For values ofe from0 to just under1 the orbit's shape is an increasingly elongated (or flatter) ellipse; for values ofe just over1 to infinity the orbit is ahyperbola branch making a total turn of 2arccsc(e) , decreasing from 180 to 0 degrees. Here, the total turn is analogous toturning number, but for open curves (an angle covered by velocity vector). Thelimit case between an ellipse and a hyperbola, whene equals1, 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 the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory whilee tends to1 (or in the parabolic case, remains1).
For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable.
For elliptical orbits, a simple proof shows that gives the projection angle of a perfect circle to anellipse of eccentricitye. For example, to view the eccentricity of the planet Mercury (e = 0.2056), one must simply calculate theinverse 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 fromMedieval Latineccentricus, derived fromGreekἔκκεντροςekkentros "out of the center", fromἐκ-ek-, "out of" +κέντρονkentron "center". "Eccentric" first appeared in English in 1551, with the definition "...a circle in which the earth, sun. etc. deviates from its center".[citation needed] In 1556, five years later, an adjectival form of the word had developed.
ra is the radius atapoapsis (also "apofocus", "aphelion", "apogee"), i.e., the farthest distance of the orbit to thecenter of mass of the system, which is afocus of the ellipse.
rp is the radius atperiapsis (or "perifocus" etc.), the closest distance.
The semi-major axis, a, is also the path-averaged distance to the centre of mass,[2]: 24–25 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 theapoapsis radius to theperiapsis radius:
For Earth, orbital eccentricitye ≈0.01671,apoapsis is aphelion andperiapsis is perihelion, relative to the Sun.
For Earth's annual orbit path, the ratio of longest radius (ra) / shortest radius (rp) is
Plot of the changing orbital eccentricities ofMercury,Venus,Earth andMars over the next 50 000 years. The arrows indicate the different scales used, as the eccentricities of Mercury and Mars are much greater than those of Venus and Earth. The 0 point on x-axis in this plot is the year 2007.
The table lists the values for all planets and dwarf planets, and selected asteroids, comets, and moons.Mercury has the greatest orbital eccentricity of any planet in theSolar System (e =0.2056), followed byMars of0.0934. Such eccentricity is sufficient for Mercury to receive twice as muchsolar irradiation at perihelion compared to aphelion. Before its demotion fromplanet status in 2006,Pluto was considered to be the planet with the most eccentric orbit (e =0.248). OtherTrans-Neptunian objects have significant eccentricity, notably the dwarf planetEris (0.44). Even further out,Sedna has an extremely-high eccentricity of0.855 due to its estimated aphelion of 937 AU and perihelion of about 76 AU, possibly under influence ofunknown object(s).
The eccentricity ofEarth's orbit is currently about0.0167; its orbit is nearly circular.Neptune's andVenus's have even lower eccentricities of0.0086 and0.0068 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 nearly0.0034 to almost 0.058 as a result of gravitational attractions among the planets.[4]
Luna's value is0.0549, the most eccentric of the large moons in the Solar System. The fourGalilean moons (Io,Europa,Ganymede andCallisto) have their eccentricities of less than 0.01.Neptune's largest moonTriton has an eccentricity of1.6×10−5 (0.000016),[5] the smallest eccentricity of any known moon in the Solar System;[citation needed] its orbit is as close to a perfect circle as can be currently[when?] measured. Smaller moons, particularlyirregular moons, can have significant eccentricities, such as Neptune's third largest moon,Nereid, of0.75.
Most of the Solar System'sasteroids have orbital eccentricities between 0 and 0.35 with an average value of 0.17.[6] Their comparatively high eccentricities are probably due to under influence ofJupiter and to past collisions.
Comets have very different values of eccentricities.Periodic comets have eccentricities mostly between 0.2 and 0.7,[7] but some of them have highly eccentric elliptical orbits with eccentricities just below 1; for example,Halley's Comet has a value of 0.967. Non-periodic comets follow near-parabolic orbits and thus have eccentricities even closer to 1. Examples includeComet Hale–Bopp with a value of0.9951,[8]Comet Ikeya-Seki with a value of0.9999 andComet McNaught (C/2006 P1) with a value of1.000019.[9] As first two's values are less than 1, their orbit are elliptical and they will return.[8] McNaught has ahyperbolic orbit but within the influence of the inner planets,[9] is still bound to the Sun with an orbital period of about 105 years.[3]Comet C/1980 E1 has the largest eccentricity of any known hyperbolic comet of solar origin with an eccentricity of 1.057,[10] and will eventually leave the Solar System.
ʻOumuamua is the firstinterstellar object to be found passing through the Solar System. Its orbital eccentricity of 1.20 indicates that ʻOumuamua has never been gravitationally bound to the Sun. It was discovered 0.2 AU (30000000 km;19000000 mi) from Earth and is roughly 200 meters in diameter. It has an interstellar speed (velocity at infinity) of 26.33 km/s (58900 mph).
The mean eccentricity of an object is the average eccentricity as a result ofperturbations over a given time period. Neptune currently has an instant (currentepoch) eccentricity of0.0113,[13] but from 1800 to 2050 has a mean eccentricity of0.00859.[14]
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Orbital mechanics require that the duration of the seasons be proportional to the area of Earth's orbit swept between thesolstices andequinoxes, 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 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.[15][16]
Apsidal precession also slowly changes 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 asaxial precession. The climatic effects of this change are part of theMilankovitch cycles. Over the next10000 years, the northern hemisphere winters will become gradually longer and summers will become shorter. Any cooling effect in one hemisphere 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.[17] This will reduce the mean orbital radius and raise temperatures in both hemispheres closer to the mid-interglacial peak.
Of the manyexoplanets 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 aretidally-locked to 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.[18] 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 othermultiplanetary systems have been found, but none resemble the Solar System. The Solar System has uniqueplanetesimal systems, which led the planets to have near-circular orbits. Solar planetesimal systems include theasteroid belt,Hilda family,Kuiper belt,Hills cloud, and theOort cloud. The exoplanet systems discovered have either no planetesimal systems or a very large one. Low eccentricity is needed for habitability, especially advanced life.[19] High multiplicity planet systems are much more likely to have habitable exoplanets.[20][21] Thegrand tack hypothesis of the Solar System also helps understand its near-circular orbits and other unique features.[22][23][24][25][26][27][28][29]
^Youdin, Andrew N.; Rieke, George H. (15 December 2015). "Planetesimals in Debris Disks".arXiv:1512.04996.{{cite journal}}:Cite journal requires|journal= (help)
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