The measurement of time is based on the observation of some periodic (or nearly so) phenomenon chosen as reference. The rotation of the earth on its axis, causing the succession of nights and days, and the motion of the earth around the sun, causing the repetition of the cycle of seasons, are two important such phenomena. They still dominate the definition of civil time scales even though the official definition of the second has been based on atomic phenomena since the 1960's.[citation needed]

The rotation of the earth can be measured precisely at a particular location on earth by determining the instant of culmination of some reference celestial object (the instant when the object is highest above the horizon) on successive days. At this instant, the object lies in the meridian plane of the place, the half-plane bordered by the axis of the earth and passing through the observer. Any other instant between culminations can also be evaluated precisely by measuring the angle between the meridian plane of the place and the meridian plane containing the reference object.

The angle between two meridian planes can be measured along the celestial equator, defined as the intersection of the equatorial plane of the earth, perpendicular to its axis and passing through its center, and the celestial sphere, an imaginary sphere of immense (or infinite) radius centered at the center of the earth, on which the celestial objects seen from earth are projected and to which they appear to be attached. The angle between the meridian plane of the place and the meridian plane of an object, measured from east to west, is called the hour angle of the object at that time. It is conveniently measured in hours, minutes, seconds of time, 24 hours for a whole turn.

If the reference object is a star or some fixed point of the celestial sphere (typically, the vernal point, where the sun lies on the celestial equator at the March equinox), the hour angle is a measure of sidereal time. Sidereal time is preferred by astronomers. Before the advent of modern technologies, they would use pendulum clocks synchronized with the culmination of a reference star to evaluate the sidereal time of their observations.

However, for the needs of daily life, a clock synchronized with the culminations of the sun is more adequate.


When complete, these explanations will lead to the definition of the Equation of Time and the Analemma. The images below show the corresponding curves for the planets of the solar system (and Pluto).

Equation of Time on Mercury Analemma of Mercury

Equation of Time on Venus Analemma of Venus

Equation of Time on Earth Analemma of Earth

Equation of Time on Mars Analemma of Mars

Equation of Time on Jupiter Analemma of Jupiter

Equation of Time on Saturn Analemma of Saturn

Equation of Time on Uranus Analemma of Uranus

Equation of Time on Neptune Analemma of Neptune

Equation of Time on Pluto Analemma of Pluto