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39-496: Endate is a presumed stony S-type asteroid . It orbits the Sun in the inner main-belt at a distance of 2.0–2.7  AU once every 3 years and 8 months (1,351 days). Its orbit has an eccentricity of 0.15 and an inclination of 3 ° with respect to the ecliptic . The first precovery was taken at Palomar Observatory in 1954, extending the body's observation arc by 33 years prior to its official discovery observation. In April 2014,

78-638: A + r p = r a / r p − 1 r a / r p + 1 = 1 − 2 r a r p + 1 {\displaystyle {\begin{aligned}e&={\frac {r_{\text{a}}-r_{\text{p}}}{r_{\text{a}}+r_{\text{p}}}}\\\,\\&={\frac {r_{\text{a}}/r_{\text{p}}-1}{r_{\text{a}}/r_{\text{p}}+1}}\\\,\\&=1-{\frac {2}{\;{\frac {r_{\text{a}}}{r_{\text{p}}}}+1\;}}\end{aligned}}} where: The semi-major axis, a,

117-524: A 5:2 resonance, may have been more rapid when Jupiter's and Saturn's orbits were closer together. More recently, a relatively small number of asteroids have been found to possess high eccentricity orbits which do lie within the Kirkwood gaps. Examples include the Alinda and Griqua groups . These orbits slowly increase their eccentricity on a timescale of tens of millions of years, and will eventually break out of

156-431: A mean eccentricity of 0.008 59 . Orbital mechanics require that the duration of the seasons be proportional to the area of Earth's orbit swept between the solstices and equinoxes , so when the orbital eccentricity is extreme, the seasons that occur on the far side of the orbit ( aphelion ) can be substantially longer in duration. Northern hemisphere autumn and winter occur at closest approach ( perihelion ), when Earth

195-414: A rotational lightcurve of Endate was obtained from photometric observations by Hungarian astronomer Gyula M. Szabó. Lightcurve analysis gave it a longer-than average rotation period of 34 hours with a brightness amplitude of 0.5 magnitude ( U=n.a. ). Most minor planets have a spin rate between 2 and 20 hours. Endate ' s rotation period is significantly longer but still much shorter than that of

234-406: A semi-major axis of 2.71 AU). The main or core population of the asteroid belt may be divided into the inner and outer zones, separated by the 3:1 Kirkwood gap at 2.5 AU, and the outer zone may be further divided into middle and outer zones by the 5:2 gap at 2.82 AU: 4 Vesta is the largest asteroid in the inner zone, 1 Ceres and 2 Pallas in the middle zone, and 10 Hygiea in

273-549: A standard albedo for stony asteroids of 0.20 and consequently calculates a smaller diameter of 5.66 kilometers. This minor planet was named in honor of Japanese amateur astronomer Kin Endate from Bihoro in northern Japan. He is a prolific observer and discoverer of minor planets . The official naming citation was published by the Minor Planet Center on 8 July 1990 ( M.P.C. 16593 ). Kirkwood gap A Kirkwood gap

312-424: A value of 0.967. Non-periodic comets follow near- parabolic orbits and thus have eccentricities even closer to 1. Examples include Comet Hale–Bopp with a value of 0.995 1 , Comet Ikeya-Seki with a value of 0.999 9 and Comet McNaught (C/2006 P1) with a value of 1.000 019 . As first two's values are less than 1, their orbit are elliptical and they will return. McNaught has a hyperbolic orbit but within

351-431: Is a Kepler orbit . The eccentricity of this Kepler orbit is a non-negative number that defines its shape. The eccentricity may take the following values: The eccentricity e is given by e = 1 + 2 E L 2 m red α 2 {\displaystyle e={\sqrt {1+{\frac {2EL^{2}}{m_{\text{red}}\,\alpha ^{2}}}}}} where E

390-456: Is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola . The term derives its name from the parameters of conic sections , as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem , but extensions exist for objects following a rosette orbit through the Galaxy. In a two-body problem with inverse-square-law force, every orbit

429-652: Is a gap or dip in the distribution of the semi-major axes (or equivalently of the orbital periods ) of the orbits of main-belt asteroids . They correspond to the locations of orbital resonances with Jupiter . The gaps were first noticed in 1866 by Daniel Kirkwood , who also correctly explained their origin in the orbital resonances with Jupiter while a professor at Jefferson College in Canonsburg, Pennsylvania . For example, there are very few asteroids with semimajor axis near 2.50 AU , period 3.95 years, which would make three orbits for each orbit of Jupiter (hence, called

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468-643: Is also the path-averaged distance to the centre of mass, while the time-averaged distance is a(1 + e e / 2). [1] The eccentricity of an elliptical orbit can be used to obtain the ratio of the apoapsis radius to the periapsis radius: r a r p = a ( 1 + e ) a ( 1 − e ) = 1 + e 1 − e {\displaystyle {\frac {r_{\text{a}}}{r_{\text{p}}}}={\frac {\,a\,(1+e)\,}{\,a\,(1-e)\,}}={\frac {1+e}{1-e}}} For Earth, orbital eccentricity e ≈ 0.016 71 , apoapsis

507-456: Is aphelion and periapsis is perihelion, relative to the Sun. For Earth's annual orbit path, the ratio of longest radius ( r a ) / shortest radius ( r p ) is r a r p = 1 + e 1 − e  ≈ 1.03399 . {\displaystyle {\frac {\,r_{\text{a}}\,}{r_{\text{p}}}}={\frac {\,1+e\,}{1-e}}{\text{ ≈ 1.03399 .}}} The table lists

546-572: Is balanced by warming in the other, and any overall change will be counteracted by the fact that the eccentricity of Earth's orbit will be almost halved. This will reduce the mean orbital radius and raise temperatures in both hemispheres closer to the mid-interglacial peak. Of the many exoplanets discovered, most have a higher orbital eccentricity than planets in the Solar System. Exoplanets found with low orbital eccentricity (near-circular orbits) are very close to their star and are tidally-locked to

585-460: Is currently about 0.016 7 ; its orbit is nearly circular. Neptune's and Venus's have even lower eccentricities of 0.008 6 and 0.006 8 respectively, the latter being the least orbital eccentricity of any planet in the Solar System. Over hundreds of thousands of years, the eccentricity of the Earth's orbit varies from nearly 0.003 4 to almost 0.058 as a result of gravitational attractions among

624-466: Is moving at its maximum velocity—while the opposite occurs in the southern hemisphere. As a result, in the northern hemisphere, autumn and winter are slightly shorter than spring and summer—but in global terms this is balanced with them being longer below the equator. In 2006, the northern hemisphere summer was 4.66 days longer than winter, and spring was 2.9 days longer than autumn due to orbital eccentricity. Apsidal precession also slowly changes

663-457: Is negative for an attractive force, positive for a repulsive one; related to the Kepler problem ) or in the case of a gravitational force: e = 1 + 2 ε h 2 μ 2 {\displaystyle e={\sqrt {1+{\frac {2\varepsilon h^{2}}{\mu ^{2}}}}}} where ε is the specific orbital energy (total energy divided by

702-467: Is the total orbital energy , L is the angular momentum , m red is the reduced mass , and α {\displaystyle \alpha } the coefficient of the inverse-square law central force such as in the theory of gravity or electrostatics in classical physics : F = α r 2 {\displaystyle F={\frac {\alpha }{r^{2}}}} ( α {\displaystyle \alpha }

741-441: The periapsis and apoapsis since r p = a ( 1 − e ) {\displaystyle r_{\text{p}}=a\,(1-e)} and r a = a ( 1 + e ) , {\displaystyle r_{\text{a}}=a\,(1+e)\,,} where a is the length of the semi-major axis . e = r a − r p r

780-481: The 3:1 orbital resonance). Other orbital resonances correspond to orbital periods whose lengths are simple fractions of Jupiter's. The weaker resonances lead only to a depletion of asteroids, while spikes in the histogram are often due to the presence of a prominent asteroid family (see List of asteroid families ) . Most of the Kirkwood gaps are depleted, unlike the mean-motion resonances (MMR) of Neptune or Jupiter's 3:2 resonance, that retain objects captured during

819-471: The Solar System's asteroids have orbital eccentricities between 0 and 0.35 with an average value of 0.17. Their comparatively high eccentricities are probably due to under influence of Jupiter and to past collisions. Comets have very different values of eccentricities. Periodic comets have eccentricities mostly between 0.2 and 0.7, but some of them have highly eccentric elliptical orbits with eccentricities just below 1; for example, Halley's Comet has

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858-570: The Solar System. The Solar System has unique planetesimal systems, which led the planets to have near-circular orbits. Solar planetesimal systems include the asteroid belt , Hilda family , Kuiper belt , Hills cloud , and the Oort cloud . The exoplanet systems discovered have either no planetesimal systems or a very large one. Low eccentricity is needed for habitability, especially advanced life. High multiplicity planet systems are much more likely to have habitable exoplanets. The grand tack hypothesis of

897-454: The Sun. It was discovered 0.2 AU ( 30 000 000  km; 19 000 000  mi) from Earth and is roughly 200 meters in diameter. It has an interstellar speed (velocity at infinity) of 26.33 km/s ( 58 900  mph). The mean eccentricity of an object is the average eccentricity as a result of perturbations over a given time period. Neptune currently has an instant (current epoch ) eccentricity of 0.011 3 , but from 1800 to 2050 has

936-628: The center", from ἐκ- ek- , "out of" + κέντρον kentron "center". "Eccentric" first appeared in English in 1551, with the definition "...a circle in which the earth, sun. etc. deviates from its center". In 1556, five years later, an adjectival form of the word had developed. The eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector : e = | e | {\displaystyle e=\left|\mathbf {e} \right|} where: For elliptical orbits it can also be calculated from

975-461: The energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1 (or in the parabolic case, remains 1). For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin ⁡ ( e ) {\displaystyle \arcsin(e)} yields

1014-600: The giant planet migration of the Nice model . The loss of objects from the Kirkwood gaps is due to the overlapping of the ν 5 and ν 6 secular resonances within the mean-motion resonances. The orbital elements of the asteroids vary chaotically as a result and evolve onto planet-crossing orbits within a few million years. The 2:1 MMR has a few relatively stable islands within the resonance, however. These islands are depleted due to slow diffusion onto less stable orbits. This process, which has been linked to Jupiter and Saturn being near

1053-462: The influence of the planets, is still bound to the Sun with an orbital period of about 10 years. Comet C/1980 E1 has the largest eccentricity of any known hyperbolic comet of solar origin with an eccentricity of 1.057, and will eventually leave the Solar System. ʻOumuamua is the first interstellar object to be found passing through the Solar System. Its orbital eccentricity of 1.20 indicates that ʻOumuamua has never been gravitationally bound to

1092-467: The outer zone. 87 Sylvia is probably the largest Main Belt asteroid beyond the outer zone. Eccentricity (orbit) In astrodynamics , the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle . A value of 0 is a circular orbit , values between 0 and 1 form an elliptic orbit , 1

1131-473: The place in Earth's orbit where the solstices and equinoxes occur. This is a slow change in the orbit of Earth, not the axis of rotation, which is referred to as axial precession . The climatic effects of this change are part of the Milankovitch cycles . Over the next 10 000 years, the northern hemisphere winters will become gradually longer and summers will become shorter. Any cooling effect in one hemisphere

1170-597: The planets. Luna 's value is 0.054 9 , the most eccentric of the large moons in the Solar System. The four Galilean moons ( Io , Europa , Ganymede and Callisto ) have their eccentricities of less than 0.01. Neptune 's largest moon Triton has an eccentricity of 1.6 × 10 ( 0.000 016 ), the smallest eccentricity of any known moon in the Solar System; its orbit is as close to a perfect circle as can be currently measured. Smaller moons, particularly irregular moons , can have significant eccentricities, such as Neptune's third largest moon, Nereid , of 0.75 . Most of

1209-519: The projection angle of a perfect circle to an ellipse of eccentricity e . For example, to view the eccentricity of the planet Mercury ( e = 0.2056), one must simply calculate the inverse sine to find the projection angle of 11.86 degrees. Then, tilting any circular object by that angle, the apparent ellipse of that object projected to the viewer's eye will be of the same eccentricity. The word "eccentricity" comes from Medieval Latin eccentricus , derived from Greek ἔκκεντρος ekkentros "out of

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1248-492: The radii corresponding to the gaps. The actual spatial density of asteroids in these gaps does not differ significantly from the neighboring regions. The main gaps occur at the 3:1, 5:2, 7:3, and 2:1 mean-motion resonances with Jupiter. An asteroid in the 3:1 Kirkwood gap would orbit the Sun three times for each Jovian orbit, for instance. Weaker resonances occur at other semi-major axis values, with fewer asteroids found than nearby. (For example, an 8:3 resonance for asteroids with

1287-445: The reduced mass), μ the standard gravitational parameter based on the total mass, and h the specific relative angular momentum ( angular momentum divided by the reduced mass). For values of e from 0 to 1 the orbit's shape is an increasingly elongated (or flatter) ellipse; for values of e from 1 to infinity the orbit is a hyperbola branch making a total turn of 2 arccsc ( e ) , decreasing from 180 to 0 degrees. Here,

1326-416: The resonance due to close encounters with a major planet. This is why asteroids are rarely found in the Kirkwood gaps. The most prominent Kirkwood gaps are located at mean orbital radii of: Weaker and/or narrower gaps are also found at: The gaps are not seen in a simple snapshot of the locations of the asteroids at any one time because asteroid orbits are elliptical, and many asteroids still cross through

1365-486: The so-called slow rotators , which take at least 100 hours to rotate once around their axis. According to the surveys carried out by the Japanese Akari satellite and NASA's Wide-field Infrared Survey Explorer with its subsequent NEOWISE mission, Endate measures between 7.386 and 13.73 kilometers in diameter and its surface has an albedo between 0.038 and 0.15. The Collaborative Asteroid Lightcurve Link assumes

1404-417: The star. All eight planets in the Solar System have near-circular orbits. The exoplanets discovered show that the Solar System, with its unusually-low eccentricity, is rare and unique. One theory attributes this low eccentricity to the high number of planets in the Solar System; another suggests it arose because of its unique asteroid belts. A few other multiplanetary systems have been found, but none resemble

1443-407: The total turn is analogous to turning number , but for open curves (an angle covered by velocity vector). The limit case between an ellipse and a hyperbola, when e equals 1, is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits have zero angular momentum and hence eccentricity equal to one. Keeping

1482-460: The values for all planets and dwarf planets, and selected asteroids, comets, and moons. Mercury has the greatest orbital eccentricity of any planet in the Solar System ( e = 0.2056 ), followed by Mars of 0.093 4 . Such eccentricity is sufficient for Mercury to receive twice as much solar irradiation at perihelion compared to aphelion. Before its demotion from planet status in 2006, Pluto

1521-420: Was considered to be the planet with the most eccentric orbit ( e = 0.248 ). Other Trans-Neptunian objects have significant eccentricity, notably the dwarf planet Eris (0.44). Even further out, Sedna has an extremely-high eccentricity of 0.855 due to its estimated aphelion of 937 AU and perihelion of about 76 AU, possibly under influence of unknown object(s) . The eccentricity of Earth's orbit

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