mean solar day

Solar time

Solar times are measures of the apparent position of the Sun on the celestial sphere. They are not actually the physical time, but rather hour angles, that is, angles expressed in time units. They are also local times in the sense that they depend on the longitude of the observer.

Apparent solar time

Apparent solar time or true solar time is the hour angle of the Sun. It is based on the apparent solar day, which is the interval between two successive returns of the Sun to the local meridian. Note that the solar day starts at noon, so apparent solar time 00:00 means noon and 12:00 means midnight. Solar time can be measured by a sundial.

The length of a solar day varies throughout the year for two reasons. First, Earth's orbit is an ellipse, not a circle, so the Earth moves faster when it is nearest the Sun (perihelion) and slower when it is farthest from the Sun (aphelion) (see Kepler's laws of planetary motion). Second, due to Earth's axial tilt, the Sun moves along a great circle (the ecliptic) that is tilted to Earth's celestial equator. When the Sun crosses the equator at both equinoxes, it is moving at an angle to it, so the projection of this tilted motion onto the equator is slower than its mean motion; when the Sun is farthest from the equator at both solstices, it moves parallel to it and closer to the polar axis than the equator, so the projection of this parallel motion onto the equator is faster than its mean motion (see tropical year). Consequently, apparent solar days are shorter in March (26–27) and September (12–13) than they are in June (18–19) or December (20–21). These dates are shifted from those of the equinoxes and solstices by the fast/slow Sun at Earth's perihelion/aphelion.

Mean solar time

Mean solar time is the hour angle of the mean Sun (see below). As the mean Sun is a mathematical construction only and cannot be physically observed, the mean solar time is computed from an artificial clock time adjusted via observations of the diurnal rotation of the fixed stars to agree with average apparent solar time. Though the amount of daylight varies significantly, the length of a mean solar day does not change on a seasonal basis. However, the length of a mean solar day increases at a rate of approximately 1.4 milliseconds each century. It was exactly 86,400 (i.e. 24 hours × 60 minutes/hour × 60 seconds/minute) SI seconds in approximately 1820. Currently, the length of a mean solar day is approximately 86400.002 SI seconds. An apparent solar day may differ from a mean solar day by as much as nearly 22 seconds shorter to nearly 29 seconds longer. Because many of these long or short days occur in succession, the difference builds up to as much as nearly 17 minutes early or a little over 14 minutes late. Since these periods are cyclical, they do not accumulate from year to year. The difference between apparent solar time and mean solar time is called the equation of time. The mean solar day also starts at noon, with 00:00 meaning noon and 12:00 meaning midnight. As this is inconvenient for civilian use, the civil time is defined as mean solar time minus 12 hours.

The length of the mean solar day is increasing due to the tidal acceleration of the Moon by Earth, and the corresponding deceleration of the Earth by the Moon.

The mean Sun is defined as follows. First, consider a fictitious Sun that moves along the ecliptic at a constant speed and occupies the same position as the real Sun when Earth passes through the perihelion and also when it passes through the aphelion. Then, the mean sun is a second fictive Sun that moves along the celestial equator at constant speed and passing through the vernal point simultaneously with the first fictive sun.


Many methods have been used to simulate mean solar time throughout history. The earliest were clepsydras or water clocks, used for almost four millennia from as early as the middle of the second millennium BC until the early second millennium. Before the middle of the first millennium BC, the water clocks were only adjusted to agree with the apparent solar day, thus were no better than the shadow cast by a gnomon (a vertical pole), except that they could be used at night.

Nevertheless, it has long been known that the sun moves eastward relative to the fixed stars along the ecliptic. Thus since the middle of the first millennium BC, the diurnal rotation of the fixed stars has been used to determine mean solar time, against which clocks were compared to determine their error rate. Babylonian astronomers knew of the equation of time and were correcting for it as well as the different rotation rate of stars, sidereal time, to obtain a mean solar time much more accurate than their water clocks. This ideal mean solar time has been used ever since then to describe the motions of the planets, Moon, and Sun.

Mechanical clocks did not achieve the accuracy of Earth's "star clock" until the beginning of the 20th century. Even though today's atomic clocks have a much more constant rate than the Earth, its star clock is still used to determine mean solar time. Since sometime in the late 20th century, Earth's rotation has been defined relative to an ensemble of extra-galactic radio sources and then converted to mean solar time by an adopted ratio. The difference between this calculated mean solar time and Coordinated Universal Time (UTC) is used to determine whether a leap second is needed.

Solar time can be calcluated without a sundial or any knowledge about trigonometry, by basing the solar time calculation on UTC (Coordinated Universal Time), an approximation of UT (Universal Time). By taking the longitude and dividing it by 15, the number of degrees the Sun moves per hour, the difference is obtained between local solar time & Universal Time. From this, take the UTC time and add the time difference.

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