Solar times are measures of the apparent position of the Sun on the celestial sphere. They are not actually the physical time, but they are hour angles, 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 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.
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) 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 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. 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. The length of a mean solar day increases at a rate of approximately 1.4 milliseconds each century. An apparent solar day can differ from a mean solar day by as much as 22 seconds shorter to 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. 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.
In astronomy and navigation, the celestial sphere is an imaginary rotating sphere of "gigantic radius", concentric and coaxial with the Earth. All objects in the sky can be thought of as lying upon the sphere. Projected from their corresponding geographic equivalents are the celestial equator and the celestial poles. The celestial sphere projection is a very practical tool for positional astronomy.
In astronomy, the hour angle is one of the coordinates used in the equatorial coordinate system for describing the position of a point on the celestial sphere. The hour angle of a point is the angle between the half plane determined by the Earth axis and the zenith (half of the meridian plane) and the half plane determined by the Earth axis and the given point. The angle is taken with minus sign if the point is eastward of the meridian plane and with the plus sign if the point is westward of the meridian plane.
The hour angle is usually expressed in time units, with 24 hours corresponding to 360 degrees. The hour angle must be paired with the declination in order to fully specify the position of a point on the celestial sphere as seen by the observer at a given time.
