Elongation (astronomy) - Elongation Period

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 (for example the time between two greatest eastern elongations), ω be the relative angular velocity, ωe Earth's angular velocity and ωp the planet's angular velocity. Then

T = {2\pi\over \omega} = {2\pi\over \omega_p - \omega_e} = {2\pi\over {2\pi\over T_p} - {2\pi\over T_e}} = {T_e \over {T_e \over T_p} - 1}

where Te and Tp are Earth's and the planet's years (i.e. periods of revolution around the Sun, called sidereal periods).

For example, Venus's year (sidereal period) is 225 days, and Earth's is 365 days. Thus Venus' synodic period, which gives the time between two subsequent eastern (or western) greatest elongations, is 584 days.

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.

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