The Comet Nucleus Tour ( CONTOUR ) was a NASA Discovery -class space probe that failed shortly after its July 2002 launch. It was the only Discovery mission to fail.
90-464: The two comets scheduled to be visited were Encke and Schwassmann-Wachmann-3 , and the third target was d'Arrest . It was hoped that a new comet would have been discovered in the inner Solar System between 2006 and 2008, in which case the spacecraft trajectory would have been changed if possible to rendezvous with the new comet. Scientific objectives included imaging the nuclei at resolutions of up to 4 meters (13 ft), performing spectral mapping of
180-475: A radiation source (e.g. star) at the standard distance of 10 parsecs , it follows that the zero point of the apparent bolometric magnitude scale m bol = 0 corresponds to irradiance f 0 = 2.518 021 002 × 10 W/m . Using the IAU 2015 scale, the nominal total solar irradiance (" solar constant ") measured at 1 astronomical unit ( 1361 W/m ) corresponds to an apparent bolometric magnitude of
270-650: A close approach of roughly 0.1735 AU. On 18 November 2013, it passed 0.02496 AU (3.734 million km; 2.320 million mi) from Mercury. Close approaches to Earth usually occur every 33 years. Comet Encke has a perihelion (closest approach to the Sun) of 0.34 AU (51 million km; 32 million mi), and at perihelion Comet Encke passes the Sun at 69.5 km/s (250,000 km/h). Between 1769 and 2103, Comet Encke's perihelion distance only varies from 0.330 AU (in 2050) and 0.347 AU (in 1782). Of
360-427: A diffuse flat disk of the same diameter. A quarter phase ( α = 90 ∘ {\displaystyle \alpha =90^{\circ }} ) has 1 π {\textstyle {\frac {1}{\pi }}} as much light as full phase ( α = 0 ∘ {\displaystyle \alpha =0^{\circ }} ). By contrast, a diffuse disk reflector model
450-419: A diffuse reflector. Bodies with no atmosphere, like asteroids or moons, tend to reflect light more strongly to the direction of the incident light, and their brightness increases rapidly as the phase angle approaches 0 ∘ {\displaystyle 0^{\circ }} . This rapid brightening near opposition is called the opposition effect . Its strength depends on the physical properties of
540-417: A flyby of comet d'Arrest might have occurred on 16 August 2008 at a relative velocity of 11.8 km/s, 1.35 AU from the Sun and 0.36 AU from Earth. All flybys would have had a closest encounter distance of about 100 km and would have occurred near the period of maximum activity for each comet. After the comet Encke encounter, CONTOUR might have been retargeted towards a new comet if one was discovered with
630-435: A periodic source of additional dust, for example, a cometary debris field. More than one theory has associated Encke's Comet with impacts of cometary material on Earth, and with cultural significance. The Tunguska event of 1908 may have been caused by the impact of a cometary body and has also been postulated by Czechoslovakian astronomer Ľubor Kresák as possibly caused by a fragment of Comet Encke. A theory holds that
720-477: A phase angle of α = 93.0 ∘ {\displaystyle \alpha =93.0^{\circ }} (near quarter phase). Under full-phase conditions, Venus would have been visible at m = − 4.384 + 5 log 10 ( 0.719 ⋅ 0.645 ) = − 6.09. {\displaystyle m=-4.384+5\log _{10}{\left(0.719\cdot 0.645\right)}=-6.09.} Accounting for
810-518: A single filter band, as expressed on a logarithmic magnitude scale. To convert from an absolute magnitude in a specific filter band to absolute bolometric magnitude, a bolometric correction (BC) is applied. In stellar and galactic astronomy, the standard distance is 10 parsecs (about 32.616 light-years, 308.57 petameters or 308.57 trillion kilometres). A star at 10 parsecs has a parallax of 0.1″ (100 milliarcseconds ). Galaxies (and other extended objects ) are much larger than 10 parsecs; their light
900-490: A standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale. For Solar System bodies that shine in reflected light, a different definition of absolute magnitude (H) is used, based on a standard reference distance of one astronomical unit . Absolute magnitudes of stars generally range from approximately −10 to +20. The absolute magnitudes of galaxies can be much lower (brighter). The more luminous an object,
990-422: A value close to that, m 1 = + 0.5 {\displaystyle m_{1}=+0.5} . The absolute magnitude of any given comet can vary dramatically. It can change as the comet becomes more or less active over time or if it undergoes an outburst. This makes it difficult to use the absolute magnitude for a size estimate. When comet 289P/Blanpain was discovered in 1819, its absolute magnitude
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#17328557124191080-426: A very low albedo , reflecting only 4.6% of the light its nucleus receives, although comets generate a large coma and tail that can make them much more visible during their perihelion (closest approach to the Sun). The diameter of the nucleus of Encke's Comet is 4.8 km. As its official designation implies, Encke's Comet was the first periodic comet discovered after Halley's Comet (designated 1P/Halley). It
1170-716: A visual magnitude m V of 0.12 and distance of about 860 light-years: M V = 0.12 − 5 ( log 10 860 3.2616 − 1 ) = − 7.0. {\displaystyle M_{\mathrm {V} }=0.12-5\left(\log _{10}{\frac {860}{3.2616}}-1\right)=-7.0.} Vega has a parallax p of 0.129″, and an apparent magnitude m V of 0.03: M V = 0.03 + 5 ( log 10 0.129 + 1 ) = + 0.6. {\displaystyle M_{\mathrm {V} }=0.03+5\left(\log _{10}{0.129}+1\right)=+0.6.} The Black Eye Galaxy has
1260-414: A visual magnitude m V of 9.36 and a distance modulus μ of 31.06: M V = 9.36 − 31.06 = − 21.7. {\displaystyle M_{\mathrm {V} }=9.36-31.06=-21.7.} The absolute bolometric magnitude ( M bol ) takes into account electromagnetic radiation at all wavelengths . It includes those unobserved due to instrumental passband ,
1350-539: Is a measure of the luminosity of a celestial object on an inverse logarithmic astronomical magnitude scale; the more luminous (intrinsically bright) an object, the lower its magnitude number. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs (32.6 light-years ), without extinction (or dimming) of its light due to absorption by interstellar matter and cosmic dust . By hypothetically placing all objects at
1440-565: Is assumed that extinction from gas and dust is negligible. Typical extinction rates within the Milky Way galaxy are 1 to 2 magnitudes per kiloparsec, when dark clouds are taken into account. For objects at very large distances (outside the Milky Way) the luminosity distance d L (distance defined using luminosity measurements) must be used instead of d , because the Euclidean approximation
1530-1669: Is based on the diffuse disk reflector model. The absolute magnitude H {\displaystyle H} , diameter D {\displaystyle D} (in kilometers ) and geometric albedo p {\displaystyle p} of a body are related by D = 1329 p × 10 − 0.2 H k m , {\displaystyle D={\frac {1329}{\sqrt {p}}}\times 10^{-0.2H}\mathrm {km} ,} or equivalently, H = 5 log 10 1329 D p . {\displaystyle H=5\log _{10}{\frac {1329}{D{\sqrt {p}}}}.} Example: The Moon's absolute magnitude H {\displaystyle H} can be calculated from its diameter D = 3474 km {\displaystyle D=3474{\text{ km}}} and geometric albedo p = 0.113 {\displaystyle p=0.113} : H = 5 log 10 1329 3474 0.113 = + 0.28. {\displaystyle H=5\log _{10}{\frac {1329}{3474{\sqrt {0.113}}}}=+0.28.} We have d B S = 1 AU {\displaystyle d_{BS}=1{\text{ AU}}} , d B O = 384400 km = 0.00257 AU . {\displaystyle d_{BO}=384400{\text{ km}}=0.00257{\text{ AU}}.} At quarter phase , q ( α ) ≈ 2 3 π {\textstyle q(\alpha )\approx {\frac {2}{3\pi }}} (according to
1620-418: Is changing slowly due to seasonal effects as the planet moves along its 165-year orbit around the Sun, and the approximation above is only valid after the year 2000. For some circumstances, like α ≥ 179 ∘ {\displaystyle \alpha \geq 179^{\circ }} for Venus, no observations are available, and the phase curve is unknown in those cases. The formula for
1710-536: Is close to the value of m = − 4.62 {\displaystyle m=-4.62} predicted by the Jet Propulsion Laboratory. Example 2: At first quarter phase , the approximation for the Moon gives − 2.5 log 10 q ( 90 ∘ ) = 2.71. {\textstyle -2.5\log _{10}{q(90^{\circ })}=2.71.} With that,
1800-460: Is impossible in practice). Because Solar System bodies are illuminated by the Sun, their brightness varies as a function of illumination conditions, described by the phase angle . This relationship is referred to as the phase curve . The absolute magnitude is the brightness at phase angle zero, an arrangement known as opposition , from a distance of one AU. The absolute magnitude H {\displaystyle H} can be used to calculate
1890-400: Is invalid for distant objects. Instead, general relativity must be taken into account. Moreover, the cosmological redshift complicates the relationship between absolute and apparent magnitude, because the radiation observed was shifted into the red range of the spectrum. To compare the magnitudes of very distant objects with those of local objects, a K correction might have to be applied to
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#17328557124191980-443: Is radiated over an extended patch of sky, and their overall brightness cannot be directly observed from relatively short distances, but the same convention is used. A galaxy's magnitude is defined by measuring all the light radiated over the entire object, treating that integrated brightness as the brightness of a single point-like or star-like source, and computing the magnitude of that point-like source as it would appear if observed at
2070-434: Is simply q ( α ) = cos α {\displaystyle q(\alpha )=\cos {\alpha }} , which isn't realistic, but it does represent the opposition surge for rough surfaces that reflect more uniform light back at low phase angles. The definition of the geometric albedo p {\displaystyle p} , a measure for the reflectivity of planetary surfaces,
2160-462: Is somewhat lower than that, m = − 10.0. {\displaystyle m=-10.0.} This is not a good approximation, because the phase curve of the Moon is too complicated for the diffuse reflector model. A more accurate formula is given in the following section. Because Solar System bodies are never perfect diffuse reflectors, astronomers use different models to predict apparent magnitudes based on known or assumed properties of
2250-594: Is still brighter than the Sun , whose absolute visual magnitude is 4.83. The Sun's absolute bolometric magnitude is set arbitrarily, usually at 4.75. Absolute magnitudes of stars generally range from approximately −10 to +20. The absolute magnitudes of galaxies can be much lower (brighter). For example, the giant elliptical galaxy M87 has an absolute magnitude of −22 (i.e. as bright as about 60,000 stars of magnitude −10). Some active galactic nuclei ( quasars like CTA-102 ) can reach absolute magnitudes in excess of −32, making them
2340-620: Is the Astronomical Unit , and K 1 , 2 {\displaystyle K_{1,2}} are the slope parameters characterising the comet's activity. For K = 2 {\displaystyle K=2} , this reduces to the formula for a purely reflecting body (showing no cometary activity). For example, the lightcurve of comet C/2011 L4 (PANSTARRS) can be approximated by M 1 = 5.41 , K 1 = 3.69. {\displaystyle M_{1}=5.41{\text{, }}K_{1}=3.69.} On
2430-461: Is the absolute visual magnitude , which uses the visual (V) band of the spectrum (in the UBV photometric system ). Absolute magnitudes are denoted by a capital M, with a subscript representing the filter band used for measurement, such as M V for absolute magnitude in the V band. An object's absolute bolometric magnitude (M bol ) represents its total luminosity over all wavelengths , rather than in
2520-818: Is the phase angle , the angle between the body-Sun and body–observer lines. q ( α ) {\displaystyle q(\alpha )} is the phase integral (the integration of reflected light; a number in the 0 to 1 range). By the law of cosines , we have: cos α = d B O 2 + d B S 2 − d O S 2 2 d B O d B S . {\displaystyle \cos {\alpha }={\frac {d_{\mathrm {BO} }^{2}+d_{\mathrm {BS} }^{2}-d_{\mathrm {OS} }^{2}}{2d_{\mathrm {BO} }d_{\mathrm {BS} }}}.} Distances: The value of q ( α ) {\displaystyle q(\alpha )} depends on
2610-405: Is the comet with the smallest nucleus that has ever been physically characterised, and usually doesn't become brighter than 18 mag. For some comets that have been observed at heliocentric distances large enough to distinguish between light reflected from the coma, and light from the nucleus itself, an absolute magnitude analogous to that used for asteroids has been calculated, allowing to estimate
2700-490: Is the effective inclination of Saturn's rings (their tilt relative to the observer), which as seen from Earth varies between 0° and 27° over the course of one Saturn orbit, and ϕ ′ {\displaystyle \phi '} is a small correction term depending on Uranus' sub-Earth and sub-solar latitudes. t {\displaystyle t} is the Common Era year. Neptune's absolute magnitude
2790-529: Is the radiant flux measured at distance d (in parsecs), F 10 the radiant flux measured at distance 10 pc . Using the common logarithm , the equation can be written as M = m − 5 log 10 ( d pc ) + 5 = m − 5 ( log 10 d pc − 1 ) , {\displaystyle M=m-5\log _{10}(d_{\text{pc}})+5=m-5\left(\log _{10}d_{\text{pc}}-1\right),} where it
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2880-444: Is the shortest period of a reasonably bright comet; the faint main-belt comet 311P/PanSTARRS has a period of 3.2 years.) Encke was first recorded by Pierre Méchain on 17 January 1786, but it was not recognized as a periodic comet until 1819 when its orbit was computed by Johann Franz Encke . Like Halley's Comet , it is unusual in its being named after the calculator of its orbit rather than its discoverer. Like most comets, it has
2970-405: Is valid for phase angles α < 120 ∘ {\displaystyle \alpha <120^{\circ }} , and works best when α < 20 ∘ {\displaystyle \alpha <20^{\circ }} . The slope parameter G {\displaystyle G} relates to the surge in brightness, typically 0.3 mag , when
3060-586: The H G {\displaystyle HG} -system was officially replaced by an improved system with three parameters H {\displaystyle H} , G 1 {\displaystyle G_{1}} and G 2 {\displaystyle G_{2}} , which produces more satisfactory results if the opposition effect is very small or restricted to very small phase angles. However, as of 2022, this H G 1 G 2 {\displaystyle HG_{1}G_{2}} -system has not been adopted by either
3150-715: The International Astronomical Union passed Resolution B2 defining the zero points of the absolute and apparent bolometric magnitude scales in SI units for power ( watts ) and irradiance (W/m ), respectively. Although bolometric magnitudes had been used by astronomers for many decades, there had been systematic differences in the absolute magnitude-luminosity scales presented in various astronomical references, and no international standardization. This led to systematic differences in bolometric corrections scales. Combined with incorrect assumed absolute bolometric magnitudes for
3240-548: The Mawangdui Silk Texts , which includes a swastika-shaped comet, and suggest that some comet drawings were related to the breakup of the progenitor of Encke and the Taurid meteoroid stream. Fred Whipple in his The Mystery of Comets (1985, page 163) points out that Comet Encke's polar axis is only 5 degrees from its orbital plane: such an orientation is ideal to have presented a pinwheel like aspect to our ancestors when Encke
3330-494: The Minor Planet Center . m = H + 5 log 10 ( d B S d B O d 0 2 ) − 2.5 log 10 q ( α ) , {\displaystyle m=H+5\log _{10}{\left({\frac {d_{BS}d_{BO}}{d_{0}^{2}}}\right)}-2.5\log _{10}{q(\alpha )},} where This relation
3420-672: The Sun of m bol,⊙ = −26.832 . Following Resolution B2, the relation between a star's absolute bolometric magnitude and its luminosity is no longer directly tied to the Sun's (variable) luminosity: M b o l = − 2.5 log 10 L ⋆ L 0 ≈ − 2.5 log 10 L ⋆ + 71.197425 {\displaystyle M_{\mathrm {bol} }=-2.5\log _{10}{\frac {L_{\star }}{L_{0}}}\approx -2.5\log _{10}L_{\star }+71.197425} where The new IAU absolute magnitude scale permanently disconnects
3510-725: The Taurids (which are encountered as the Northern and Southern Taurids across November, and the Beta Taurids in late June and early July). A shower has similarly been reported affecting Mercury. Near-Earth object 2004 TG 10 may be a fragment of Encke. Measurements on board the NASA satellite MESSENGER have revealed Encke may contribute to seasonal meteor showers on Mercury. The Mercury Atmospheric and Surface Composition Spectrometer (MASCS) instrument discovered seasonal surges of calcium since
3600-453: The nuclei of the comets. Although mission scientists predicted that the spacecraft would take no significant damage during the Encke and Schwassmann-Wachmann-3 encounters, the shield and its prototypes were tested vigorously during the construction of the spacecraft, including one where a shield prototype was shot at with surrogate nylon particles from a two stage light-gas gun . The results of
3690-500: The numbered comets less than 321P, only 96P/Machholz gets closer to the Sun. The comet has been observed at every perihelion since 1818 except 1944. An attempt to photograph the comet close to aphelion was made on 2 July 1913 using the Mount Wilson 60-inch telescope but the resulting photographic plate was lost in the mail. A second attempt using the same telescope was made on 1 September 1913 and this showed an object in about
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3780-1188: The Earth's atmospheric absorption, and extinction by interstellar dust . It is defined based on the luminosity of the stars. In the case of stars with few observations, it must be computed assuming an effective temperature . Classically, the difference in bolometric magnitude is related to the luminosity ratio according to: M b o l , ⋆ − M b o l , ⊙ = − 2.5 log 10 ( L ⋆ L ⊙ ) {\displaystyle M_{\mathrm {bol,\star } }-M_{\mathrm {bol,\odot } }=-2.5\log _{10}\left({\frac {L_{\star }}{L_{\odot }}}\right)} which makes by inversion: L ⋆ L ⊙ = 10 0.4 ( M b o l , ⊙ − M b o l , ⋆ ) {\displaystyle {\frac {L_{\star }}{L_{\odot }}}=10^{0.4\left(M_{\mathrm {bol,\odot } }-M_{\mathrm {bol,\star } }\right)}} where In August 2015,
3870-482: The Minor Planet Center nor Jet Propulsion Laboratory . The apparent magnitude of asteroids varies as they rotate , on time scales of seconds to weeks depending on their rotation period , by up to 2 mag {\displaystyle 2{\text{ mag}}} or more. In addition, their absolute magnitude can vary with the viewing direction, depending on their axial tilt . In many cases, neither
3960-572: The Moon is about 0.06 mag fainter than at first quarter, because that part of its surface has a lower albedo. Earth's albedo varies by a factor of 6, from 0.12 in the cloud-free case to 0.76 in the case of altostratus cloud . The absolute magnitude in the table corresponds to an albedo of 0.434. Due to the variability of the weather , Earth's apparent magnitude cannot be predicted as accurately as that of most other planets. If an object has an atmosphere, it reflects light more or less isotropically in all directions, and its brightness can be modelled as
4050-414: The Moon is only applicable to the near side of the Moon , the portion that is visible from the Earth. Example 1: On 1 January 2019, Venus was d B S = 0.719 AU {\displaystyle d_{BS}=0.719{\text{ AU}}} from the Sun, and d B O = 0.645 AU {\displaystyle d_{BO}=0.645{\text{ AU}}} from Earth, at
4140-511: The Sun and 0.27 AU from Earth. During the August 2002 injection maneuver, the probe was lost. Three more Earth flybys would have followed, on August 14, 2004, February 10, 2005, and February 10, 2006. On June 18, 2006, CONTOUR would have encountered comet Schwassmann-Wachmann-3 at 14 km/s, 0.95 AU from the Sun and 0.33 AU from Earth. Two more Earth flybys were scheduled in February 2007 and 2008, and
4230-524: The Sun, this could lead to systematic errors in estimated stellar luminosities (and other stellar properties, such as radii or ages, which rely on stellar luminosity to be calculated). Resolution B2 defines an absolute bolometric magnitude scale where M bol = 0 corresponds to luminosity L 0 = 3.0128 × 10 W , with the zero point luminosity L 0 set such that the Sun (with nominal luminosity 3.828 × 10 W ) corresponds to absolute bolometric magnitude M bol,⊙ = 4.74 . Placing
4320-434: The V filter band. The Sun has absolute magnitude M V = +4.83. Highly luminous objects can have negative absolute magnitudes: for example, the Milky Way galaxy has an absolute B magnitude of about −20.8. As with all astronomical magnitudes , the absolute magnitude can be specified for different wavelength ranges corresponding to specified filter bands or passbands ; for stars a commonly quoted absolute magnitude
4410-490: The ancient symbol of the swastika appeared in a variety of cultures across the world at a similar time, and could have been inspired by the appearance of a comet from head on, as the curved jets would be reminiscent of the swastika shape (see Comets and the swastika motif ). Comet Encke has sometimes been identified as the comet in question. In their 1982 book Cosmic Serpent (page 155) Victor Clube and Bill Napier reproduce an ancient Chinese catalogue of cometary shapes from
4500-682: The apparent magnitude m {\displaystyle m} of a body. For an object reflecting sunlight, H {\displaystyle H} and m {\displaystyle m} are connected by the relation m = H + 5 log 10 ( d B S d B O d 0 2 ) − 2.5 log 10 q ( α ) , {\displaystyle m=H+5\log _{10}{\left({\frac {d_{BS}d_{BO}}{d_{0}^{2}}}\right)}-2.5\log _{10}{q(\alpha )},} where α {\displaystyle \alpha }
4590-419: The apparent magnitude of the Moon is m = + 0.28 + 5 log 10 ( 1 ⋅ 0.00257 ) + 2.71 = − 9.96 , {\textstyle m=+0.28+5\log _{10}{\left(1\cdot 0.00257\right)}+2.71=-9.96,} close to the expected value of about − 10.0 {\displaystyle -10.0} . At last quarter ,
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#17328557124194680-450: The body's surface, and hence it differs from asteroid to asteroid. In 1985, the IAU adopted the semi-empirical H G {\displaystyle HG} -system, based on two parameters H {\displaystyle H} and G {\displaystyle G} called absolute magnitude and slope , to model the opposition effect for the ephemerides published by
4770-584: The body. For planets, approximations for the correction term − 2.5 log 10 q ( α ) {\displaystyle -2.5\log _{10}{q(\alpha )}} in the formula for m have been derived empirically, to match observations at different phase angles . The approximations recommended by the Astronomical Almanac are (with α {\displaystyle \alpha } in degrees): Here β {\displaystyle \beta }
4860-772: The brightness of each star appearing in the sky. The brightest stars in the sky were assigned an apparent magnitude m = 1 , and the dimmest stars visible to the naked eye are assigned m = 6 . The difference between them corresponds to a factor of 100 in brightness. For objects within the immediate neighborhood of the Sun, the absolute magnitude M and apparent magnitude m from any distance d (in parsecs , with 1 pc = 3.2616 light-years ) are related by 100 m − M 5 = F 10 F = ( d 10 p c ) 2 , {\displaystyle 100^{\frac {m-M}{5}}={\frac {F_{10}}{F}}=\left({\frac {d}{10\;\mathrm {pc} }}\right)^{2},} where F
4950-1325: The brightness of the core region alone). Both are different scales than the magnitude scale used for planets and asteroids, and can not be used for a size comparison with an asteroid's absolute magnitude H . The activity of comets varies with their distance from the Sun. Their brightness can be approximated as m 1 = M 1 + 2.5 ⋅ K 1 log 10 ( d B S d 0 ) + 5 log 10 ( d B O d 0 ) {\displaystyle m_{1}=M_{1}+2.5\cdot K_{1}\log _{10}{\left({\frac {d_{BS}}{d_{0}}}\right)}+5\log _{10}{\left({\frac {d_{BO}}{d_{0}}}\right)}} m 2 = M 2 + 2.5 ⋅ K 2 log 10 ( d B S d 0 ) + 5 log 10 ( d B O d 0 ) , {\displaystyle m_{2}=M_{2}+2.5\cdot K_{2}\log _{10}{\left({\frac {d_{BS}}{d_{0}}}\right)}+5\log _{10}{\left({\frac {d_{BO}}{d_{0}}}\right)},} where m 1 , 2 {\displaystyle m_{1,2}} are
5040-462: The comet on 15 August. R.E. McCrosky and C.-Y. Shao photographed it on 5 September and Elizabeth Roemer this time with M.R. Gonzales photographed the comet on 13 September. In 1980 Encke was the first comet to be detected by radar. In April 1984 the Pioneer Venus Orbiter observed the comet in ultra-violet and made measurements of its rate of water loss. The failed CONTOUR mission
5130-419: The comet on March 12, comparing to the early March 9 observation, "The comet much shaper, brighter, smaller; its diameter was 1 1/2', magnitude 7 7 (B.D. scale). Its magnitude in the 6-inch Corbett was almost stellar, but in the 28 inch no definitive nucleus could be seen." A number of attempts were made to image the comet around the aphelion of 3 September 1972. Elizabeth Roemer and G. McCorkle photographed
5220-646: The comet's course). The authors of this 1860 textbook of course could not know that the pole of the comet would tumble as it does over such a long period of time, or that outgassing would induce a thrust to change its course. The supposed shortening of the orbit of Encke's Comet demonstrating the existence of ether was mentioned in Edgar Alen Poe's story, "The Unparalleled Adventures Of One Hans Pfaall". http://www.itc.nl/library/Papers_2004/tech_rep/woldai_umm.pdf (1.56 MB) Absolute magnitude In astronomy , absolute magnitude ( M )
5310-544: The course of the satellite, leading to the speculation that it had disintegrated. Attempts to contact the probe were ended on December 20, 2002. The probe thus accomplished none of its primary scientific objectives, but did prove some spaceflight technologies, such as the APL-developed non-coherent Doppler tracking spacecraft navigation technique, which was later used on the New Horizons spacecraft. The CONTOUR spacecraft
5400-787: The day of its perihelion passage, 10 March 2013, comet PANSTARRS was 0.302 AU {\displaystyle 0.302{\text{ AU}}} from the Sun and 1.109 AU {\displaystyle 1.109{\text{ AU}}} from Earth. The total apparent magnitude m 1 {\displaystyle m_{1}} is predicted to have been m 1 = 5.41 + 2.5 ⋅ 3.69 ⋅ log 10 ( 0.302 ) + 5 log 10 ( 1.109 ) = + 0.8 {\displaystyle m_{1}=5.41+2.5\cdot 3.69\cdot \log _{10}{\left(0.302\right)}+5\log _{10}{\left(1.109\right)}=+0.8} at that time. The Minor Planet Center gives
5490-467: The desired characteristics (e.g. active, brighter than absolute magnitude 10, perihelion within 1.5 AU). According to NASA: "An investigation board concluded that the most likely cause of the mishap was structural failure of the spacecraft due to plume heating during the solid-rocket motor burn. Alternate possible but less likely causes determined were catastrophic failure of the solid rocket motor, collision with space debris, and loss of dynamic control of
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#17328557124195580-479: The diffuse reflector model), this yields an apparent magnitude of m = + 0.28 + 5 log 10 ( 1 ⋅ 0.00257 ) − 2.5 log 10 ( 2 3 π ) = − 10.99. {\displaystyle m=+0.28+5\log _{10}{\left(1\cdot 0.00257\right)}-2.5\log _{10}{\left({\frac {2}{3\pi }}\right)}=-10.99.} The actual value
5670-521: The earlier tests allowed mission planners to determine a safe distance from which the CONTOUR would pass by comets targeted on the mission. Three of the four scientific instruments aboard the spacecraft were embedded within this shield. Power for CONTOUR derives from solar cells , which are mounted onto the spacecraft, decorating the sides and rear and generating up to 670 watts of power. A nickel–cadmium battery designed to last up to nine ampere hours
5760-747: The high phase angle, the correction term above yields an actual apparent magnitude of m = − 6.09 + ( − 1.044 × 10 − 3 ⋅ 93.0 + 3.687 × 10 − 4 ⋅ 93.0 2 − 2.814 × 10 − 6 ⋅ 93.0 3 + 8.938 × 10 − 9 ⋅ 93.0 4 ) = − 4.59. {\displaystyle m=-6.09+\left(-1.044\times 10^{-3}\cdot 93.0+3.687\times 10^{-4}\cdot 93.0^{2}-2.814\times 10^{-6}\cdot 93.0^{3}+8.938\times 10^{-9}\cdot 93.0^{4}\right)=-4.59.} This
5850-490: The magnitudes of the distant objects. The absolute magnitude M can also be written in terms of the apparent magnitude m and stellar parallax p : M = m + 5 ( log 10 p + 1 ) , {\displaystyle M=m+5\left(\log _{10}p+1\right),} or using apparent magnitude m and distance modulus μ : M = m − μ . {\displaystyle M=m-\mu .} Rigel has
5940-454: The mission. The spacecraft was fitted with a 25 cm (9.8 in) whipple shield , similar to the one used on Stardust , on its leading face, designed with four layers of nextel fabric and seven layers of kevlar . The shield was built to allow the spacecraft to withstand the respective 28.2 and 14 km/s velocity flybys of comets Encke and Schwassmann-Wachmann-3, where the spacecraft would be subjected to numerous particles ejecting from
6030-410: The most luminous persistent objects in the observable universe, although these objects can vary in brightness over astronomically short timescales. At the extreme end, the optical afterglow of the gamma ray burst GRB 080319B reached, according to one paper, an absolute r magnitude brighter than −38 for a few tens of seconds. The Greek astronomer Hipparchus established a numerical scale to describe
6120-456: The nuclei at resolutions of up to 100 meters (330 ft), and obtaining detailed compositional data on gas and dust in the near-nucleus environment, with the goal of improving knowledge of the characteristics of comet nuclei. After the solid rocket motor intended to inject the spacecraft into solar orbit was ignited on August 15, 2002, contact with the probe could not be re-established. Ground-based telescopes later found three objects along
6210-410: The object is near opposition. It is known accurately only for a small number of asteroids, hence for most asteroids a value of G = 0.15 {\displaystyle G=0.15} is assumed. In rare cases, G {\displaystyle G} can be negative. An example is 101955 Bennu , with G = − 0.08 {\displaystyle G=-0.08} . In 2012,
6300-540: The orbit of Encke is frequently perturbed by the inner planets. Encke is currently close to a 7:2 mean motion resonance with Jupiter , and it is possible that some of the larger fragments shed by the comet, or released by a larger progenitor of the comet, are trapped in this resonance. Encke's orbit gets as close as 0.173 AU (25.9 million km ; 16.1 million mi ) to Earth ( minimum orbit intersection distance ). On 4 July 1997, Encke passed 0.19 AU from Earth, and on June 29, 2172, it will make
6390-534: The phase angle in degrees , then q ( α ) = 2 3 ( ( 1 − α 180 ∘ ) cos α + 1 π sin α ) . {\displaystyle q(\alpha )={\frac {2}{3}}\left(\left(1-{\frac {\alpha }{180^{\circ }}}\right)\cos {\alpha }+{\frac {1}{\pi }}\sin {\alpha }\right).} A full-phase diffuse sphere reflects two-thirds as much light as
6480-455: The probe began orbiting the planet in March 2011. The spikes in calcium levels are thought to originate from small dust particles hitting the planet and knocking calcium-bearing molecules into the atmosphere in a process called impact vaporization. However, the general background of interplanetary dust in the inner Solar System cannot, by itself, account for the periodic spikes in calcium. This suggests
6570-500: The properties of the reflecting surface, in particular on its roughness . In practice, different approximations are used based on the known or assumed properties of the surface. The surfaces of terrestrial planets are generally more difficult to model than those of gaseous planets, the latter of which have smoother visible surfaces. Planetary bodies can be approximated reasonably well as ideal diffuse reflecting spheres . Let α {\displaystyle \alpha } be
6660-557: The right position (1.5 arcminutes from its then predicted position) but orbital uncertainties made it impossible to be sure of its identity. A recalculation of Encke's orbit in the 1970s resulted in a calculated position only a few arcseconds (2.0 in ascension and 4.6 in declination) from the imaged object meaning the object probably was Encke. In March 1918 the Greenwich 28-inch aperture telescope took observations of Encke (1917c). An observer of Encke's in March 1918 had this to say of
6750-432: The rotation period nor the axial tilt are known, limiting the predictability. The models presented here do not capture those effects. The brightness of comets is given separately as total magnitude ( m 1 {\displaystyle m_{1}} , the brightness integrated over the entire visible extend of the coma ) and nuclear magnitude ( m 2 {\displaystyle m_{2}} ,
6840-446: The same object. In 1819 he published his conclusions in the journal Correspondance astronomique , and predicted correctly its return in 1822 (2P/1822 L1). It was recovered by Carl Ludwig Christian Rümker at Parramatta Observatory on 2 June 1822. Comets are in unstable orbits that evolve over time due to perturbations and outgassing . Given Encke's low orbital inclination near the ecliptic and brief orbital period of 3 years,
6930-547: The scale from the variable Sun. However, on this SI power scale, the nominal solar luminosity corresponds closely to M bol = 4.74 , a value that was commonly adopted by astronomers before the 2015 IAU resolution. The luminosity of the star in watts can be calculated as a function of its absolute bolometric magnitude M bol as: L ⋆ = L 0 10 − 0.4 M b o l {\displaystyle L_{\star }=L_{0}10^{-0.4M_{\mathrm {bol} }}} using
7020-431: The smaller the numerical value of its absolute magnitude. A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100 . For example, a star of absolute magnitude M V = 3.0 would be 100 times as luminous as a star of absolute magnitude M V = 8.0 as measured in
7110-406: The spacecraft." After the loss of CONTOUR, a replacement spacecraft – CONTOUR 2 – was proposed, scheduled for launch in 2006. However, the replacement did not ultimately materialize. Comet Encke Comet Encke / ˈ ɛ ŋ k i / , or Encke's Comet (official designation: 2P/Encke ), is a periodic comet that completes an orbit of the Sun once every 3.3 years. (This
7200-515: The standard 10 parsecs distance. Consequently, the absolute magnitude of any object equals the apparent magnitude it would have if it were 10 parsecs away. Some stars visible to the naked eye have such a low absolute magnitude that they would appear bright enough to outshine the planets and cast shadows if they were at 10 parsecs from the Earth. Examples include Rigel (−7.8), Deneb (−8.4), Naos (−6.2), and Betelgeuse (−5.8). For comparison, Sirius has an absolute magnitude of only 1.4, which
7290-436: The total and nuclear apparent magnitudes of the comet, respectively, M 1 , 2 {\displaystyle M_{1,2}} are its "absolute" total and nuclear magnitudes, d B S {\displaystyle d_{BS}} and d B O {\displaystyle d_{BO}} are the body-sun and body-observer distances, d 0 {\displaystyle d_{0}}
7380-463: The variables as defined previously. For planets and asteroids , a definition of absolute magnitude that is more meaningful for non-stellar objects is used. The absolute magnitude, commonly called H {\displaystyle H} , is defined as the apparent magnitude that the object would have if it were one astronomical unit (AU) from both the Sun and the observer, and in conditions of ideal solar opposition (an arrangement that
7470-407: Was also installed aboard the spacecraft in the event that the solar cell system fails, or does not provide enough power for the spacecraft or its instruments to function. CONTOUR launched on a Delta 7425 (a Delta II Lite launch vehicle with four strap-on solid-rocket boosters and a Star 27 third stage) on July 3, 2002, at 6:47:41 UT (2:47:41 a.m. EDT) from Cape Canaveral Air Force Station . It
7560-538: Was constructed in-house at the Johns Hopkins University Applied Physics Laboratory . CONTOUR was shaped as an octagonal prism , measuring at 2.1 metres (6.9 ft) tall and 1.8 metres (5.9 ft) long, had a total fueled mass of 398 kg (877 lb) at launch, not including the 377 kg (831 lb) mass of the Star 30 booster it was attached to, during the launch phase of
7650-444: Was estimated as M 1 = 8.5 {\displaystyle M_{1}=8.5} . It was subsequently lost and was only rediscovered in 2003. At that time, its absolute magnitude had decreased to M 1 = 22.9 {\displaystyle M_{1}=22.9} , and it was realised that the 1819 apparition coincided with an outburst. 289P/Blanpain reached naked eye brightness (5–8 mag) in 1819, even though it
7740-461: Was independently observed by several astronomers, the first two being Pierre Méchain and Charles Messier in 1786. It was next observed by Caroline Herschel in 1795 and was "discovered" for a third time by Jean-Louis Pons in 1818. Its orbit was calculated by Johann Franz Encke , who through laborious calculations was able to link observations of comets in 1786 (designated 2P/1786 B1), 1795 (2P/1795 V1), 1805 (2P/1805 U1) and 1818 (2P/1818 W1) to
7830-479: Was launched into a high- apogee Earth orbit with a period of 5.5 days. Following a series of phasing orbits, the Star 30 solid rocket motor was used to perform an injection maneuver on August 15, 2002, to put CONTOUR in the proper trajectory for an Earth flyby on August 15, 2003, followed by an encounter with comet Encke on November 12, 2003, at a distance of 100 to 160 km and a flyby speed of 28.2 km/s, 1.07 AU from
7920-443: Was launched to study this comet, and also Schwassmann–Wachmann 3 . On 20 April 2007, STEREO-A observed the tail of Comet Encke to be temporarily torn off by magnetic field disturbances caused by a coronal mass ejection (a blast of solar particles from the Sun). The tail grew back due to the continuous shedding of dust and gas by the comet. Comet Encke is believed to be the originator of several related meteor showers known as
8010-459: Was more active. Astronomers planned a 2019 search campaign for fragments of comet Encke which would have been visible from Earth as the Taurid swarm passed between July 5–11, and July 21 – August 10. There were no reports of discoveries of any such objects. Comet Encke (and Biela's Comet ) had a role in scientific history in the generally discredited concept of luminiferous aether . As its orbit
8100-430: Was perturbed and shortened, the shortening could only be ascribed to the drag of an "ether" through which it orbited in outer space . One reference reads: Encke's pole tumbles in an 81-year period, therefore it will accelerate for half that time, and decelerate for the other half of the time (since the orientation of the comets rotation to solar heating determines how its orbit changes due to outgassing forward or aft of
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