In
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
, evection (Latin for "carrying away") is the largest
inequality produced by the action of 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 ...
in the
monthly revolution of the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
around the
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 ...
. The evection, formerly called the moon's second anomaly, was approximately known in ancient times, and its discovery is attributed to
Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
. The current name itself dates much more recently, from the 17th century: it was coined by
Bullialdus in connection with his own theory of the Moon's motion.
Evection causes the Moon's
ecliptic longitude to vary by approximately ± 1.274° (
degrees), with a period of about 31.8 days. The evection in longitude is given by the expression
, where
is the mean angular distance of the Moon from the Sun (its ''elongation''), and
is the mean angular distance of the Moon from its perigee (''mean anomaly'').
It arises from an approximately six-monthly periodic variation of the
eccentricity of the Moon's orbit and a
libration
In lunar astronomy, libration is the wagging or wavering of the Moon perceived by Earth-bound observers and caused by changes in their perspective. It permits an observer to see slightly different hemispheres of the surface at different tim ...
of similar period in the position of the Moon's
perigee
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion.
General description
There are two apsides in any ellip ...
, caused by the action of the Sun.
[Godfray, 1871.]
The evection opposes the Moon's
equation of the center
In Two-body problem, two-body, Kepler orbit, Keplerian orbital mechanics, the equation of the center is the angular difference between the actual position of a body in its elliptic orbit, elliptical orbit and the position it would occupy if its mot ...
at the new and full moons, and augments the equation of the center at the Moon's quarters. This can be seen from the combination of the principal term of the equation of the center with the evection:
At new and full moons, D=0° or 180°, 2D is effectively zero in either case, and the combined expression reduces to
At the quarters, D=90° or 270°, 2D is effectively 180° in either case, changing the sign of the expression for the evection, so that the combined expression then reduces to
.
References
Bibliography
*
Brown, E.W. ''An Introductory Treatise on the Lunar Theory.'' Cambridge University Press, 1896 (republished by Dover, 1960).
*Brown, E.W. ''Tables of the Motion of the Moon.'' Yale University Press, New Haven CT, 1919, at pp. 1–28.
*H Godfray, ''Elementary Treatise on the Lunar Theory'', (London, 1871, 3rd ed.).
*O Neugebauer, ''A History of Ancient Mathematical Astronomy'' (Springer, 1975), vol. 1, at pp. 84–85.
*R Taton & C Wilson (eds.), ''Planetary astronomy from the Renaissance to the rise of astrophysics, part A: Tycho Brahe to Newton'', (Cambridge University Press, 1989), at pp. 194–195.
Orbit of the Moon
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