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Theme B — The Particulate Nature of Matter

B.2.2 The Solar Constant — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 20 of 53 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

B.2.2 The Solar Constant — IB PHYSICS SL notes: Define the solar constant and use the inverse-square law to find solar intensity at different distances and the average intensity over a planet's surface.Solar constant S = the intensity of the Sun's radiation arriving perpendicular…

  • Above the atmosphere
  • Elliptical orbit
  • Sunspot cycle
  • IB calculations
  • Position dependence
  • Spherical shell

Part 1 of 7Definition

Solar constant S
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.
Value
  • Value the average is 1.36 × 103 W m−2.
Above the atmosphere
  • Above the atmosphere it is the radiation at the top of the atmosphere, not at the Earth's surface.
Purpose
  • Purpose life depends on the Sun's energy, so it quantifies how much reaches the top of the atmosphere.

Part 2 of 7Why it varies

1Elliptical orbit
  • Elliptical orbit the distance changes by about 3% through the year, so S varies by about 7% between January and July.
2Sunspot cycle
  • Sunspot cycle the Sun's output varies by about 0.1% over the 11-year cycle.
3IB calculations
  • S is taken as fixed.
4Position dependence
  • Position dependence different planets have different values.
  • Venus receives about 2.6 × 103 W m−2 and Mars about 590 W m−2.

Part 3 of 7Intensity and the inverse-square law

Intensity
  • I = P/A, the power per unit area at right angles to the direction of travel, in W m−2.
    What the symbols mean: I = intensity (W m−2) · P = power (W) · A = area the power falls on (m2)
Source
  • Source the Sun's luminosity L is about 3.83 × 1026 W, from fusion in its core.
Spherical shell
  • Spherical shell the power passes through a sphere of radius d and area 4πd2.
Equation
  • I = L/(4πd2), so the solar constant is L/(4πr2) with r the Earth–Sun distance.
Proportion
  • I ∝ 1/d2, so doubling the distance gives a quarter of the intensity.
Graphs
  • I against d is a steeply falling curve, and I against 1/d2 is a straight line through the origin with gradient L/4π.

Part 4 of 7Average intensity over a planet

Intercepted power
  • Intercepted power a planet of radius R presents a disc of area πR2 to the parallel beam, so Pin = SπR2.
Spread over the sphere
  • Spread over the sphere the surface area is 4πR2, since the planet rotates, light falls obliquely at higher latitudes and not at all on the night side.
Mean intensity
  • Iavg = SπR2/4πR2 = S/4.
Earth
  • S/4 is about 340 W m−2.
Factor of four
  • Factor of four it is the ratio of the surface area of a sphere to its cross-sectional area.

Part 5 of 7Absorbed and reflected power

Albedo
  • Albedo a fraction a of the incident power is reflected.
Absorbed intensity
  • Iabs = (S/4)(1 − a).
Earth
  • Earth with a = 0.30 this gives about 238 W m−2.
Balance
  • Balance this absorbed power must be balanced by outgoing radiation if the temperature is to stay constant.
Real atmosphere
  • Real atmosphere gases and clouds absorb part of the sunlight before it reaches the ground.

Part 6 of 7Assumptions

Perpendicular surface
  • Perpendicular surface the radiation is taken as incident on a surface perpendicular to the rays.
Mean distance
  • Mean distance the Earth is at its mean distance from the Sun.
Uniform spreading
  • Uniform spreading the Sun's power spreads uniformly through space.

Part 7 of 7More from the specification

Solar irradiance blackbody model
  • Solar irradiance blackbody model treating the Sun as an ideal blackbody radiator in an idealized model explains solar constant measurements above Earth.
Emissivity
  • The ratio of power radiated per unit area by a surface to that radiated by a black body at the same temperature
Infrared
  • The part of the electromagnetic spectrum emitted by warm objects.
Wavelength
  • Distance between a point on one wave and the same point on the next wave
Activity
  • Number of decays per second of a sample.
Infrared radiation
  • Long-wavelength thermal radiation emitted by the Earth
Ozone layer
  • Ozone layer it absorbs harmful ultraviolet radiation, and ozone depletion is a separate problem from the greenhouse effect.

Key terms

TermMeaning
Solar constantIntensity of the Sun's radiation on a perpendicular surface above the Earth's atmosphere at the mean distance
IntensityPower per unit area, in W m−2
LuminosityTotal power emitted by a star
Inverse-square lawIntensity falls as 1/d2 from a point source
AlbedoFraction of incident radiation that is scattered
Cross-sectional areaArea of the disc that a planet presents to the incoming beam, πR2

Avoid these mistakes

1
Saying the solar constant is measured at the surface — it is measured above the atmosphere.
2
Using S instead of S/4 for the mean over the planet — divide by four.
3
Using 4πR2 for the intercepted area — the intercepted area is πR2.
4
Believing the solar constant never varies — it varies slightly with the orbit and the sunspot cycle.
5
Forgetting the albedo factor (1 − a) — only the unreflected part is absorbed.

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