IB Physics SLTopic B.2 — Climate & the Greenhouse EffectPaper 1 & 2Solar Constant · Radiative Intensity~6 min read
The Solar Constant
Every calculation about Earth’s climate starts with the same question: how much energy from the Sun actually reaches us? The solar constant answers that — and a bit of sphere geometry explains why the planet as a whole only “sees” a quarter of it on average.
📘 What you need to know
The solar constant, S, is the intensity of the Sun’s radiation striking a plane held perpendicular to the rays, at the top of the atmosphere, when Earth is at its mean distance from the Sun.
Its average value is about 1.36 × 103 W m−2.
S fluctuates slightly because Earth’s orbit is elliptical and because the Sun’s own output drifts by roughly 0.1% over its 11-year sunspot cycle.
The radiation is assumed to hit a surface perpendicular to the beam — any tilt reduces the intensity actually absorbed.
Because Earth is a sphere, not a flat disc facing the Sun, the mean intensity spread over its whole surface works out to S⁄4, not S itself.
Defining the Solar Constant
Think of the Sun as a source radiating power equally in every direction. By the time that energy has travelled out to Earth’s orbit, it has spread across the surface of an enormous imaginary sphere with radius equal to the Sun–Earth distance. The solar constant is simply the power passing through one square metre of that sphere’s surface.
Solar constantS = P ÷ (4πr2)
where P is the Sun’s total power output (W) and r is the mean Sun–Earth distance (m). It’s worth being precise in an exam: the solar constant is defined above the atmosphere, not at ground level — plenty of that energy gets absorbed or scattered before it ever reaches the surface.
Radiation from the Sun spreads evenly across an imaginary sphere of radius r. Earth intercepts only a small disc of that sphere — which is why its whole-surface average intensity works out to S⁄4.
Why the Solar Constant Isn’t Perfectly Constant
Elliptical orbit — Earth’s path around the Sun isn’t a perfect circle, so the Sun–Earth distance changes slightly through the year, moving S up and down.
The 11-year sunspot cycle — the Sun’s own output varies by about 0.1% over this cycle, adding a small long-term wobble on top of the orbital effect.
Calculations of the solar constant always assume the radiation lands on a plane perpendicular to the beam and that Earth sits at its mean orbital distance — that’s what keeps S a single, quotable figure rather than a constantly shifting one.
From a Point Source to a Whole Planet
A planet’s radius rp gives it a spherical surface area of 4πrp2, but from the Sun’s point of view, the planet only ever presents its cross-sectional disc, πrp2, to the incoming beam. Spreading the intercepted power back out over the whole sphere gives the mean radiative intensity:
Mean radiative intensity over a planetS × (πrp2 ÷ 4πrp2) = S ÷ 4
This S⁄4 figure is what you plug into an energy-balance model as the average incoming intensity over Earth’s whole surface — day side, night side, poles and equator all averaged together.
Quick recap: S = P ÷ 4πr² is the intensity at the top of the atmosphere facing the Sun directly. Averaged over the whole planet’s surface, that becomes S⁄4.
WE 1
A star radiates energy at a rate of 5.0 × 10²⁶ W. A planet orbits at a mean distance of 2.0 × 10¹¹ m from the star. Calculate the solar constant experienced by the planet.
Step 1 — Write the equationS = P ÷ (4πr2)
Step 2 — Substitute valuesS = (5.0 × 10²⁶) ÷ [4π × (2.0 × 10¹¹)²]S = (5.0 × 10²⁶) ÷ (5.03 × 10²³)S ≈ 990 W m⁻²Notably lower than Earth’s 1360 W m⁻² — this planet orbits further out relative to its star’s output.
WE 2
Using S = 1360 W m⁻² for Earth, calculate the mean radiative intensity averaged over Earth’s entire surface.
Step 1 — Recall the relationship
mean intensity = S ÷ 4
Step 2 — Substitutemean intensity = 1360 ÷ 4= 340 W m⁻²This is the figure energy-balance models use as Earth’s average incoming intensity, before albedo removes a further slice of it.
💡 Top tips
Always state that the solar constant is measured above the atmosphere — examiners specifically look for this in definitions.
Keep S and S⁄4 straight: use S for a surface facing the Sun directly, and S⁄4 when averaging over an entire spherical planet.
The 4πr² in the solar-constant formula is the surface area of a sphere, not the planet’s own cross-section — don’t mix the two radii up.
⚠ Common mistakes
Saying the solar constant is measured at Earth’s surface — it isn’t; it’s defined at the top of the atmosphere, before any absorption or scattering happens.
Using S directly in a whole-planet energy balance instead of S⁄4, which overestimates the incoming intensity by a factor of four.
Treating the solar constant as truly fixed — it’s an average, not a fixed universal constant, since both orbital distance and solar output vary slightly.
Up next: Greenhouse Gases — where we look at exactly which gases in the atmosphere absorb Earth’s outgoing radiation, and why some matter far more to the greenhouse effect than others.
Want this to actually stick before the exam?
Book a free session and we’ll work through solar constant and energy-balance problems until they’re second nature.
