Seasonal change on the cubic Earth
Temperature is determined by intensity of the Sun light (energy of the solar radiation). The spinning axis of the cubic Earth makes an angle of 23.4 degrees against the vertical direction of the orbital plane of the Earth. It produces the seasonal change of the solar radiation. If the spinning axis is fixed to the vertical direction, the direction of the solar radiation changes as shown in Fig. 2.
Days and nights on the cubic Earth
The sides of the cubic Earth without the spinning axis experience alternation of days and nights. On the real Earth, the length of daytime has a seasonal change; it is long in summer and short in winter. However, on the cubic Earth, they are always 12 hours regardless seasons and latitudes.
The intensity of the solar radiation has a diurnal variation on the cubic Earth as shown in Fig. 3. The maximum intensity has the seasonal variation as shown in Fig. 4. However, the period is a half of a year with a maximum at spring equinox and autumn equinox. The Solar constant S＝1,370 W/m2.
The solar energy given at the surface is 435 W/m2 in average of one day.
This value is smaller than the maximum value at the polar plane. The minimum is 399 W/m2 at the summer solstice and the winter solstice. The annual average is 417 W/m2.
On the other hand, the polar plane has no alternation of days and nights with the period of 24 hours. Days continue a half of a year and nights continue other a half year. The seasonal variation of solar radiation at the polar plane is expressed as shown in Fig. 5.
Let us consider about temperature.
Fig. 6 shows ground temperatures in thermal equilibrium at a place without the air produced by solar radiation. In the polar square, there is no diurnal variation of ground temperatures. Only seasonal variations are present. In the middle of white nights, the ground temperatures reach in maximum value of 2℃. Then, the temperature decreases until -118℃ at the end of the polar nights. It is possible to live in the polar square in the season of white nights, but the polar square in the season of polar nights is too cold for us to live.
The similar calculation was performed for the side squares. The results are shown in the lower part of Fig. 6. Seasonal change has a period of a half year. The amplitude of diurnal variation is greater than that of seasonal variation. The maximum temperature is 290 K and the minimum temperature is 253 K. Thus, we can live in side squares throughout one year. In the real Earth, if there is no atmosphere, thermal equilibrium temperature is -18℃, which is slightly lower than the thermal equilibrium temperature at the cubic Earth.
The temperatures calculated above are the ground temperatures on a plane without air. However, similar results are expected on a plane with a thin air. We can expect a comfortable life on side squares of the cubic Earth. The climate between 800 km and 1000 km from the center of squares will be similar with that of the subtropical climate on the real Earth.
Air temperature is almost constant along a constant pressure surface, i.e., constant temperature surfaces cover in the form of domes on the surface of the cubic Earth. Thus, both temperatures and pressures decrease in the radial direction from the center of the square. This property resembles mountains on real Earth, where both temperatures and pressures decrease when altitudes increase. The temperature distribution depends also on the amount of water vapor contained in the air, because water vapor controls the intensity of the greenhouse effect. Here, we calculated temperatures, assuming the same amount of water vapor at 1atm as that of the real Earth. The air in 100atm contains water vapor 100 times greater than the water vapor in the air in 1atm. The albedo is assumed as 85% (it is 30% on the real Earth). The radiation equilibrium temperature under these conditions is 201K.
Fig. 7 shows the vertical temperature distribution. The ground temperature is 1,210 K. The center of a square is not only high pressure, but also high temperature. Rocks on the surface are heated by the air and they are bright in red as lava of volcanoes.
Temperature decreases with a constant rate of 8.3K/km.
Fig. 14 shows temperature distribution along the radial direction from the center of a square. Constant temperature lines distribute in the form of concentric circles.
[Ecliptic plane]
When we observe the orbital motion of the Sun, it looks like travelling on the celestial sphere passing 12 constellations. The pass of the sun is called the zodiac.
The ecliptic plane is the orbital plane of the Earth. It makes an angle of 23.4degrees against the equatorial plane. This inclination brings 4 seasons.
[K(kelvin)]
There are several ways to show temperatures. Kelvin is unit of absolute temperature which is related with unit of Celsius as
C ＝ T – 273
where C is temperatures in Celsius(℃)and T is temperatures in Kelvin(K). Notice that 0℃＝273 K and 27℃＝300 K.
There is no temperature below 0K. The heat is produced by oscillation of atoms and molecules. There is no oscillation at 0 K, so that heat is not produced at 0 K.
[thermal equilibrium temperature]
Sun produces a huge amount of energy. Visible, infrared, ultraviolet, and X rays are emitted as light from the Sun. Amount of energy radiated from Sun is called solar radiation.
Earth reflects 30% of solar radiation, and 70% of the solar radiation will reach to Earth surface. Suppose Earth will absorb the all reached radiation, that is, Earth will be heated by its radiation and the all heat will radiate to the space beyond Earth. Under these supposision, income and outgo of the heat between Sun and Solar will be constant all of the time. As a result, the temperature of Sun and Earth will be constant, respectively. The constant temperatures under this assumption are named as the thermal equibrium temperature.
Under present solar radiation, the thermal equibrium temperature of Earth is 255 K (= −18 ℃).
