The Solar Constant

Since life on Earth is entirely dependent on the Sun’s energy, it is useful to quantify how much of its energy reaches the top of the atmosphere
- This is known as the solar constant, S

The solar constant is defined as:

The amount of solar radiation across all wavelengths that is incident in one second on one square metre at the mean distance of the Earth from the Sun

The value of the solar constant varies year-round because:
- The Earth is in an elliptical orbit around the Sun, meaning at certain times of year the Earth is closer to the Sun, and at other times of year it is further away
- The Sun’s output varies by about 0.1% during its 11-year sunspot cycle
Calculations of the solar constant assume that:
- This radiation is incident on a plane perpendicular to the Earth's surface
- The Earth is at its mean distance from the Sun
Different planets have different solar constants
- Venus' solar constant is higher than Earth's because it is closer to the Sun

Incoming Radiative Power

The surface area of a planet, with radius r, equals the surface area of a sphere, 4πr²
A planet's radiative intensity covers a cross-sectional area of πr²
So the mean value of the radiative power or intensity is:

$S \times (\frac{π r^{2}}{4 π r^{2}}) = \frac{S}{4}$

Worked example

The Sun emits 4 × 10²⁶ J in one second. The mean distance of the Earth from the Sun is 1.5 × 10¹¹ m.

Using this data, calculate the solar constant.

Answer:

Step 1: List the known quantities

- Power output of Sun, P = 4 × 10²⁶ W
- Distance between the Earth and Sun, r = 1.5 × 10¹¹ m

Step 2: Model the scenario using geometry

- As light leaves the surface of the Sun, it begins to spread out uniformly through a spherical shell
- The surface area of a sphere = 4πr²
- The radius r of this sphere is equal to the distance between the Sun and the Earth

8-2-3-we-solar-constant_sl-physics-rn

Step 3: Write an equation to calculate the solar constant

Solar constant = $\frac{P}{4 π r^{2}}$

Step 4: Calculate the solar constant

Solar constant = $\frac{4 \times 10^{26}}{4 π {(1.5 \times 10^{11})}^{2}}$ = 1415 W m^–2

Solar constant = 1.4 kW m^–2(2 s.f)

The Solar Constant (HL IB Physics)

Revision Note