What Is the Solar Constant?

SL and HL: The solar constant is the solar power received per unit area at Earth’s mean distance from the Sun, measured on a surface perpendicular to the Sun’s rays above Earth’s atmosphere. Its IB data booklet value is $S = 1.36 \times 10^3\ \text{W m}^{-2}$.

Why Is It Called a Constant?

The Sun emits energy with luminosity $L$, meaning its total power output. At distance $d$, this power is spread over a spherical area $4\pi d^2$, so the intensity is

$$S = \frac{L}{4\pi d^2}.$$

At Earth’s mean orbital distance, this gives approximately $1360\ \text{W m}^{-2}$. The value is treated as constant in most IB calculations, although it varies slightly because Earth’s orbit is not perfectly circular and the Sun’s output changes slightly.

A common misconception is that every square metre of Earth receives $1360\ \text{W}$. This is incorrect. The solar constant applies only to an area perpendicular to the rays. Earth intercepts sunlight over a circular projected area $\pi R^2$, but the energy is distributed across its total surface area $4\pi R^2$. Therefore, the mean incident intensity over the whole planet is

$$\frac{S}{4} = \frac{1360}{4} = 340\ \text{W m}^{-2}.$$

If Earth’s albedo is $\alpha$, the mean absorbed intensity is

$$P_{\text{absorbed per unit area}} = \frac{S(1-\alpha)}{4}.$$

For example, if $\alpha = 0.30$, Earth reflects $30\%$ of the incoming radiation and absorbs $70\%$. The globally averaged absorbed intensity is

$$\frac{(1.36 \times 10^3)(1-0.30)}{4} = 238\ \text{W m}^{-2}.$$

The total solar power intercepted by Earth is $S\pi R^2$, not $S4\pi R^2$, because sunlight reaches only Earth’s projected circular area. Albedo then determines the fraction of that intercepted power absorbed by the planet.

Exam Technique

This concept belongs to B.2 Greenhouse effect for both SL and HL. Distinguish between $S$, the intensity on a perpendicular surface, and $S/4$, the global mean intensity. Examiners may ask you to calculate incoming power using $S\pi R^2$ or apply albedo when determining absorbed power.