elongation

 

in astronomy, the angular distance between two points in the sky as measured from a third point. The elongation of a planet is usually measured as the angular distance from the sun to the planet as measured from the earth. When a planet lies on the line drawn from the earth to the sun, its elongation is 0° and is said to be in conjunction. When a planet's elongation is 90°, it is in quadrature. When its elongation is 180°, it is in opposition. Elongation is measured east (eastern quadrature) or west (western quadrature) from the sun. The superior planets can have elongations between 0° and 180°; the elongations of the inferior planets are limited by their proximity to the sun. The greatest elongation of Mercury is 28°, and of Venus, 47°.

Elongation is an astronomical term that refers to the angle between the Sun and a planet, as viewed from Earth.

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 value of the greatest elongation (west or east), for Mercury, is between 18° and 28°; and for Venus between 45° and 47°. This value varies because the orbits of the planets are elliptical, rather than perfect circles.

Refer to astronomical tables and websites such as www.heavens-above.com to see when the planets reaches their next elongations.

In 2007 Venus has a greatest eastern elongation on June 9, and a western one on October 28.

In 2007 Mercury has greatest eastern elongations on February 7, June 2, and September 29. Western ones happen on March 22, July 20, and November 8.

Elongation period

Greatest elongations of a planet happen periodically, with a greatest eastern elongation followed by a 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, ω_e earth's angular velocity and ω_p the planet's angular velocity. Then

where T_e and T_p 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.

Elongation of superior planets

Superior planets, dwarf planets and asteroids undergo a different cycle. They do not have a maximum elongation because their motion as viewed from Earth is independent of the Sun. This means that after superior conjunction, their elongation continues to increase until it reaches 180°, which is known as opposition and corresponds to a heliocentric conjunction with Earth.

All superior planets are most easily visible at their oppositions, because they are closest to Earth as well as above the horizon most often when it is dark. The differences in magnitude caused by changes in elongation are greater the closer the planet is to Earth and the smaller is its size. Mars' magnitude in particular changes with elongation: it can be as low as +1.8 when in conjunction mear aphelion but at a favourable opposition it is as high as -3.0, or eighty times brighter than its minimum brightness. As one moves further out, the difference in magnitude caused by difference in elongaiton gradually fall. the maximum and minimum brightness of Jupiter differ by only a factor of 2.5 times, whilst those of Uranus - which is the most distant Solar System body visible to the naked eye - differ by only a factor of 60 percent.

Small size means the magnitude of asteroids can vary greatly depending on elongation. Although more than a dozen objects in the asteroid belt can be seen with 10x50 binoculars at an average opposition, only Ceres and Vesta are always above the binocular limit of +9.5 at small elongations. (Pallas is above +9.5 at small elongations only when near perihelion).

See also

• Aspects of Mercury for greatest elongations of Mercury
• Aspects of Venus for greatest elongations of Venus
• Astronomical conjunction

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