- This page refers to eccentricity in astrodynamics. Orbital mechanics or astrodynamics is the application of Celestial mechanics to the practical problems concerning the motion of Rockets and other Spacecraft For other uses, see the disambiguation page eccentricity.
In astrodynamics, under standard assumptions, any orbit must be of conic section shape. Orbital mechanics or astrodynamics is the application of Celestial mechanics to the practical problems concerning the motion of Rockets and other Spacecraft For most of the problems in Astrodynamics involving two bodies m_1\ and m_2\ standard assumptions are usually the following A1 In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star In Mathematics, a conic section (or just conic) is a Curve obtained by intersecting a cone (more precisely a circular Conical surface The eccentricity of this conic section, the orbit's eccentricity, is an important parameter of the orbit that defines its absolute shape. In Mathematics, the eccentricity, denoted e or \varepsilon is a parameter associated with every conic section. Eccentricity may be interpreted as a measure of how much this shape deviates from a circle.
Under standard assumptions eccentricity (
) is strictly defined for all circular, elliptic, parabolic and hyperbolic orbits and may take following values:
- for circular orbits:
, - for elliptic orbits:
, - for parabolic trajectories:
, - for hyperbolic trajectories:
. For most of the problems in Astrodynamics involving two bodies m_1\ and m_2\ standard assumptions are usually the following A1 For other meanings of the term "orbit" see Orbit (disambiguation In Astrodynamics or Celestial mechanics a circular In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1 In Astrodynamics or Celestial mechanics a Parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 In Astrodynamics or Celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1 In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star For other meanings of the term "orbit" see Orbit (disambiguation In Astrodynamics or Celestial mechanics a circular In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1 In Astrodynamics or Celestial mechanics a Parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 In Astrodynamics or Celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1
For elliptical orbits, a simple proof shows that sin−1e yields the projection angle of a perfect circle to an ellipse of eccentricity e. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a So to view the eccentricity of, say, the planet Mercury (0. 2056), simply calculate the inverse sine to find the projection angle of 11. 86 degrees. Then tilt any circular object (such as a coffee mug viewed from the top) by that angle and the apparent ellipse projected to your eye will be of that same eccentricity. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a
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Calculation
Eccentricity of an orbit can be calculated from orbital state vectors as a magnitude of eccentricity vector:
where:
is eccentricity vector. In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star In Astrodynamics or Celestial dynamics orbital state vectors (sometimes state vectors) are vectors of Position (\mathbf{r} and The magnitude of a mathematical object is its size a property by which it can be larger or smaller than other objects of the same kind in technical terms an Ordering In Astrodynamics, the eccentricity vector of a Conic section Orbit is the vector pointing towards the Periapsis and with magnitude In Astrodynamics, the eccentricity vector of a Conic section Orbit is the vector pointing towards the Periapsis and with magnitude
For elliptic orbits it can also be calculated from distance at apoapsis and periapsis:
where:
is radius at apoapsis (farthest approach),
is radius at periapsis (closest approach). In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1 In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from
Examples
The eccentricity of the Earth's orbit is currently about 0. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 0167. Over thousands of years, the eccentricity of the Earth's orbit varies from nearly 0. 0034 to almost 0. 058 as a result of gravitational attractions between the planets (see graph [1]).
In other values, Mercury (with an eccentricity of 0. 2056) holds the title as the largest value among the planets of the Solar System. Prior to the redefinition of its planetary status, the dwarf planet Pluto held this title with an eccentricity of about 0. 248. The Moon also holds a notable value at 0. 0549. For the values for all planets in one table, see Table of planets in the solar system.
Most of the solar system's asteroids have eccentricities between 0 and 0. Asteroids, sometimes called Minor planets or planetoids', are bodies—primarily of the inner Solar System —that are smaller than planets but 35 with an average value of 0. 17. [1] Their comparatively high eccentricities are probably due to the influence of Jupiter and to past collisions.
The eccentricity of comets is most often close to 1. A comet is a small Solar System body that orbits the Sun and when close enough to the Sun exhibits a visible coma (atmosphere or a tail — Periodic comets have highly eccentric elliptical orbits, with eccentricities just below 1; Halley's Comet's elliptical orbit, for example, has a value of 0. Periodic comets are defined for these purposes as those Comets having orbital periods of less than 200 years (also known as "short-period comets" or which In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1 Halley's Comet, officially designated 1P/Halley and also referred to as Comet Halley after Edmond Halley, is a Comet that can be seen every 967. Non-periodic comets follow near-parabolic orbits and thus have eccentricities very close to 1. In Astrodynamics or Celestial mechanics a Parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 Examples include Comet Hale-Bopp with a value of 0. Comet Hale-Bopp ( formally designated C/1995 O1) was probably the most widely observed Comet of the twentieth century and one of the brightest 995086 and Comet McNaught with a value of 1. Comet McNaught, also known as the Great Comet of 2007 and given the designation C/2006 P1, is a non-periodic Comet discovered on 000030. As Hale-Bopp's value is less than 1, its orbit is elliptical and so the comet will in fact return (in about 4380AD). Comet McNaught on the other hand has a hyperbolic orbit and so may leave the solar system indefinitely. In Astrodynamics or Celestial mechanics a hyperbolic trajectory is a Kepler orbit with the eccentricity greater than 1 The Solar System consists of the Sun and those celestial objects bound to it by Gravity.
Planet Neptune's largest moon Triton has the smallest eccentricity of any known body in the solar system; its orbit is as close to a perfect circle as can be currently measured. Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System. TemplateInfobox Planet.--> Triton (ˈtraɪtən, or as in Greek
Climatic effect
Orbital mechanics require that the duration of the seasons be proportional to the area of the 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. Solstices occur twice a year when the tilt of the Earth's axis is most oriented toward or away from the Sun, causing the Sun to reach its northernmost and southernmost extremes An equinox is the event of the Sun passing over the Earth's equator in its annual cycle In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from Today, northern hemisphere fall and winter occur at closest approach (perihelion), when the earth is moving at its maximum velocity. In Celestial mechanics, an apsis, plural apsides (ˈæpsɨdɪːz is the point of greatest or least distance of the Elliptical orbit of an object from As a result, in the northern hemisphere, fall and winter are slightly shorter than spring and summer. In 2006, summer is 4. 66 days longer than winter and spring is 2. 9 days longer than fall [2]. Axial precession slowly changes the place in the Earth's orbit where the solstices and equinoxes occur. In Astronomy, Precession refers to the movement of the rotational axis of a body such as a planet with respect to Inertial space. Over the next 10,000 years, northern hemisphere winters will become gradually longer and summers will become shorter. Any cooling effect, however, will be counteracted by the fact that the eccentricity of Earth's orbit will be almost halved, reducing the mean orbital radius and raising temperatures in both hemispheres closer to the mid-interglacial peak. Also, now in north hemisphere, if the orbital eccentricity increases, the annual range will be decreased. (Other way round on the south hemisphere)
See also
References
Prussing, John E. In Mathematics, the eccentricity, denoted e or \varepsilon is a parameter associated with every conic section. In Astrodynamics, the eccentricity vector of a Conic section Orbit is the vector pointing towards the Periapsis and with magnitude The equation of time is the difference over the course of a year between time as read from a Sundial and time as read from a Clock, measured in an ideal situation Milankovitch cycles are the collective effect of changes in the Earth 's movements upon its climate named after Serbian civil engineer and Mathematician , and Bruce A. Conway. Orbital Mechanicsc. New York: Oxford University Press, 1993.
External links
- World of Physics: Eccentricity
- The NOAA page on Climate Forcing Data includes (calculated) data from Berger (1978), Berger and Loutre (1991) and Laskar et al. (2004) on Earth orbital variations, including eccentricity, over the last 50 million years and for the coming 20 million years
- The orbital simulations by Varadi, Ghil and Runnegar (2003) provide another, slightly different series for Earth orbital eccentricity, and also a series for orbital inclination
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