As the rotation axis of the Earth is not perpendicular to its orbital plane, the ecliptic plane, which is the geometric plane containing the mean orbit of the Earth around the Sun, is inclined relative to the celestial equatorial plane, which is the projection of the Earth's equator into space. This angle is called the obliquity of the ecliptic ${\epsilon}_{obl}$. At present, it is about 23°26' (Fig. 2.7).

The intersections of those two planes are used to define the seasons. In particular, the vernal equinox, which is often used as a reference in the coordinate system to define the true longitude ${\lambda}_{t}$ (or ecliptic longitude, Fig. 2.8), corresponds to the intersection of the ecliptic plane with the celestial equator when the Sun moves from the austral to the boreal hemisphere in its apparent movement around the Earth. This occurs around March 2021 and is often called the spring equinox. However, this term could be misleading as this date corresponds to the beginning of autumn in the Southern Hemisphere.
By definition the vernal equinox corresponds to a true longitude equal to zero, the solstices to the true longitudes equal to 90° and 270° and the "autumn" equinox to a true longitude equal to 180°. If we define PERH as the longitude of the perihelion measured from the autumn equinox (PERH = 102.04 in presentday conditions, corresponding to a true longitude of 180° + PERH = 282.04), we can write
This definition can be used to compute the length of the different seasons, using Kepler's second law which states that, as the Earth moves in its orbit, a line from the Sun to the planet sweeps out equal areas in equal times.
S_{h}, the amount of solar energy received per unit time on a unit horizontal surface at the top of the atmosphere is proportional to the cosine of ${\theta}_{s}$, the solar zenith distance which is defined as the angle between the solar rays and the normal to the Earth's surface at any particular point.
S_{h} rises as ${\theta}_{s}$ becomes closer to 1, as the horizontal surface becomes more normal to the Sun's rays. When the surface is inclined at an oblique angle to the solar rays, the amount of energy received by the surface per square metre is lower, because the total amount of energy received by the perpendicular surface (S_{r}A_{1} on figure 2.9) is distributed across a larger surface (S_{r}A_{1} = S_{h}A_{2} = (S_{h}A_{1})/(cos${\theta}_{s}$)).

cos${\theta}_{s}$ could be computed using standard astronomical formula:
$$\mathrm{cos}{\theta}_{s}=\mathrm{sin}\phi \mathrm{sin}\delta +\mathrm{cos}\phi \mathrm{cos}\delta \mathrm{cos}HA\phantom{\rule{0ex}{0ex}}$$  (2.21) 
where $\phi $ is the latitude of the point on Earth, $\delta $ is the solar declination, HA is the hour angle. The declination $\delta $ is defined as the angle between a line from the centre of the Earth towards the Sun and the celestial equator (Fig. 2.10). It varies from +${\epsilon}_{obl}$ at the summer solstice in the Northern Hemisphere to ${\epsilon}_{obl}$ at the winter solstice and zero at the equinoxes. During the day, its value is constant to a very good approximation. Knowing the true longitude and the obliquity, the declination $\delta $ can be estimated using the formula:
$$\mathrm{sin}\delta =\mathrm{sin}{\lambda}_{t}\mathrm{sin}{\epsilon}_{obl}\phantom{\rule{0ex}{0ex}}$$  (2.22) 
Furthermore, if we denote the number of the day, starting on the first of January, by NDAY, the value of $\delta $ could also be estimated using the raw approximation (zero order to eccentricity):
$$\delta =23.45{}^{\circ}\mathrm{sin}\left(\frac{36{0}^{\circ}\left(\mathrm{NDAY}80\right)}{365}\right)\phantom{\rule{0ex}{0ex}}$$  (2.23) 
The hour angle HA indicates the time since the Sun was at local meridian, measured from the observer's meridian westward. HA is thus zero at the local solar noon. It is generally measured in radians or in hours (2 $\pi $ rad=24 hours). It could more formally be defined as the angle between the half plane determined by the Earth's axis and the zenith (local meridian halfplane), and the half plane determined by the Earth's axis and the Sun.
