Editing Elongation (astronomy)

{{short description|In astronomy, angular separation between the Sun and a planet, with the Earth as a reference point}}
{{other uses|Elongation (disambiguation)}}
{{more citations needed|date=September 2024}}
[[File:Positional astronomy.svg|thumb|350px|This diagram shows various possible elongations (ε), each of which is the [[angular distance]] between a [[planet]] and the [[Sun]] from Earth's perspective.|alt=An angle ε is drawn between two straight lines from Earth to the Sun, and from Earth to the planet. This is demonstrated for different positions along circular orbits, both for planets closer to the Sun (where the angle is always less than 90°), and for outer planets (for which the angle can range from 0° to 180°), while distinguishing east and west sides.]]

In [[astronomy]], a planet's '''elongation''' is the [[angular separation]] between the [[Sun]] and the planet, with [[Earth]] as the [[vertex (geometry)|reference point]].<ref>{{cite EB1911 |wstitle=Elongation |volume=9 |page=298}}</ref>

The '''greatest elongation''' is the maximum angular separation. [[ephemeris|Astronomical tables]] and websites, such as [[Heavens-Above]], forecast when and where the planets reach their next maximum elongations.

Sometimes '''elongation''' may instead refer to the angular distance of the [[Moon]] relative Earth or the [[natural satellite]] of another planet from its central planet, for instance the angular distance of [[Io (moon)|Io]] from [[Jupiter]].

A [[Quadrature (astronomy)|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 inferior planets==
The greatest elongation of a given [[inferior planet]] occurs when this planet's position, in its [[orbit]]al path around the Sun, is at [[tangent]] 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]]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]], it is near its '''greatest western elongation'''. The angle of the maximum elongation (east or west) for [[Mercury (planet)|Mercury]] is between 18° and 28°, while that for [[Venus]] is between 45° and 47°. These values vary because the planetary orbits are [[elliptic orbit|elliptical]] rather than perfectly [[circular orbit|circular]]. Another factor contributing to this [[orbital eccentricity|inconsistency]] is [[orbital inclination]], in which each planet's [[orbital plane]] is slightly tilted relative to a [[reference plane]], like the [[ecliptic]] and [[invariable plane]]s.

=== Greatest 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]] of the planet.

Let ''T'' be the [[period (physics)|period]] (for example the time between two greatest eastern elongations), ''ω'' be the relative angular velocity, ''ω''<sub>e</sub> Earth's angular velocity and ''ω''<sub>p</sub> the planet's angular velocity. Then

:<math>T = {2\pi\over \omega} = {2\pi\over \omega_\mathrm{p} - \omega_\mathrm{e}} = {2\pi\over {2\pi\over T_\mathrm{p}} - {2\pi\over T_\mathrm{e}}} = {1\over {{1\over T_\mathrm{p}} - {1\over T_\mathrm{e} }}}
= {T_\mathrm{e} \over {T_\mathrm{e} \over T_\mathrm{p}} - 1} </math>

where ''T''<sub>e</sub> and ''T''<sub>p</sub> are Earth's and the planet's years (i.e. [[period (physics)|period]]s of revolution around the Sun, called [[sidereal period]]s).

For example, [[Venus]]'s year ([[sidereal period]]) is 225 days, and [[Earth]]'s is 365 days. Thus Venus's [[synodic period]], 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]] 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 planet]]s, [[dwarf planet]]s and [[asteroid]]s undergo a different cycle. After [[Conjunction (astronomy)|conjunction]], 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 (astronomy)|opposition]]'' 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]] 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]], 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 [[Apparent magnitude|magnitude]] caused by changes in elongation are greater the closer the planet's orbit is to the Earth's. [[Mars]]' 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 &minus;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]] from Earth ranges 3.3-fold; whereas that of [[Uranus]] &ndash; the most distant Solar System body visible to the [[naked eye]] &ndash; 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]] can be seen with 10×50 [[binoculars]] at an average opposition, but of these only [[Ceres (dwarf planet)|Ceres]] and [[4 Vesta|Vesta]] are always above the binocular limit of +9.5 when the objects at their worst points in their orbital opposition (smallest elongations).

==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 (moon)|Io]] from [[Jupiter]].  Here we can also talk about ''greatest eastern elongation'' and ''greatest western elongation''.  In the case of the moons of [[Uranus]], 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]]
* [[Conjunction (astronomy)]]

== References ==
{{reflist}}

== External links ==
*[http://www.fourmilab.ch/images/3planets/elongation.html Mercury Chaser's Calculator] (Greatest Elongations of Mercury)

{{Portal bar|Astronomy|Stars|Spaceflight|Outer space|Solar System}}
[[Category:Spherical astronomy]]
[[Category:Celestial mechanics]]