Annual curves

Equation of Time

The equation of time represents the difference between mean solar time (as measured by our watches, using a constant offset) and true solar time (given by the actual position of the Sun). It is expressed in minutes and indicates the correction to apply to the uniform time to obtain the true solar time.

Origin of the Phenomenon

At true solar time, noon corresponds to the moment when the Sun is at its highest point on the meridian. However, the duration between two successive transits (solar day) is not constant for two reasons:

• The eccentricity of Earth's orbit: The Earth follows an elliptical path around the Sun, moving faster at perihelion (early January) and slower at aphelion (early July). This variation in speed changes the apparent position of the Sun from day to day.
• Earth's axial tilt: The Earth's rotation axis is tilted at 23.5° relative to the orbital plane. This obliquity causes a shift in the projection of the Sun's motion onto the celestial equator, creating additional irregularities.

The Mean Sun

To standardize time measurement, astronomers imagined a fictitious Sun moving at a constant speed along the celestial equator. The equation of time quantifies the difference between this theoretical model and the actual position of the Sun, which can reach ±16 minutes depending on the season.

Solar Declination

The declination of the Sun corresponds to the angle between its apparent position and the plane of the celestial equator. This value varies cyclically throughout the year due to Earth's tilt.

Seasonal Variation

• Summer Solstice (≈June 21): Maximum declination of about +23.5° (Sun at the zenith of the Tropic of Cancer)
• Equinoxes (≈March 20 / September 23): Zero declination (Sun directly above the equator)
• Winter Solstice (≈December 21): Minimum declination of about -23.5° (Sun at the zenith of the Tropic of Capricorn)

This astronomical parameter directly influences:

• The Sun's maximum height in the sky
• The length of the day
• The design of sundials