Earth's motion, solar constant and seasons

Movement of the earth

The earth has two motions: rotation about its own axis once in 24 hours (which causes day and night) and revolution around the sun in an elliptical orbit once in 365.25 days. The axis is tilted by 23.45° from the normal to the orbital plane and keeps a fixed direction in space.

The sun-earth distance varies from 1.471×10¹¹ m (about 3 January) to 1.521×10¹¹ m (about 4 July), with a mean of 1.496×10¹¹ m (1 AU).

Cause of seasons

Because of the fixed tilt, the angle between the sun's rays and the surface at a place changes through the year. The declination $\delta$ (the angle of the sun north or south of the equator) varies from +23.45° on 21 June (summer solstice) to −23.45° on 22 December, and is zero at the equinoxes (21 March, 23 September). When the northern hemisphere leans towards the sun, it has longer days and more direct rays, i.e. summer. The distance from the sun is not the cause.

Declination (Cooper): $\delta = 23.45 \sin\left[\frac{360(284+n)}{365}\right]$, where $n$ = day of the year.

Definitions

• Solar constant $G_{sc}$: the energy from the sun per unit time on a unit area perpendicular to the rays, at the mean earth-sun distance, outside the atmosphere. Value = 1367 W/m² (WRC value; recent satellite measurements give about 1361 W/m²).
• Air mass $m$: the ratio of the path length of the rays through the atmosphere to the path length when the sun is overhead. $m \approx 1/\cos\theta_z$ (for $\theta_z < 70°$). Air mass zero (AM0) is outside the atmosphere; AM1.5 is the standard for testing solar cells.
• Beam (direct) radiation: radiation that reaches the surface directly from the sun without being scattered.
• Diffuse radiation: radiation scattered by air molecules, dust and clouds, arriving from all directions of the sky.
• Global (total) radiation: the sum of beam and diffuse radiation on a surface, $G = G_b + G_d$.