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a Latitudes are approximate, and for illustrative purposes only. The data shown do not contain corrections for refraction or for the radius of the Sun's disk (assuming daylight to be from first gleam to last gleam), both of which extend the time of daylight. See the text for details of these effects.

a Latitudes are approximate, and for illustrative purposes only. The data shown do not contain corrections for refraction or for the radius of the Sun's disk (assuming daylight to be from first gleam to last gleam), both of which extend the time of daylight. See the text for details of these effects.

4.1.1.2. Types of Solar Time

Annual motion

The modern sundial provides an indication of apparent solar time:

where HA& is the hour angle of the Sun. Twelve hours are added because most communities prefer to start the day at midnight rather than at noon, when the hour angle is zero. Apparent solar time is not uniform throughout the year, however: As we indicate later in this section, the arrival times of the Sun at the celestial meridian may differ by up to about half an hour in the course of the year. Its progress is retarded or advanced by two effects: First, because it moves on the ecliptic (not on the celestial equator), and second, because it moves on the ecliptic at a variable rate. The last is a consequence of the eccentric orbit of the Earth around the Sun, discussed in §2.4.4.

To understand the significance of the first (more important) effect, consider the appearance of the celestial equator where it crosses the celestial meridian. Its orientation is constant from hour to hour and from day to day, and an object moving along the celestial equator, would, in a circular orbit (like the ancient view of the sphere of the fixed stars), move at a constant rate. On the other hand, the orientation of the ecliptic where it crosses the celestial meridian varies with time of day and year. The diurnal motion of objects in the sky, caused by the rotation of the Earth beneath them, is westward. The annual motion of the Sun, which is caused by the revolution of the Earth, and is eastward, effectively slows the diurnal motion, if ever so slightly. But the Sun's annual motion is along the ecliptic, not along the celestial

át summer solstice

Annual motion

át summer solstice

Spring annual motion components

I north

Figure 4.8. The ecliptic movement of the Sun resolved into N-S (declination) and E-W (right ascension) motions. Drawing by E.F. Milone.

equator. The small arc represented by the eastward angular motion on the ecliptic in the course of one day can be resolved into components along declination and hour circles. So, even if the motion along the ecliptic were uniform, there would be an apparent northward or southward component to the annual motion for all times of the year (except precisely at the solstices), and the remaining eastward motion would be variable from day-to-day (see Figure 4.8). The eastward component is greater at the solstices than it is at the equinoxes, because the motion is then exclusively eastward, without a N-S component; at those times of year, it is also greater than the average speed of the Sun, because that motion is along a small circle of declination.

The second effect—the Sun's variable motion along the ecliptic—results from the Earth's orbital motion (see §2.3.5 and Figure 2.16 for definitions of the orbital elements)6 and Table 2.9 for a list of the orbital elements of the Earth and planets.

The Earth moves most rapidly along its orbit in early January, and most slowly in early July; this effect is reflected

6 The Earth's velocity around the Sun averages 30 Km/sec. However, the eccentricity of its orbit causes a variation in this velocity, which can be expressed as

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