Mean Solar Day

We have seen that the Sun appears to describe an elliptical orbit around the Earth and its rate of change of direction in the orbit is not constant, i.e. the Sun appears to move somewhat non-uniformly in the zodiac. It moves faster when the Earth is at its perihelion, i.e. the nearest point from the Sun. Conversely the angular speed is slowest when the Earth is at aphelion point (the farthest from the Sun). The other factor is that the Sun appears to move in the ecliptic and not in the celestial equator, so its right ascension does not increase uniformly, it being measured along the celestial equator.
The apparent solar day is the interval elapsed between two successive transits of the Sun across the observer’s meridian.
As the Sun’s motion is not uniform throughout the year, the apparent solar days will be of different duration. It will be much troublesome in day-to-day working cf the society. So, a fictitious body called the “mean Sun” was devised which is assumed to move on the celestial equator at a uniform rate. The
successive  transits of this fictitious body or the mean Sun across the observer’s meridian is defined as a mean solar day which is equal to the average daily motion of the real Sun in the ecliptic. The duration of such a mean solar day is divided into 24 hours. It implies that the right ascension of mean Sun increases at a uniform rate. When the mean Sun is at the meridian of a place, it is local mean noon there and the hour-angle of the mean Sun is zero. When the hour-angle of the mean Sun is 12 hours, it is said to be midnight there and this is the moment when  the  new civil day begins there.

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