Elongation (astronomy)
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astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
, a planet's elongation is the angular separation between the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
and the planet, with
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
as the reference point. The greatest elongation of a given
inferior planet In the Solar System, a planet is said to be inferior or interior with respect to another planet if its orbit lies inside the other planet's orbit around the Sun. In this situation, the latter planet is said to be superior to the former. In the ref ...
occurs when this planet's position, in its
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
al path around the Sun, is at
tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...
to the observer on Earth. Since an inferior planet is well within the area of Earth's orbit around the Sun, observation of its elongation should not pose that much a challenge (compared to
deep-sky object A deep-sky object (DSO) is any astronomical object that is not an individual star or Solar System object (such as Sun, Moon, planet, comet, etc.). The classification is used for the most part by amateur astronomers to denote visually observed f ...
s, for example). When a planet is at its greatest elongation, it appears farthest from the Sun as viewed from Earth, so its apparition is also best at that point. When an inferior planet is visible after sunset, it is near its greatest eastern elongation. When an inferior planet is visible before
sunrise Sunrise (or sunup) is the moment when the upper rim of the Sun appears on the horizon in the morning. The term can also refer to the entire process of the solar disk crossing the horizon and its accompanying atmospheric effects. Terminology A ...
, it is near its greatest western elongation. The angle of the maximum elongation (east or west) for Mercury is between 18° and 28°, while that for
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
is between 45° and 47°. These values vary because the planetary orbits are
elliptical Elliptical may mean: * having the shape of an ellipse, or more broadly, any oval shape ** in botany, having an elliptic leaf shape ** of aircraft wings, having an elliptical planform * characterised by ellipsis (the omission of words), or by conc ...
rather than perfectly
circular Circular may refer to: * The shape of a circle * ''Circular'' (album), a 2006 album by Spanish singer Vega * Circular letter (disambiguation) ** Flyer (pamphlet), a form of advertisement * Circular reasoning, a type of logical fallacy * Circular ...
. Another factor contributing to this inconsistency is
orbital inclination Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth ...
, in which each planet's
orbital plane The orbital plane of a revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane. A common example would be the positions of the centers of a massive body (host) an ...
is slightly tilted relative to a
reference plane In celestial mechanics, the plane of reference (or reference plane) is the plane used to define orbital elements (positions). The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longi ...
, like the
ecliptic The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agains ...
and
invariable plane The invariable plane of a planetary system, also called Laplace's invariable plane, is the plane passing through its barycenter (center of mass) perpendicular to its angular momentum vector. In the Solar System, about 98% of this effect is contr ...
s.
Astronomical tables In astronomy and celestial navigation, an ephemeris (pl. ephemerides; ) is a book with tables that gives the trajectory of naturally occurring astronomical objects as well as artificial satellites in the sky, i.e., the Position (vector), positio ...
and websites, such as
Heavens-Above Heavens-Above is a non-profit website developed and maintained by Chris Peat as ''Heavens-Above GmbH''. The web site is dedicated to helping people observe and track satellites orbiting the Earth without the need for optical equipment such as b ...
, forecast when and where the planets reach their next maximum elongations.


Elongation period

Greatest elongations of a planet happen periodically, with a greatest eastern elongation followed by a greatest western elongation, and ''vice versa''. The period depends on the relative angular velocity of Earth and the planet, as seen from the Sun. The time it takes to complete this period is the
synodic period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, ...
of the planet. Let ''T'' be the
period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...
(for example the time between two greatest eastern elongations), ''ω'' be the relative angular velocity, ''ω''e Earth's angular velocity and ''ω''p the planet's angular velocity. Then :T = = = = where ''T''e and ''T''p are Earth's and the planet's years (i.e.
period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...
s of revolution around the Sun, called
sidereal period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, ...
s). For example,
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
's year (
sidereal period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, ...
) is 225 days, and
Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
's is 365 days. Thus Venus's
synodic period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, ...
, which gives the time between every two eastern greatest elongations, is 584 days; this also applies to the western counterparts. These values are approximate, because (as mentioned above) the planets do not have perfectly circular,
coplanar In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. How ...
orbits. When a planet is closer to the Sun it moves faster than when it is further away, so exact determination of the date and time of greatest elongation requires a much more complicated analysis of orbital mechanics.


Of superior planets

Superior planets,
dwarf planet A dwarf planet is a small planetary-mass object that is in direct orbit of the Sun, smaller than any of the eight classical planets but still a world in its own right. The prototypical dwarf planet is Pluto. The interest of dwarf planets to ...
s and asteroids undergo a different cycle. After
conjunction Conjunction may refer to: * Conjunction (grammar), a part of speech * Logical conjunction, a mathematical operator ** Conjunction introduction, a rule of inference of propositional logic * Conjunction (astronomy), in which two astronomical bodies ...
, such an object's elongation continues to increase until it approaches a maximum value larger than 90° (impossible with inferior planets) which is known as ''
opposition Opposition may refer to: Arts and media * ''Opposition'' (Altars EP), 2011 EP by Christian metalcore band Altars * The Opposition (band), a London post-punk band * '' The Opposition with Jordan Klepper'', a late-night television series on Com ...
'' and can also be examined as a heliocentric conjunction with Earth. This is archetypally very near 180°. As seen by an observer on the superior planet at opposition, the Earth appears at conjunction with the Sun. Technically, the point of opposition can be different from the time and point of maximum elongation. Opposition is defined as the moment when the apparent
ecliptic longitude The ecliptic coordinate system is a celestial coordinate system commonly used for representing the apparent positions, orbits, and pole orientations of Solar System objects. Because most planets (except Mercury) and many small Solar System b ...
of any such object versus the Sun (seen from earth) differs by (is) 180°; it thus ignores how much the object differs from the plane of the Earth's orbit. For example,
Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the Sun. It is the largest ...
, whose orbit is highly inclined to the essentially matching plane of the planets, has maximum elongation much less than 180° at opposition. The six-word term "maximum apparent elongation from the sun" provides a fuller definition of elongation. All superior planets are most conspicuous at their oppositions because they are near, or at, their closest to Earth and are also above the horizon all night. The variation in
magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...
caused by changes in elongation are greater the closer the planet's orbit is to the Earth's.
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...
' magnitude in particular changes with elongation: it can be as low as +1.8 when in conjunction near aphelion but at a rare favourable opposition it is as high as −2.9, which translates to seventy-five times brighter than its minimum brightness. As one moves further out, the difference in magnitude that correlates to the difference in elongation gradually falls. At opposition, the brightness of
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth t ...
from Earth ranges 3.3-fold; whereas that of
Uranus Uranus is the seventh planet from the Sun. Its name is a reference to the Greek god of the sky, Uranus ( Caelus), who, according to Greek mythology, was the great-grandfather of Ares (Mars), grandfather of Zeus (Jupiter) and father of ...
– the most distant Solar System body visible to the
naked eye Naked eye, also called bare eye or unaided eye, is the practice of engaging in visual perception unaided by a magnifying, light-collecting optical instrument, such as a telescope or microscope, or eye protection. Vision corrected to normal ...
– ranges by 1.7 times. Since asteroids travel in an orbit not much larger than the Earth's, their magnitude can vary greatly depending on elongation. More than a dozen objects in the
asteroid belt The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, c ...
can be seen with 10×50 binoculars at an average opposition, but of these only
Ceres Ceres most commonly refers to: * Ceres (dwarf planet), the largest asteroid * Ceres (mythology), the Roman goddess of agriculture Ceres may also refer to: Places Brazil * Ceres, Goiás, Brazil * Ceres Microregion, in north-central Goiás ...
and Vesta are always above the binocular limit of +9.5 when the objects at their worst points in their orbital opposition (smallest elongations). A quadrature occurs when the position of a body (moon or planet) is such that its elongation is 90° or 270°; i.e. the body-earth-sun angle is 90°.


Of moons of other planets

Sometimes elongation may instead refer to the angular distance of a moon of another planet from its central planet, for instance the angular distance of Io from
Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousandth t ...
. Here we can also talk about ''greatest eastern elongation'' and ''greatest western elongation''. In the case of the moons of
Uranus Uranus is the seventh planet from the Sun. Its name is a reference to the Greek god of the sky, Uranus ( Caelus), who, according to Greek mythology, was the great-grandfather of Ares (Mars), grandfather of Zeus (Jupiter) and father of ...
, studies often deal with ''greatest northern elongation'' and ''greatest southern elongation'' instead, due to the very high inclination of Uranus' axis of rotation.


See also

* Aspects of Venus for greatest elongations of
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
* Conjunction (astronomy)


References


External links


Mercury Chaser's Calculator
(Greatest Elongations of Mercury) {{Portal bar, Astronomy, Stars, Spaceflight, Outer space, Solar System Spherical astronomy Celestial mechanics