Libration

In astronomy, libration refers to a real or apparent wobbling motion of a moon, seen from its central body.

Almost all the larger moons of the solar system are in a bound rotation around their central planet, that is, they rotate during one revolution around the planet once around its own axis. Therefore, these moons should always contact their planet, in principle, to the same page. Since the moon but not orbiting on exact circular orbits with constant angular velocity of their planet, while the self-rotation has a constant angular velocity, and as an observer on the planet does not have to exactly be on the line connecting the centers of mass, the observer sees in the course of a " month" not always exactly the same side of the moon. The different effects that lead to this tumbling motion can be seen from the surface over time a total of 59 percent of the lunar surface.

Description

We distinguish the following types of libration, here the example of the Moon:

• Optical libration The libration in longitude seen as lateral rotation of up to 7.9 degrees and is primarily caused by the slightly elliptical orbit of the moon. If the Moon's orbit circular, so its angular velocity would always be the same ( " degrees per second "). Because of the elliptical orbit changes the distance between the Earth and Moon ( Perizentrumsdistanz ) during a revolution and thus the angular velocity. It is the greater, the smaller the distance - that the greatest near the Earth. The speed of rotation of the moon on its axis remains constant. Therefore rotates the moon at perigee apparently too slow and if it is further away, faster than its orbital motion. Other small Librationseffekte caused by the change in the moon's orbit because of the attractive forces of the sun and planets.
• For the libration in latitude is the angle of the rotation axis of the Moon against the Lot to the lunar orbital plane (not against the Lot of the Earth's orbital plane! ) Responsible. He is 6.7 degrees and causes an apparent vertical tilt of the moon, so that you can see through his alternately north and south poles of time.
• The equatorial or daily libration is caused by the rotation of the earth and makes up about 1 degree from. From sunrise to moonset moon, the earth rotates 180 degrees. Here, every point on the Earth's surface moves, depending on latitude, up to 12,756 km ( a diameter of Earth ). An observer thus sees the moon at moonrise from a slightly different position and thus, when the moon goes down under a different viewing angle than 12 hours later.

Calculation

The optical libration can be calculated to a good approximation from the sky mechanical properties of the Earth-Sun - Moon system. Neglecting in first approximation the influence of the sun, so is obtained from the solution of the two-body problem Earth-Moon following values:

• For the libration in longitude is the "Great Inequality" relevant. This is the difference between the true anomaly, ie seen the angle between perigee and moon from the earth, and medium anomaly, ie the angle between perigee and " moderate " moon. The average moon moves at the constant angular velocity, where is the anomalistic month. The Great inequality is then sufficient approximation for small eccentricities of the formula in radians, where the eccentricity of the lunar orbit is. In degree results numerically

• For the libration width in the axial inclination of the moon compared to its orbit is responsible and therefore, the axial inclination, and is the angle between the moon and the ascending node of the lunar orbit. It should be noted at this point that the axial inclination of the moon and the orbital inclination divide the nodes together, so always, that Orbital inclination ( 5.145 ° ) and inclination of the lunar axis to the ecliptic ( 1.543 ° ) add up to the axial inclination (see Cassini's laws). is therefore

The large disturbances of the Earth- Moon system mainly by the sun cause additional deviations, the most important are the following:

• The libration in longitude is disturbed by the already known Ptolemy evection by a maximum of 1.27 °. The reason is the different position of the apsides to the sun. The period of this disorder is 31.8 days. Somewhat smaller the variation with maximum 0.66 °. The period of this interference is a half synodic month, and the variation disappears at the main phases of the moon. As equation is derived

• The libration in longitude is subject to fluctuations as changes the orbital inclination of the moon with a period of 173 days between 4.6 ° and 5.3 °. The period of 173 days is the time when the line of nodes rotates in relation to the Sun by 180 ° ( half eclipse year ).