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( Solar day)
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.[citation needed] 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.[2]
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