And Visibility of the

The sidereal year is the real orbital period of the Earth around the Sun. After one sidereal year, the Sun is seen at the same position relative to the stars. The length of the sidereal year is 365.256363051 days of 86,400 SI seconds at the epoch J2000.0 = 2000 January 1 12:00:00 TT.

We noted earlier that, owing to precession, the direction of the vernal equinox moves along the ecliptic at about 50" per year. This means that the Sun returns to the vernal equinox before one complete sidereal year has elapsed. This time interval, called the tropical year, is 365.24218967 days.

A third definition of the year is based on the perihelion passages of the Earth. Planetary perturbations cause a gradual change in the direction of the Earth's perihelion. The time interval between two perihelion passages is called the anomalistic year, the length of which is 365.259635864 days, a little longer than the sidereal year. It takes about 21 , 000 years for the perihelion to revolve 360° relative to the vernal equinox.

The equator of the Earth is tilted about 23.5° with respect to the ecliptic. Owing to perturbations, this angle changes with time. If periodic terms are neglected, the obliquity of the ecliptic e can be expressed as:

- 0.00059" T + 0.001813" T3, where T is the time elapsed since the epoch 2000.0 in Julian centuries (see Sect. 2.14). The expression is valid for a few centuries before and after the year 2000. The obliquity varies between 22.1° and 24.5° with a 41,000 year periodicity. At present the tilt is decreasing. There are also small short term variations, the nutation.

The declination of the Sun varies between — e and +e during the year. At any given time, the Sun is seen at zenith from one point on the surface of the Earth. The latitude of this point is the same as the declination of the Sun. At the latitudes — e (the Tropic of Capricorn) and +e (the Tropic of Cancer), the Sun is seen at zenith once every year, and between these latitudes twice a year. In the Northern hemisphere the Sun will not set if the latitude is greater than 90° — 8, where 8 is the declination of the Sun.

The southernmost latitude where the midnight Sun can be seen is thus 90° — e = 66.55°. This is called the Arctic Circle. (The same holds true in the Southern hemisphere.) The Arctic Circle is the southernmost place where the Sun is (in theory) below the horizon during the whole day at the winter solstice. The sunless time lasts longer and longer when one goes north (south in the Southern hemisphere). At the poles, day and night last half a year each. In practise, refraction and location of the observing site will have a large influence on the visibility of the midnight Sun and the number of sunless days. Because refraction raises objects seen at the horizon, the midnight Sun can be seen a little further south than at the Arctic Circle. For the same reason the Sun can be seen simultaneously at both poles around the time of vernal and autumnal equinox.

The eccentricity of the Earth's orbit is about 0.0167. The distance from the Sun varies between 147-152 million km. The flux density of solar radiation varies somewhat at different parts of the Earth's orbit, but this has practically no effect on the seasons. In fact the Earth is at perihelion in the beginning of January, in the middle of the northern hemisphere's winter. The seasons are due to the obliquity of the ecliptic.

The energy received from the Sun depends on three factors. First the flux per unit area is proportional to sin a, where a is the altitude of the Sun. In summer the altitude can have greater values than in winter, giving more energy per unit area. Another effect is due to the atmosphere: When the Sun is near the horizon, the radiation must penetrate thick atmospheric layers. This means large extinction and less radiation at the surface. The third factor is the length of the time the Sun is above the horizon. This is important at high latitudes, where the low altitude of the Sun is compensated by the long daylight time in summer. These effects are discussed in detail in Example 7.2.

There are also long-term variations in the annual Solar flux. Serbian geophysicist Milutin Milankovic (1879-1958) published in the 1930's and 1940's his theory of ice ages. During last 2-3 million years, large ice ages have been repeated approximately every 100,000 years. He proposed that variations of the Earth's orbit cause long-term periodic climate change, now known as Milankovic cycles. Milankovic claimed that the cycles in eccentricity, direction of the perigee, obliquity, and precession result in 100,000 year ice age cycle. The cycle of precession is 26,000 years, direction of the perigee relative to the equinoxes is 22, 000 years, and the obliquity of the ecliptic has a 41,000 year cycle. Changes in orbital eccentricity are not fully periodic but some periods above 100,000 years can be found. The eccentricity varies between 0.005-0.058 and is currently 0.0167.

The annual incoming Solar flux varies with these orbital changes and the effect is largest at high latitudes. If, for example, the eccentricity is high, and the Earth is near the apogee during the hemisphere's winter, then winters are long and cold and summers are short. However, the theory is controversial, orbital forcing on the climate change is not well understood, and probably not enough to trigger glaciation. There exist also positive feedback loops, like the effect of low albedo of snow and ice. It means that ice reflects more radiation back into space, thus cooling the climate. The system is highly chaotic so that even minor changes in the primary conditions will result in large differences in the outcome. There are also other effects causing climate change, including emerging gases from large lava flows and eruptions of volcanos and, nowadays, anthropogenic reasons.

The future is also uncertain. Some theories predict that the warm period will continue next 50,000 years, whereas others conclude that the climate is already

cooling. Anthropogenic reasons, like ever increasing fraction of green house gases, e.g. carbon dioxide, will change the short-term predictions.

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