The Inconstant Earth

The motion of the Earth around the Sun and the position of the axis of Earth's rotation are disturbed by the Moon, the Sun, and by the planets.

The position of the axis of Earth's rotation (R) is disturbed by precession (P) and nutation (N):

The axial precession is completing one circuit in about 26,000 years (Platonic year).

The nutation is mainly caused by the Sun and Moon, continuously changing location relative to each other and to the Earth.
The angle between the rotational axis of the Earth, and a line perpendicular to its orbital plane (eliptic) is called obliquity of the ecliptic.

The principal period of +/- 9.2'' of the nutation in obliquity is 18.61 years (6798 days), corresponding to the regression (retrograde rotation) of the moon's nodal line.
As shown bekow there are smaller periods of half a year (182.62 days) and 13.66 days (half of a sidereal month).

The nutation in longitude has an amplitude of +/- 17.2'' and the same periods:

18.61 years period

nutation longitude

half a year and half a sidereal month periods.

The annual change of the Earth's orbital velocity around the Sun is also showing perturbations:

According to Kepler's second law the orbital velocity of a planet should have a maximum passing the perigee, which is around Jan 3 for the Earth. Due to the perturbation by the moon the date of maximum orbital velocity of the Earth differs by up to 10 days from the perigee:

2010 perigee: Jan 03, maximum velocity 8 days later on Jan 11.

velocity perigee

2011 perigee: Jan 03, maximum velocity on Jan 03.

velocity perigee

2012 perigee: Jan 05, maximum velocity 10 days earlier on Dec 26.

The distance of the Earth from the Sun is also disturbed:

The radial velocity of the Earth.

earth distance

The radial acceleration of the Earth.

Furthermore the Earth's axial tilt (obliquity of the ecliptic) is not constant: it varies between 22.1° and 24.5°, with a 42,000 year period, and at present, the tilt is decreasing by 0.013° per century or 0.47'' per year.

The data of the diagrams are computed by my Planet Applet, using the most important terms of the VSOP87 planetary theory used to to compute the heliocentric ecliptic longitude, latitude and distance of the planets. The accuracy is 0.5'' for the nutation in longitude, and 0.1'' for the nutation in obliquity.