Editing Elongation (astronomy) (section)

==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.