Variation (astronomy)

In astronomy variation referred to in the celestial mechanics moon theory, a periodic perturbation of the lunar orbit.

Discovery

The Greek astronomer Ptolemy describes this in his famous work Almagest that the moon its path does not go through with uniform angular velocity, but to vary with a period of 27.55 days, the anomalistic month about ± 6.3 degrees from the center position. This difference is called Great Inequality ( anomaly ). Ptolemy also describes 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. Only in 1590 the Danish astronomer Tycho Brahe noticed that there is another periodic variation of about 0.66 degrees, which has a period of half a synodic month at 14.8 days. In contrast to the Great Inequality is this variation called deviation, as the evection not be determined by the second Kepler law and the resulting Kepler 's equation, but found only in the framework of Newtonian gravity by analyzing the Earth-Moon - Sun three-body system, a satisfactory explanation.

Calculation

The Earth-Moon system is not an isolated two-body system, so that the calculation of the position of the moon one about the Great inequality beyond correction, which are mainly due to the gravitational influences of the sun needed. In a perturbation theory, one can calculate that the kepler between orbital elements of the Moon changes over time are due to the influence of the sun: the location of the perigee and the ascending node "walk" through the fault linearly in time ( so-called secular interference ), all 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. Some error terms in this case have periodic dependencies on the twice the angle between the Sun and the Moon, including a term which relates to the semi-major axis. This term can be understood as a compression of the lunar orbit toward the sun. These disorders lead to a change in the ecliptic longitude of the moon in a first approximation to the summand:

Where μ = ωs /? m ≈ 0.075, the ratio of the sidereal month sidereal year. This provides a first approximation with an amplitude of only about 0.44 degrees, only a rough estimate. More detailed analysis shows that the amplitude of a total of 39.5 minutes of arc, ie 0.66 degrees. The first members

Depend, in contrast to the Great Deviation and evection not depend on the numerical eccentricity. The remaining 5 minutes of arc, however, arise from terms which both depend on the eccentricity of the Moon and the Earth's orbit. The period of the disturbance is given by

That is, exactly one synodic month.

The calculation presented here is also valid for moons of other planets in principle. Since it depends practically only on the frequency μ, one sees quickly that it is much smaller for all other large moons of the solar system than the Earth's moon ( μ ≈ 1/13). Saturn's moon Iapetus is with μ ≈ 1/135. Before Jupiter's moon Callisto with μ ≈ 1/260 second However, by the quadratic dependence of the effect of only 1%, or 0.25 % of the size of the effect at the Earth's moon has. In addition, unequal relevant as well as in the evection, with the large moons of the gas planet disturbances caused by the oblateness of the central planet and interference from neighboring planet.

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