Evection

The evection (Latin evehere, evectum: lead out, go out ) refers to celestial mechanics lunar theory, a periodic perturbation of the lunar orbit.

Discovery

In ancient times it was known that the moon does not pass through its orbit with a uniform angular velocity. Thus varies the position of the moon, with a period of 27.55 days, the anomalistic month to about ± 6.3 ° from the central position. This difference caused by the elliptical shape of the lunar orbit is called Great Inequality ( anomaly ) and was later declared by Kepler through the second Kepler law in the context of the two-body problem. The Greek astronomer Ptolemy remarked in his famous work Almagest (, quoting in turn Hipparchus ) that there is another deviation from the steady motion, which is significantly less with ± 1.27 degrees and has a period of 31.8 days. This second variation is called evection.

The name goes back to Ishmael Boulliau, who in his " Astronomia Philolaica " (1645 ) tried the second variation of the moon's motion through a " evectio " to describe said periodic movement of the free focal point of the lunar orbital ellipse.

Calculation

If the Earth-Moon system, an isolated two-body system, the Grand inequality would explain the position of the moon already with high accuracy. This assumption, however, is not justified; in particular the sun affects the Earth-Moon system and leads to deviations from the elliptical lunar orbit, as follows from the Kepler 's laws. In a perturbation theory, one can calculate these deviations by assuming that the orbital elements of the moon are subject to changes over time due to the influence of the sun. While the location of the perigee and the ascending node of the fault linearly in time " wander" (so-called secular disorders), subject to all other orbital elements and, in particular semi-major axis, eccentricity, and orbital inclination periodic disturbances that? M from the ecliptic longitude of the moon and the sun? s depend. A special error term shows that the numerical eccentricity of the lunar orbit changes by a number, which is proportional to, where Π denotes the mean secular ecliptic longitude of the perigee. Another term changes the position of the perigee increases proportionately. These disorders lead to a change in the ecliptic longitude of the moon in a first approximation to the summand:

Where em ≈ 0.0549, the mean eccentricity of the lunar orbit and μ = ωs /? m ≈ 0.075, the ratio of the sidereal month sidereal year. This provides a first approximation with an amplitude of only about 0.88 degrees, only a rough estimate. More detailed analysis shows that the amplitude

The period of the disturbance is given by

Where c ≈ 0.992 a dependent of μ correction factor.

Important compared to other disorders of the lunar orbit (variation, and annual parallactic inequality, etc. ) is the proportionality to the numerical eccentricity of the lunar orbit, which has in common with the evection the Great inequality. Since the presented calculation in principle also has moons of other planets validity, it is relevant for μ moons with large eccentricity and large frequency ratio. However, one quickly sees that μ for all other large moons of the solar system is much smaller than the Earth's moon ( ≈ 1 /13). The Jupiter's moon Callisto has a ratio of ≈ 1/260, due to the lower eccentricity of about 0.007 but the effect is not even 1% of the size on Earth's moon. When Saturn's moon Iapetus is μ ≈ 1/135 and the eccentricity is about 0.3, so in this moon, the effect is about half as large as the Earth's moon. However, with the large moons of the gas planet disturbances by the oblateness of the central planet and interference from neighboring planets are much more relevant.