus that survives does not provide sufficient information to decide whether Hipparchus's knowledge (such as his usage of the units cubit and finger, degrees and minutes, or the concept of hour stars) was based on Babylonian practice. However, Franz Xaver Kugler demonstrated that

4290-533: The Almagest . Some claim the table of Hipparchus may have survived in astronomical treatises in India, such as the Surya Siddhanta . Trigonometry was a significant innovation, because it allowed Greek astronomers to solve any triangle, and made it possible to make quantitative astronomical models and predictions using their preferred geometric techniques. Hipparchus must have used a better approximation for π than

4420-479: The Centre de données astronomiques de Strasbourg . The Hipparcos results have affected a very broad range of astronomical research, which can be classified into three major themes: Associated with these major themes, Hipparcos has provided results in topics as diverse as Solar System science, including mass determinations of asteroids, Earth's rotation and Chandler wobble ; the internal structure of white dwarfs ;

4550-529: The Hipparcos and Tycho catalogues. A detailed review of the Hipparcos scientific literature between 1997 and 2007 was published in 2009, and a popular account of the project in 2010. Some examples of notable results include (listed chronologically): One controversial result has been the derived proximity, at about 120 parsecs, of the Pleiades cluster, established both from the original catalogue as well as from

4680-682: The Hipparcos Input Catalogue (HIC): each star in the final Hipparcos Catalogue was contained in the Input Catalogue. The Input Catalogue was compiled by the INCA Consortium over the period 1982–1989, finalised pre-launch, and published both digitally and in printed form. Although fully superseded by the satellite results, it nevertheless includes supplemental information on multiple system components as well as compilations of radial velocities and spectral types which, not observed by

4810-492: The Hubble Space Telescope ; photographic programmes to determine stellar proper motions with respect to extragalactic objects (Bonn, Kiev, Lick, Potsdam, Yale/San Juan); and comparison of Earth rotation parameters obtained by Very-long-baseline interferometry (VLBI) and by ground-based optical observations of Hipparcos stars. Although very different in terms of instruments, observational methods and objects involved,

4940-543: The Millennium Star Atlas : an all-sky atlas of one million stars to visual magnitude 11. Some 10,000 nonstellar objects are also included to complement the catalogue data. Between 1997 and 2007, investigations into subtle effects in the satellite attitude and instrument calibration continued. A number of effects in the data that had not been fully accounted for were studied, such as scan-phase discontinuities and micrometeoroid-induced attitude jumps. A re-reduction of

5070-495: The PPN formalism . Residuals were examined to establish limits on any deviations from this general relativistic value, and no significant discrepancies were found. The satellite observations essentially yielded highly accurate relative positions of stars with respect to each other, throughout the measurement period (1989–1993). In the absence of direct observations of extragalactic sources (apart from marginal observations of quasar 3C 273 )

5200-572: The eccentricity attributed to Hipparchus by Ptolemy is that the offset is 1 ⁄ 24 of the radius of the orbit (which is a little too large), and the direction of the apogee would be at longitude 65.5° from the vernal equinox . Hipparchus may also have used other sets of observations, which would lead to different values. One of his two eclipse trios' solar longitudes are consistent with his having initially adopted inaccurate lengths for spring and summer of 95 + 3 ⁄ 4 and 91 + 1 ⁄ 4 days. His other triplet of solar positions

5330-451: The precession of the equinoxes . Hipparchus was born in Nicaea , Bithynia , and probably died on the island of Rhodes , Greece. He is known to have been a working astronomer between 162 and 127 BC. Hipparchus is considered the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity . He was the first whose quantitative and accurate models for

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5460-476: The 4th century BC and Timocharis and Aristillus in the 3rd century BC already divided the ecliptic in 360 parts (our degrees , Greek: moira) of 60 arcminutes and Hipparchus continued this tradition. It was only in Hipparchus's time (2nd century BC) when this division was introduced (probably by Hipparchus's contemporary Hypsikles) for all circles in mathematics. Eratosthenes (3rd century BC), in contrast, used

5590-528: The Geography of Eratosthenes"). It is known to us from Strabo of Amaseia, who in his turn criticised Hipparchus in his own Geographia . Hipparchus apparently made many detailed corrections to the locations and distances mentioned by Eratosthenes. It seems he did not introduce many improvements in methods, but he did propose a means to determine the geographical longitudes of different cities at lunar eclipses (Strabo Geographia 1 January 2012). A lunar eclipse

5720-594: The Greek. Prediction of a solar eclipse, i.e., exactly when and where it will be visible, requires a solid lunar theory and proper treatment of the lunar parallax. Hipparchus must have been the first to be able to do this. A rigorous treatment requires spherical trigonometry , thus those who remain certain that Hipparchus lacked it must speculate that he may have made do with planar approximations. He may have discussed these things in Perí tēs katá plátos mēniaías tēs selēnēs kinēseōs ("On

5850-578: The Hellespont and are thought by many to be more likely possibilities for the eclipse Hipparchus used for his computations.) Ptolemy later measured the lunar parallax directly ( Almagest V.13), and used the second method of Hipparchus with lunar eclipses to compute the distance of the Sun ( Almagest V.15). He criticizes Hipparchus for making contradictory assumptions, and obtaining conflicting results ( Almagest V.11): but apparently he failed to understand Hipparchus's strategy to establish limits consistent with

5980-409: The Moon eclipsed while apparently it was not in exact opposition to the Sun. Parallax lowers the altitude of the luminaries; refraction raises them, and from a high point of view the horizon is lowered. Hipparchus and his predecessors used various instruments for astronomical calculations and observations, such as the gnomon , the astrolabe , and the armillary sphere . Hipparchus is credited with

6110-452: The Moon's equation of the center in the Hipparchan model.) Before Hipparchus, Meton , Euctemon , and their pupils at Athens had made a solstice observation (i.e., timed the moment of the summer solstice ) on 27 June 432 BC ( proleptic Julian calendar ). Aristarchus of Samos is said to have done so in 280 BC, and Hipparchus also had an observation by Archimedes . He observed

6240-743: The Scientific Proposal Selection Committee in consultation with the Input Catalogue Consortium. This selection had to balance 'a priori' scientific interest, and the observing programme's limiting magnitude, total observing time, and sky uniformity constraints. For the main mission results, the data analysis was carried out by two independent scientific teams, NDAC and FAST, together comprising some 100 astronomers and scientists, mostly from European (ESA-member state) institutes. The analyses, proceeding from nearly 1000 Gbit of satellite data acquired over 3.5 years, incorporated

6370-564: The Sun is on the equator (i.e., in one of the equinoctial points on the ecliptic ), but the shadow falls above or below the opposite side of the ring when the Sun is south or north of the equator. Ptolemy quotes (in Almagest III.1 (H195)) a description by Hipparchus of an equatorial ring in Alexandria; a little further he describes two such instruments present in Alexandria in his own time. Hipparchus applied his knowledge of spherical angles to

6500-558: The Tycho (and Tycho-2) Catalogue, provided two colours, roughly B and V in the Johnson UBV photometric system , important for spectral classification and effective temperature determination. Classical astrometry concerns only motions in the plane of the sky and ignores the star's radial velocity , i.e. its space motion along the line-of-sight. Whilst critical for an understanding of stellar kinematics, and hence population dynamics, its effect

6630-448: The apparent diameter of the Sun and Moon. Pappus of Alexandria described it (in his commentary on the Almagest of that chapter), as did Proclus ( Hypotyposis IV). It was a four-foot rod with a scale, a sighting hole at one end, and a wedge that could be moved along the rod to exactly obscure the disk of Sun or Moon. Hipparchus also observed solar equinoxes , which may be done with an equatorial ring : its shadow falls on itself when

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6760-407: The apparent diameters of the Sun and Moon with his diopter . Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. He found that at the mean distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into

6890-428: The associated steps of the analysis was eventually undertaken. This has led to improved astrometric accuracies for stars brighter than Hp=9.0 magnitude, reaching a factor of about three for the brightest stars (Hp<4.5 magnitude), while also underlining the conclusion that the Hipparcos Catalogue as originally published is generally reliable within the quoted accuracies. All catalogue data are available online from

7020-413: The center of the Earth, but the observer is at the surface—the Moon, Earth and observer form a triangle with a sharp angle that changes all the time. From the size of this parallax, the distance of the Moon as measured in Earth radii can be determined. For the Sun however, there was no observable parallax (we now know that it is about 8.8", several times smaller than the resolution of the unaided eye). In

7150-467: The change in the length of the day (see ΔT ) we estimate that the error in the assumed length of the synodic month was less than 0.2 second in the fourth century BC and less than 0.1 second in Hipparchus's time. It had been known for a long time that the motion of the Moon is not uniform: its speed varies. This is called its anomaly and it repeats with its own period; the anomalistic month . The Chaldeans took account of this arithmetically, and used

7280-462: The chords for angles with increments of 7.5°. In modern terms, the chord subtended by a central angle in a circle of given radius R equals R times twice the sine of half of the angle, i.e.: The now-lost work in which Hipparchus is said to have developed his chord table, is called Tōn en kuklōi eutheiōn ( Of Lines Inside a Circle ) in Theon of Alexandria 's fourth-century commentary on section I.10 of

7410-403: The circle, i.e., the mean apparent diameters are 360 ⁄ 650 = 0°33′14″. Like others before and after him, he also noticed that the Moon has a noticeable parallax , i.e., that it appears displaced from its calculated position (compared to the Sun or stars ), and the difference is greater when closer to the horizon. He knew that this is because in the then-current models the Moon circles

7540-473: The common focal plane. This complex mirror consisted of two mirrors tilted in opposite directions, each occupying half of the rectangular entrance pupil, and providing an unvignetted field of view of about 1° × 1°. The telescope used a system of grids, at the focal surface, composed of 2688 alternate opaque and transparent bands, with a period of 1.208 arc-sec (8.2 micrometre). Behind this grid system, an image dissector tube ( photomultiplier type detector) with

7670-432: The data processing. The highest accuracy photometric data were provided as a by-product of the main mission astrometric observations. They were made in a broad-band visible light passband , specific to Hipparcos , and designated H p . The median photometric precision, for H p <9 magnitude, was 0.0015 magnitude , with typically 110 distinct observations per star throughout the 3.5-year observation period. As part of

7800-587: The data reduction and catalogue production, new variables were identified and designated with appropriate variable star designations . Variable stars were classified as periodic or unsolved variables; the former were published with estimates of their period, variability amplitude, and variability type. In total some 11,597 variable objects were detected, of which 8,237 were newly classified as variable. There are, for example, 273 Cepheid variables , 186 RR Lyr variables , 108 Delta Scuti variables , and 917 eclipsing binary stars . The star mapper observations, constituting

7930-563: The direction to the Sun. The spacecraft spun around its Z-axis at the rate of 11.25 revolutions/day (168.75 arc-sec/s) at an angle of 43° to the Sun . The Z-axis rotated about the Sun-satellite line at 6.4 revolutions/year. The spacecraft consisted of two platforms and six vertical panels, all made of aluminum honeycomb. The solar array consisted of three deployable sections, generating around 300 W in total. Two S-band antennas were located on

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8060-411: The discrepancy between the cluster distance of 120.2 ± 1.5 parsecs (pc) as measured by Hipparcos and the distance of 133.5 ± 1.2 pc derived with other techniques was confirmed by parallax measurements made using VLBI , which gave 136.2 ± 1.2 pc , the most accurate and precise distance yet presented for the cluster. Another distance debate set-off by Hipparcos is for the distance to

8190-463: The distances and sizes of the Sun and the Moon, in the now-lost work On Sizes and Distances ( Ancient Greek : Περὶ μεγεθῶν καὶ ἀποστημάτων Peri megethon kai apostematon ). His work is mentioned in Ptolemy's Almagest V.11, and in a commentary thereon by Pappus ; Theon of Smyrna (2nd century) also mentions the work, under the title On Sizes and Distances of the Sun and Moon . Hipparchus measured

8320-512: The effects of the Earth 's atmosphere , but were compounded by complex optical terms, thermal and gravitational instrument flexures, and the absence of all-sky visibility. A formal proposal to make these exacting observations from space was first put forward in 1967. The mission was originally proposed to the French space agency CNES , which considered it too complex and expensive for a single national programme and recommended that it be proposed in

8450-563: The first book, Hipparchus assumes that the parallax of the Sun is 0, as if it is at infinite distance. He then analyzed a solar eclipse, which Toomer presumes to be the eclipse of 14 March 190 BC. It was total in the region of the Hellespont (and in his birthplace, Nicaea); at the time Toomer proposes the Romans were preparing for war with Antiochus III in the area, and the eclipse is mentioned by Livy in his Ab Urbe Condita Libri VIII.2. It

8580-467: The first century; Ptolemy's second-century Almagest ; and additional references to him in the fourth century by Pappus and Theon of Alexandria in their commentaries on the Almagest . Hipparchus's only preserved work is Commentary on the Phaenomena of Eudoxus and Aratus ( Ancient Greek : Τῶν Ἀράτου καὶ Εὐδόξου φαινομένων ἐξήγησις ). This is a highly critical commentary in the form of two books on

8710-419: The first method is very sensitive to the accuracy of the observations and parameters. (In fact, modern calculations show that the size of the 189 BC solar eclipse at Alexandria must have been closer to 9 ⁄ 10 ths and not the reported 4 ⁄ 5 ths, a fraction more closely matched by the degree of totality at Alexandria of eclipses occurring in 310 and 129 BC which were also nearly total in

8840-429: The first surviving text discussing it is by Menelaus of Alexandria in the first century, who now, on that basis, commonly is credited with its discovery. (Previous to the finding of the proofs of Menelaus a century ago, Ptolemy was credited with the invention of spherical trigonometry.) Ptolemy later used spherical trigonometry to compute things such as the rising and setting points of the ecliptic , or to take account of

8970-400: The first to develop a reliable method to predict solar eclipses . His other reputed achievements include the discovery and measurement of Earth's precession, the compilation of the first known comprehensive star catalog from the western world, and possibly the invention of the astrolabe , as well as of the armillary sphere that he may have used in creating the star catalogue. Hipparchus

9100-456: The five astrometric parameters (Hp<9 magnitude) exceeded the original mission goals, and are between 0.6 and 1.0 mas. Some 20,000 distances were determined to better than 10%, and 50,000 to better than 20%. The inferred ratio of external to standard errors is ≈1.0–1.2, and estimated systematic errors are below 0.1 mas. The number of solved or suspected double or multiple stars is 23,882. Photometric observations yielded multi-epoch photometry with

9230-440: The geometry of book 2 it follows that the Sun is at 2,550 Earth radii, and the mean distance of the Moon is 60 + 1 ⁄ 2 radii. Similarly, Cleomedes quotes Hipparchus for the sizes of the Sun and Earth as 1050:1; this leads to a mean lunar distance of 61 radii. Apparently Hipparchus later refined his computations, and derived accurate single values that he could use for predictions of solar eclipses. See Toomer (1974) for

9360-407: The global orientation of that system but without its regional errors. Whilst of enormous astronomical importance, double stars and multiple stars provided considerable complications to the observations (due to the finite size and profile of the detector's sensitive field of view) and to the data analysis. The data processing classified the astrometric solutions as follows: If a binary star has

9490-801: The instrument switching mechanisms from Oerlikon-Contraves in Zürich , Switzerland; the image dissector tube and photomultiplier detectors assembled by the Dutch Space Research Organisation ( SRON ) in the Netherlands; the refocusing assembly mechanism designed by TNO-TPD in Delft , Netherlands; the electrical power subsystem from British Aerospace in Bristol , United Kingdom; the structure and reaction control system from Daimler-Benz Aerospace in Bremen , Germany;

9620-447: The invention or improvement of several astronomical instruments, which were used for a long time for naked-eye observations. According to Synesius of Ptolemais (4th century) he made the first astrolabion : this may have been an armillary sphere (which Ptolemy however says he constructed, in Almagest V.1); or the predecessor of the planar instrument called astrolabe (also mentioned by Theon of Alexandria ). With an astrolabe Hipparchus

9750-449: The large total lunar eclipse of 26 November 139 BC, when over a clean sea horizon as seen from Rhodes, the Moon was eclipsed in the northwest just after the Sun rose in the southeast. This would be the second eclipse of the 345-year interval that Hipparchus used to verify the traditional Babylonian periods: this puts a late date to the development of Hipparchus's lunar theory. We do not know what "exact reason" Hipparchus found for seeing

9880-432: The location of the observer at each epoch of observation, and were supplied by an appropriate Earth ephemeris combined with accurate satellite ranging. Corrections due to special relativity ( stellar aberration ) made use of the corresponding satellite velocity. Modifications due to general relativistic light bending were significant (4 milliarc-sec at 90° to the ecliptic) and corrected for deterministically assuming γ=1 in

10010-633: The lunar parallax . If he did not use spherical trigonometry, Hipparchus may have used a globe for these tasks, reading values off coordinate grids drawn on it, or he may have made approximations from planar geometry, or perhaps used arithmetical approximations developed by the Chaldeans. Hipparchus also studied the motion of the Moon and confirmed the accurate values for two periods of its motion that Chaldean astronomers are widely presumed to have possessed before him. The traditional value (from Babylonian System B) for

10140-410: The majority of stars means that the angular measurements made, astrometrically, in the plane of the sky, cannot generally be converted into true space velocities in the plane of the sky. For this reason, astrometry characterises the transverse motions of stars in angular measure (e.g. arcsec per year) rather than in km/s or equivalent. Similarly, the typical absence of reliable radial velocities means that

10270-721: The masses of brown dwarfs ; the characterisation of extra-solar planets and their host stars; the height of the Sun above the Galactic mid-plane; the age of the Universe ; the stellar initial mass function and star formation rates; and strategies for the search for extraterrestrial intelligence . The high-precision multi-epoch photometry has been used to measure variability and stellar pulsations in many classes of objects. The Hipparcos and Tycho catalogues are now routinely used to point ground-based telescopes, navigate space missions, and drive public planetaria. Since 1997, several thousand scientific papers have been published making use of

10400-475: The mean synodic month is 29 days; 31,50,8,20 (sexagesimal) = 29.5305941... days. Expressed as 29 days + 12 hours + ⁠ 793 / 1080 ⁠  hours this value has been used later in the Hebrew calendar . The Chaldeans also knew that 251 synodic months ≈ 269 anomalistic months . Hipparchus used the multiple of this period by a factor of 17, because that interval is also an eclipse period, and

10530-511: The monthly motion of the Moon in latitude"), a work mentioned in the Suda . Pliny also remarks that "he also discovered for what exact reason, although the shadow causing the eclipse must from sunrise onward be below the earth, it happened once in the past that the Moon was eclipsed in the west while both luminaries were visible above the earth" (translation H. Rackham (1938), Loeb Classical Library 330 p. 207). Toomer argued that this must refer to

10660-412: The motion of stars. The resulting Hipparcos Catalogue , a high-precision catalogue of more than 118,200 stars, was published in 1997. The lower-precision Tycho Catalogue of more than a million stars was published at the same time, while the enhanced Tycho-2 Catalogue of 2.5 million stars was published in 2000. Hipparcos ' follow-up mission, Gaia , was launched in 2013. The word "Hipparcos"

10790-570: The motion of the Sun and Moon survive. For this he certainly made use of the observations and perhaps the mathematical techniques accumulated over centuries by the Babylonians and by Meton of Athens (fifth century BC), Timocharis , Aristyllus , Aristarchus of Samos , and Eratosthenes , among others. He developed trigonometry and constructed trigonometric tables , and he solved several problems of spherical trigonometry . With his solar and lunar theories and his trigonometry, he may have been

10920-406: The name of the ancient Greek astronomer Hipparchus , who is considered the founder of trigonometry and the discoverer of the precession of the equinoxes (due to the Earth wobbling on its axis). The spacecraft carried a single all-reflective, eccentric Schmidt telescope , with an aperture of 29 cm (11 in). A special beam-combining mirror superimposed two fields of view, 58° apart, into

11050-469: The nearest stars with the largest radial velocities and proper motions, but was accounted for in the 21 cases for which the accumulated positional effect over two years exceeds 0.1 milliarc-sec. Radial velocities for Hipparcos Catalogue stars, to the extent that they are presently known from independent ground-based surveys, can be found from the astronomical database of the Centre de données astronomiques de Strasbourg . The absence of reliable distances for

11180-531: The observation made on Alexandria 's large public equatorial ring that same day (at 1 hour before noon). Ptolemy claims his solar observations were on a transit instrument set in the meridian. At the end of his career, Hipparchus wrote a book entitled Peri eniausíou megéthous ("On the Length of the Year") regarding his results. The established value for the tropical year , introduced by Callippus in or before 330 BC

11310-466: The observation of around 400,000 stars, the resulting Tycho Catalogue comprised just over 1 million stars, with a subsequent analysis extending this to the Tycho-2 Catalogue of about 2.5 million stars. The attitude of the spacecraft about its center of gravity was controlled to scan the celestial sphere in a regular precessional motion maintaining a constant inclination between the spin axis and

11440-424: The observation of some 100,000 stars, with an astrometric accuracy of about 0.002 arc-sec, the final Hipparcos Catalogue comprised nearly 120,000 stars with a median accuracy of slightly better than 0.001 arc-sec (1 milliarc-sec). An additional photomultiplier system viewed a beam splitter in the optical path and was used as a star mapper. Its purpose was to monitor and determine the satellite attitude, and in

11570-410: The observations were as follows: The Hipparcos satellite was financed and managed under the overall authority of the European Space Agency (ESA). The main industrial contractors were Matra Marconi Space (now EADS Astrium ) and Alenia Spazio (now Thales Alenia Space ). Other hardware components were supplied as follows: the beam-combining mirror from REOSC at Saint-Pierre-du-Perray , France;

11700-419: The observations, rather than a single value for the distance. His results were the best so far: the actual mean distance of the Moon is 60.3 Earth radii, within his limits from Hipparchus's second book. Theon of Smyrna wrote that according to Hipparchus, the Sun is 1,880 times the size of the Earth, and the Earth twenty-seven times the size of the Moon; apparently this refers to volumes , not diameters . From

11830-455: The on-board software and calibration. The Hipparcos satellite was launched (with the direct broadcast satellite TV-Sat 2 as co-passenger) on an Ariane 4 launch vehicle , flight V33, from Centre Spatial Guyanais , Kourou , French Guiana, on 8 August 1989. Launched into a geostationary transfer orbit (GTO), the Mage-2 apogee boost motor failed to fire, and the intended geostationary orbit

11960-482: The one given by Archimedes of between 3 + 10 ⁄ 71 (≈ 3.1408) and 3 + 1 ⁄ 7 (≈ 3.1429). Perhaps he had the approximation later used by Ptolemy, sexagesimal 3;08,30 (≈ 3.1417) ( Almagest VI.7). Hipparchus could have constructed his chord table using the Pythagorean theorem and a theorem known to Archimedes. He also might have used the relationship between sides and diagonals of

12090-510: The other way around is debatable. Hipparchus also gave the value for the sidereal year to be 365 + ⁠ 1 / 4 ⁠ + ⁠ 1 / 144 ⁠ days (= 365.25694... days = 365 days 6 hours 10 min). Another value for the sidereal year that is attributed to Hipparchus (by the physician Galen in the second century AD) is 365 + ⁠ 1 / 4 ⁠ + ⁠ 1 / 288 ⁠ days (= 365.25347... days = 365 days 6 hours 5 min), but this may be

12220-411: The parallax of the Sun decreases (i.e., its distance increases), the minimum limit for the mean distance is 59 Earth radii—exactly the mean distance that Ptolemy later derived. Hipparchus thus had the problematic result that his minimum distance (from book 1) was greater than his maximum mean distance (from book 2). He was intellectually honest about this discrepancy, and probably realized that especially

12350-557: The period of 4,267 moons is approximately five minutes longer than the value for the eclipse period that Ptolemy attributes to Hipparchus. However, the timing methods of the Babylonians had an error of no fewer than eight minutes. Modern scholars agree that Hipparchus rounded the eclipse period to the nearest hour, and used it to confirm the validity of the traditional values, rather than to try to derive an improved value from his own observations. From modern ephemerides and taking account of

12480-441: The points where the angle intersects the circle. He may have computed this for a circle with a circumference of 21,600 units and a radius (rounded) of 3,438 units; this circle has a unit length for each arcminute along its perimeter. (This was “proven” by Toomer, but he later “cast doubt“ upon his earlier affirmation. Other authors have argued that a circle of radius 3,600 units may instead have been used by Hipparchus. ) He tabulated

12610-403: The positions of Sun and Moon when a solar or lunar eclipse is possible, are explained in Almagest VI.5. Hipparchus apparently made similar calculations. The result that two solar eclipses can occur one month apart is important, because this can not be based on observations: one is visible on the northern and the other on the southern hemisphere—as Pliny indicates—and the latter was inaccessible to

12740-438: The problem of denoting locations on the Earth's surface. Before him a grid system had been used by Dicaearchus of Messana , but Hipparchus was the first to apply mathematical rigor to the determination of the latitude and longitude of places on the Earth. Hipparchus wrote a critique in three books on the work of the geographer Eratosthenes of Cyrene (3rd century BC), called Pròs tèn Eratosthénous geographían ("Against

12870-399: The process, to gather photometric and astrometric data of all stars down to about 11th magnitude. These measurements were made in two broad bands approximately corresponding to B and V in the (Johnson) UBV photometric system . The positions of these latter stars were to be determined to a precision of 0.03 arc-sec, which is a factor of 25 less than the main mission stars. Originally targeting

13000-406: The ratio of the epicycle model ( 3122 + 1 ⁄ 2  : 247 + 1 ⁄ 2 ), which is too small (60 : 4;45 sexagesimal). Ptolemy established a ratio of 60 : 5 + 1 ⁄ 4 . (The maximum angular deviation producible by this geometry is the arcsin of 5 + 1 ⁄ 4 divided by 60, or approximately 5° 1', a figure that is sometimes therefore quoted as the equivalent of

13130-546: The representative figure for astronomy. It is not certain that the figure is meant to represent him. Previously, Eudoxus of Cnidus in the fourth century BC had described the stars and constellations in two books called Phaenomena and Entropon . Aratus wrote a poem called Phaenomena or Arateia based on Eudoxus's work. Hipparchus wrote a commentary on the Arateia —his only preserved work—which contains many stellar positions and times for rising, culmination, and setting of

13260-687: The requirements. The eccentric model he fitted to these eclipses from his Babylonian eclipse list: 22/23 December 383 BC, 18/19 June 382 BC, and 12/13 December 382 BC. The epicycle model he fitted to lunar eclipse observations made in Alexandria at 22 September 201 BC, 19 March 200 BC, and 11 September 200 BC. These figures are due to the cumbersome unit he used in his chord table and may partly be due to some sloppy rounding and calculation errors by Hipparchus, for which Ptolemy criticised him while also making rounding errors. A simpler alternate reconstruction agrees with all four numbers. Hipparchus found inconsistent results; he later used

13390-658: The resulting Hipparcos celestial reference frame (HCRF) coincides, to within observational uncertainties, with the International Celestial Reference Frame (ICRF), and representing the best estimates at the time of the catalogue completion (in 1996). The HCRF is thus a materialisation of the International Celestial Reference System (ICRS) in the optical domain. It extends and improves the J2000 ( FK5 ) system, retaining approximately

13520-431: The resulting rigid reference frame was transformed to an inertial frame of reference linked to extragalactic sources. This allows surveys at different wavelengths to be directly correlated with the Hipparcos stars, and ensures that the catalogue proper motions are, as far as possible, kinematically non-rotating. The determination of the relevant three solid-body rotation angles, and the three time-dependent rotation rates,

13650-502: The revised analysis. This has been contested by various other recent work, placing the mean cluster distance at around 130 parsecs. According to a 2012 paper, the anomaly was due to the use of a weighted mean when there is a correlation between distances and distance errors for stars in clusters. It is resolved by using an unweighted mean. There is no systematic bias in the Hipparcos data when it comes to star clusters. In August 2014,

13780-507: The satellite observations and data processing, the Hipparcos mission cost about €600 million (in year 2000 economic conditions), and its execution involved some 200 European scientists and more than 2,000 individuals in European industry. The satellite observations relied on a pre-defined list of target stars. Stars were observed as the satellite rotated, by a sensitive region of the image dissector tube detector. This pre-defined star list formed

13910-514: The satellite, were not included in the published Hipparcos Catalogue . Constraints on total observing time, and on the uniformity of stars across the celestial sphere for satellite operations and data analysis, led to an Input Catalogue of some 118,000 stars. It merged two components: first, a survey of around 58,000 objects as complete as possible to the following limiting magnitudes: V<7.9 + 1.1sin|b| for spectral types earlier than G5, and V<7.3 + 1.1sin|b| for spectral types later than G5 (b

14040-586: The scientific teams in June 1997. A more extensive analysis of the star mapper (Tycho) data extracted additional faint stars from the data stream. Combined with old photographic plate observations made several decades earlier as part of the Astrographic Catalogue programme, the Tycho-2 Catalogue of more than 2.5 million stars (and fully superseding the original Tycho Catalogue) was published in 2000. The Hipparcos and Tycho-1 Catalogues were used to create

14170-504: The second and third centuries, coins were made in his honour in Bithynia that bear his name and show him with a globe . Relatively little of Hipparchus's direct work survives into modern times. Although he wrote at least fourteen books, only his commentary on the popular astronomical poem by Aratus was preserved by later copyists. Most of what is known about Hipparchus comes from Strabo 's Geography and Pliny 's Natural History in

14300-417: The shadow of the Earth is a cone rather than a cylinder as under the first assumption. Hipparchus observed (at lunar eclipses) that at the mean distance of the Moon, the diameter of the shadow cone is 2 + 1 ⁄ 2 lunar diameters. That apparent diameter is, as he had observed, 360 ⁄ 650 degrees. With these values and simple geometry, Hipparchus could determine the mean distance; because it

14430-959: The solar arrays and thermal control system from Fokker Space System in Leiden , Netherlands; the data handling and telecommunications system from Saab Ericsson Space in Gothenburg , Sweden; and the apogee boost motor from SEP in France. Groups from the Institut d'Astrophysique in Liège , Belgium and the Laboratoire d'Astronomie Spatiale in Marseille , France, contributed optical performance, calibration and alignment test procedures; Captec in Dublin . Ireland, and Logica in London contributed to

14560-505: The solstice observation of Meton and his own, there were 297 years spanning 108,478 days; this implies a tropical year of 365.24579... days = 365 days;14,44,51 (sexagesimal; = 365 days + ⁠ 14 / 60 ⁠ + ⁠ 44 / 60 ⁠ + ⁠ 51 / 60 ⁠ ), a year length found on one of the few Babylonian clay tablets which explicitly specifies the System B month. Whether Babylonians knew of Hipparchus's work or

14690-732: The spherical, folding and relay mirrors from Carl Zeiss AG in Oberkochen , Germany; the external straylight baffles from CASA in Madrid , Spain; the modulating grid from CSEM in Neuchâtel , Switzerland; the mechanism control system and the thermal control electronics from Dornier Satellite Systems in Friedrichshafen , Germany; the optical filters, the experiment structures and the attitude and orbit control system from Matra Marconi Space in Vélizy , France;

14820-423: The star Polaris. Hipparcos data is recently being used together with Gaia data. Especially the comparison of the proper motion of stars from both spacecraft is being used to search for hidden binary companions. Hipparcos-Gaia data is also used to measure the dynamical mass of known binaries, such as substellar companions. Hipparcos-Gaia data was used to measure the mass of the exoplanet Beta Pictoris b and

14950-503: The stereographic projection is found in Ptolemy 's Planisphere (2nd century AD). Besides geometry, Hipparchus also used arithmetic techniques developed by the Chaldeans . He was one of the first Greek mathematicians to do this and, in this way, expanded the techniques available to astronomers and geographers. There are several indications that Hipparchus knew spherical trigonometry, but

15080-473: The summer solstices in 146 and 135 BC both accurately to a few hours, but observations of the moment of equinox were simpler, and he made twenty during his lifetime. Ptolemy gives an extensive discussion of Hipparchus's work on the length of the year in the Almagest III.1, and quotes many observations that Hipparchus made or used, spanning 162–128 BC, including an equinox timing by Hipparchus (at 24 March 146 BC at dawn) that differs by 5 hours from

15210-462: The synodic and anomalistic periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides , specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu ). Hipparchus's long draconitic lunar period (5,458 months = 5,923 lunar nodal periods) also appears a few times in Babylonian records . But the only such tablet explicitly dated,

15340-431: The top and bottom of the spacecraft, providing an omni-directional downlink data rate of 24  kbit/s . An attitude and orbit-control subsystem (comprising 5- newton hydrazine thrusters for course manoeuvres, 20-millinewton cold gas thrusters for attitude control, and gyroscopes for attitude determination) ensured correct dynamic attitude control and determination during the operational lifetime. Some key features of

15470-425: The transverse space motion (when known) is, in any case, only a component of the complete, three-dimensional, space velocity. The final Hipparcos Catalogue was the result of the critical comparison and merging of the two (NDAC and FAST consortia) analyses, and contains 118,218 entries (stars or multiple stars), corresponding to an average of some three stars per square degree over the entire sky. Median precision of

15600-504: The various techniques generally agreed to within 10 milliarc-sec in the orientation and 1 milliarc-sec/year in the rotation of the system. From appropriate weighting, the coordinate axes defined by the published catalogue are believed to be aligned with the extragalactic radio frame to within ±0.6 milliarc-sec at the epoch J1991.25, and non-rotating with respect to distant extragalactic objects to within ±0.25 milliarc-sec/yr. The Hipparcos and Tycho Catalogues were then constructed such that

15730-551: Was 365 + 1 ⁄ 4 days. Speculating a Babylonian origin for the Callippic year is difficult to defend, since Babylon did not observe solstices thus the only extant System B year length was based on Greek solstices (see below). Hipparchus's equinox observations gave varying results, but he points out (quoted in Almagest III.1(H195)) that the observation errors by him and his predecessors may have been as large as 1 ⁄ 4 day. He used old solstice observations and determined

15860-572: Was also observed in Alexandria, where the Sun was reported to be obscured 4/5ths by the Moon. Alexandria and Nicaea are on the same meridian. Alexandria is at about 31° North, and the region of the Hellespont about 40° North. (It has been contended that authors like Strabo and Ptolemy had fairly decent values for these geographical positions, so Hipparchus must have known them too. However, Strabo's Hipparchus dependent latitudes for this region are at least 1° too high, and Ptolemy appears to copy them, placing Byzantium 2° high in latitude.) Hipparchus could draw

15990-824: Was announced that a part of it was discovered in a medieval parchment manuscript, Codex Climaci Rescriptus , from Saint Catherine's Monastery in the Sinai Peninsula , Egypt as hidden text ( palimpsest ). Hipparchus also constructed a celestial globe depicting the constellations, based on his observations. His interest in the fixed stars may have been inspired by the observation of a supernova (according to Pliny), or by his discovery of precession, according to Ptolemy, who says that Hipparchus could not reconcile his data with earlier observations made by Timocharis and Aristillus . For more information see Discovery of precession . In Raphael 's painting The School of Athens , Hipparchus may be depicted holding his celestial globe, as

16120-537: Was apparently compiled by Hipparchus, who is consequently now known as "the father of trigonometry". Earlier Greek astronomers and mathematicians were influenced by Babylonian astronomy to some extent, for instance the period relations of the Metonic cycle and Saros cycle may have come from Babylonian sources (see " Babylonian astronomical diaries "). Hipparchus seems to have been the first to exploit Babylonian astronomical knowledge and techniques systematically. Eudoxus in

16250-417: Was calculated by Delambre based on clues in his work. Hipparchus must have lived some time after 127 BC because he analyzed and published his observations from that year. Hipparchus obtained information from Alexandria as well as Babylon , but it is not known when or if he visited these places. He is believed to have died on the island of Rhodes, where he seems to have spent most of his later life. In

16380-404: Was computed for a minimum distance of the Sun, it is the maximum mean distance possible for the Moon. With his value for the eccentricity of the orbit, he could compute the least and greatest distances of the Moon too. According to Pappus, he found a least distance of 62, a mean of 67 + 1 ⁄ 3 , and consequently a greatest distance of 72 + 2 ⁄ 3 Earth radii. With this method, as

16510-518: Was conducted and completed in advance of the catalogue publication. This resulted in an accurate but indirect link to an inertial, extragalactic, reference frame. A variety of methods to establish this reference frame link before catalogue publication were included and appropriately weighted: interferometric observations of radio stars by VLBI networks, MERLIN and Very Large Array (VLA); observations of quasars relative to Hipparcos stars using charge-coupled device (CCD), photographic plates, and

16640-457: Was never achieved. However, with the addition of further ground stations, in addition to ESA operations control centre at European Space Operations Centre (ESOC) in Germany, the satellite was successfully operated in its geostationary transfer orbit (GTO) for almost 3.5 years. All of the original mission goals were, eventually, exceeded. Including an estimate for the scientific activities related to

16770-500: Was the first space experiment devoted to precision astrometry , the accurate measurement of the positions of celestial objects on the sky. This permitted the first high-precision measurements of the intrinsic brightnesses proper motions , and parallaxes of stars, enabling better calculations of their distance and tangential velocity . When combined with radial velocity measurements from spectroscopy , astrophysicists were able to finally measure all six quantities needed to determine

16900-405: Was the first to be able to measure the geographical latitude and time by observing fixed stars. Previously this was done at daytime by measuring the shadow cast by a gnomon, by recording the length of the longest day of the year or with the portable instrument known as a scaphe . Ptolemy mentions ( Almagest V.14) that he used a similar instrument as Hipparchus, called dioptra , to measure

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