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 intensity of the Sun's radiation arriving perpendicularly to the Earth's atmosphere when the Earth is at its mean distance from the Sun

The average value of the solar constant is 1.36 × 10³ W m⁻²
The value of 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

The intensity of solar radiation received by different planets in the Solar System varies depending on distance from the Sun
- For example, the intensity of solar radiation incident on Venus' atmosphere is higher than Earth's because it is closer to the Sun

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:

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

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

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

Solar constant = 1.4 kW m^–2(2 s.f)

When defining the solar constant, it is important to say that the radiation arrives above the Earth's atmosphere and not at the Earth's surface.

The Solar Constant (HL IB Physics)