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.
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.
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.
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.