## Solar flux at the Earths orbit

5.6.1 The Earth's elliptical orbit

According to Kepler's first law, the orbit of a planet around the Sun is an ellipse, with the Sun one focus. The Sun-Earth distance, r, thus varies with time as the Earth's orbit around the Sun is elliptical. The elements of this elliptical orbit are shown in Fig. 5.14 where: S is one focus corresponding to the Sun (the second focus is its reflection on the segment BO across the KO plane); A is perihelion; B is aphelion; a = OA is the semimajor axis; b = OK is the semiminor axis; e = OS/OA is the eccentricity. The eccentricity varies over timescales of hundreds of thousands of years with a present mean value of 0.0167 (Astronomical Almanac 1992). If P is the position of the planet then SP is the radius vector, of length equal to r. For an ellipse the following relation holds between a and b

Figure 5.14 shows the orbit of the Earth in a heliocentric system. For the Northern Hemisphere, the point Y is the vernal equinox, or spring equinox, and Y' is its autumnal counterpart. G is the winter solstice and F is the summer solstice.

### 5.6.2 The plane of thee ecliptic

We can also represent the apparent orbit of the Sun in a geocentric system as shown in Fig. 5.15. P is the pole of the celestial sphere, while the circle YEY'C is the celestial equator. The plane YGY'F is the ecliptic plane that defines the Sun's apparent orbit in an ascending mode from A, now called perigee (corresponding to perihelion for the Earth's orbit), to Y. The ecliptic plane makes an angle e, corresponding to the tilt in the Earth's axis of rotation, with the celestial equator arc GE, and is known as the obliquity of the ecliptic that had a value of eo = 23.439° = 0.13022^ radians in the year 2000 AD. The obliquity has varied very slowly on timescales of tens of thousands of years and its current trend can be estimated (in radians) from