Nutation

Under nutation ( for Latin nutare " nod " ) understands astronomy a small periodic fluctuation in the direction of the Earth's axis, which the uniform cone circulation of the Earth's axis, the precession is superimposed. Your period is 18.6 years and their amplitude is 9.2 " perpendicular to the ecliptic and 6.8 " parallel to the ecliptic. There are also other Nutationsanteile with amplitudes less than 1 " and shorter periods.

This conventional in astronomy term nutation is not identical to the common in the mechanical concept of nutation in the gyroscopic theory, referred to the movement of the body axis of a rotating body around the axis of angular momentum, which is also in a body, to which no torque is applied occurs.

Basics

The direction of the axis of rotation of the earth in space is not constant. Your change is essentially the precession, a cone-shaped orbit around the normal vector of the ecliptic with an opening angle of about 23.5 ° ( the obliquity of the ecliptic ) and an orbital period of 25,780 years. This uniform precession superimpose small periodic deviations: the nutation. Be Caused the precession and nutation by torques that exert gravitational forces of the moon and the sun on the not strictly spherical, but slightly oblate Earth. Nutation caused by the fact that the torque is not constant but, according to the path movements of the moon and the sun relative to the earth which have periodic variations.

The majority of the nutation changes the direction of Earth's axis with an amplitude of 9.2 " perpendicular to the ecliptic and 6.8 " parallel to the ecliptic and with a period of 18.6 years. It is caused by a slow shift of the plane of the lunar orbit that is inclined to the ecliptic by about 5.1 ° and the line of intersection of the ecliptic rotates at 18.6 years by 360 °.

The duration of the nutation is more precisely:

There are ( among others, of half a month ), each less than 1 " apart from this almost 19 -year-old main part of the nutation additional shares with shorter periods.

Nutation in longitude and obliquity

You divide the influence of computational reasons, into two components:

• Nutation in length between -17.24 " and 17.24 "

( are caused by the nutation deviation of the true vernal equinox of his middle - even changeable by the precession - Location on the ecliptic )

• Nutation in obliquity between -9.21 " and 9.21 "

( indicates the change in the obliquity of the ecliptic, ie the angle between the normal vector of the ecliptic and the Earth's axis )

Bearing on the star coordinates

Because the Earth's axis and the ecliptic to define the astronomical coordinate system, each shift of Earth's axis changes the coordinates ( star positions ) of all celestial bodies. For about 2000 fundamental stars - that underlie most of the measurements in the sky - the star positions are pre-calculated taking into account the precession and nutation in 10 -day intervals and published in the astronomical yearbooks or on the Internet. The most important of these yearbooks is called Apparent Places of Fundamental Stars and is supported by astronomical calculation Institute (ARI ) in Heidelberg published a year in advance.

The influence of the " short-period " Nutationsanteile with periods less than 35 days, however, is in stars whose loci are tabulated at intervals of ten days, not taken into account; they must be calculated with auxiliary tables or small additional programs and added to the published Sternörtern. The influence of the polar motion is, however, attached to the measurements themselves, as well as the time correction DUT1 the Earth's rotation.

Calculation model for the nutation

To calculate nutation of the earth, published by the IAU models. The position of the moon and sun are taken into account (IAU 1980 Theory of nutation ), the latest model, the planetary positions ( IAU2000A Theory of nutation ). With the theory of 1980, an accuracy of 0.0001 " can be achieved, which is sufficient for most amateur astronomical applications.

The basis elements are the periodic nutation with their different period ( see chart). An approximate calculation, therefore, the table below are abbreviated extent that only the elements having the highest coefficient of the sine and cosine functions are taken into account.

Let T be the number of Julian centuries, the nutation of the length and the nutation of obliquity. JDE means that the date and time value in TDB is passed. For calculation of the value of deltaT is required, which is about 61 seconds in 2010.

For the further calculation or 5 factors are required:

• Mean elongation of the Moon
• Mean Anomaly of the Sun
• Mean anomaly of the Moon
• Mean argument of perigee
• Mean length of the ascending node of the lunar orbit:

For further calculations it is advisable ... to reduce the angle to the range 0 ° 360 °.

With the following table now the individual terms are summed according to the following rule:

If sine and cosine require arguments in radians, the values ​​of the previous calculations in radians are to be converted. The result is in arc seconds.

Table of IAU1980 Theory of nutation

Example values

Approximate calculation

Taking into account the five polynomials only the terms up to degree 1 and using only the first four table rows ( these have the highest coefficient ), so can derive a simplified formula. For this purpose, the argument of each sine and cosine, which is a linear combination of the five input values ​​explicitly calculated. Conversion wheel is also carried out, as most implementations will need this information.

The nutation is then given by

Where the sine and cosine is defined as a vector from a vector of sine and cosine values ​​. The subsequent inner product finally multiplies the values ​​of the coefficients of the Table.

The error is for | t | <1 (ie 1900 to 2100 ) at a maximum of 0.33 " and a maximum of 0.09 ".

The IAU 2000 Theory of Nutation

The theory of 2000 consists of a lunisolar and planetary table. Here, the accuracy can be increased to arc seconds, but these tables have about 470 terms, and the exact position of the planets is also required.

History

Discovered the Nutationseffekt 1728 by James Bradley, as he made detailed analyzes of stellar coordinates. However, the cause could be cleared until 20 years later. The nutation has a similar magnitude as that discovered also by Bradley aberration of light.