Axial precession

[2] In particular, axial precession can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years.

The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.

First, the positions of the south and north celestial poles appear to move in circles against the space-fixed backdrop of stars, completing one circuit in approximately 26,000 years.

Secondly, the position of the Earth in its orbit around the Sun at the solstices, equinoxes, or other time defined relative to the seasons, slowly changes.

Ptolemy measured the longitudes of Regulus, Spica, and other bright stars with a variation of Hipparchus's lunar method that did not require eclipses.

According to Al-Battani, the Chaldean astronomers had distinguished the tropical and sidereal year so that by approximately 330 BC, they would have been in a position to describe precession, if inaccurately, but such claims generally are regarded as unsupported.

[9] Archaeologist Susan Milbrath has speculated that the Mesoamerican Long Count calendar of "30,000 years involving the Pleiades...may have been an effort to calculate the precession of the equinox.

[citation needed] Similarly, it is claimed the precession of the equinoxes was known in Ancient Egypt, prior to the time of Hipparchus (the Ptolemaic period).

Ancient Egyptians kept accurate calendars and recorded dates on temple walls, so it would be a simple matter for them to plot the "rough" precession rate.

[21] In the Middle Ages, Islamic and Latin Christian astronomers treated "trepidation" as a motion of the fixed stars to be added to precession.

[23] However, Newton's original precession equations did not work, and were revised considerably by Jean le Rond d'Alembert and subsequent scientists.

By comparing his own measurements with those of Timocharis of Alexandria (a contemporary of Euclid, who worked with Aristillus early in the 3rd century BC), he found that Spica's longitude had decreased by about 2° in the meantime (exact years are not mentioned in Almagest).

Also in VII.2, Ptolemy gives more precise observations of two stars, including Spica, and concludes that in each case a 2° 40' change occurred between 128 BC and AD 139.

The tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere).

To approximate his tropical year, Hipparchus created his own lunisolar calendar by modifying those of Meton and Callippus in On Intercalary Months and Days (now lost), as described by Ptolemy in the Almagest III.1.

Study of the Antikythera Mechanism showed that the ancients used very accurate calendars based on all the aspects of solar and lunar motion in the sky.

[29] On the other hand, Thuban in the constellation Draco, which was the pole star in 3000 BC, is much less conspicuous at magnitude 3.67 (one-fifth as bright as Polaris); today it is invisible in light-polluted urban skies.

The nominal south pole star is Sigma Octantis, which with magnitude 5.5 is barely visible to the naked eye even under ideal conditions.

The Southern Cross can be viewed from as far north as Miami (about 25° N), but only during the winter/early spring.The images at right attempt to explain the relation between the precession of the Earth's axis and the shift in the equinoxes.

The equinoxes occur where the celestial equator intersects the ecliptic (red line), that is, where the Earth's axis is perpendicular to the line connecting the centers of the Sun and Earth.The term "equinox" here refers to a point on the celestial sphere so defined, rather than the moment in time when the Sun is overhead at the Equator (though the two meanings are related).

The precessional eras of each constellation, often known as "Great Months", are given, approximately, in the table below:[30] The precession of the equinoxes is caused by the gravitational forces of the Sun and the Moon, and to a lesser extent other bodies, on the Earth.

In addition to the steady progressive motion (resulting in a full circle in about 25,700 years) the Sun and Moon also cause small periodic variations, due to their changing positions.

The value of the three sinusoidal terms in the direction of x (sinδ cosδ sinα) for the Sun is a sine squared waveform varying from zero at the equinoxes (0°, 180°) to 0.36495 at the solstices (90°, 270°).

accounts for the average distance cubed of the Sun or Moon from Earth over the entire elliptical orbit,[34] and ε (the angle between the equatorial plane and the ecliptic plane) is the maximum value of δ for the Sun and the average maximum value for the Moon over an entire 18.6 year cycle.

Applicable parameters for J2000.0 rounded to seven significant digits (excluding leading 1) are:[36][37] which yield both of which must be converted to ″/a (arcseconds/annum) by the number of arcseconds in 2π radians (1.296×106″/2π) and the number of seconds in one annum (a Julian year) (3.15576×107s/a): The solar equation is a good representation of precession due to the Sun because Earth's orbit is close to an ellipse, being only slightly perturbed by the other planets.

In reality, more elaborate calculations on the numerical model of the Solar System show that the precessional rate has a period of about 41,000 years, the same as the obliquity of the ecliptic.

Sufficient accuracy can be obtained over a limited time span by fitting a high enough order polynomial to observation data, rather than a necessarily imperfect dynamic numerical model.

[clarification needed] For present flight trajectory calculations of artificial satellites and spacecraft, the polynomial method gives better accuracy.

The precession of Earth's axis is a very slow effect, but at the level of accuracy at which astronomers work, it does need to be taken into account on a daily basis.

Although the precession and the tilt of Earth's axis (the obliquity of the ecliptic) are calculated from the same theory and are thus related one to the other, the two movements act independently of each other, moving in opposite directions.

Precessional movement of Earth. Earth rotates (white arrows) once a day around its rotational axis (red); this axis itself rotates slowly (white circle), completing a rotation in approximately 26,000 years [ 1 ]
Precession of a gyroscope . In a similar way to how the force from the table generates this phenomenon of precession in the spinning gyro, the gravitational pull of the Sun and Moon on the Earth's equatorial bulge generates a very slow precession of the Earth's axis (see §Cause ). This off-center push or pull causes a torque, and a torque on a spinning body results in precession. The gyro can be analyzed in its parts, and each part within the disk is trying to fall, but the rotation brings it from down to up, and the net result of all particles going through this is precession.
The coincidence of the annual cycles of the apses (closest and further approach to the Sun) and calendar dates (with seasons noted) at four equally spaced stages of a fictitious precessionary cycle of 20,000 years (rather than the Earth's true precessionary cycle of 26,000 years). The season dates are those in the north. The tilt of fictitious Earth's axis and the eccentricity of its orbit are exaggerated. Approximate estimates. Effects of weak planetary precession on the stages shown are ignored.
Precession of Earth's axis around the north ecliptical pole
Precession of Earth's axis around the south ecliptical pole
Precessional movement as seen from 'outside' the celestial sphere
The 25,700 year cycle of precession as seen from near the Earth. The current north pole star is Polaris (top). In about 8,000 years it will be the bright star Deneb (left), and in about 12,000 years, Vega (left center). The Earth's rotation is not depicted to scale – in this span of time, it would actually rotate over 4 million times.
Diagram showing the westward shift of the March equinox among the stars over the past 6,000 years.
Tidal force on Earth due to the Moon or another celestial body. It shows both the tidal field (thick red arrows) and the gravity field (thin blue arrows) exerted on Earth's surface and center (label O) by the Moon (label S).