Lec 3: Physics of propagation of solar radiation from the sun to the earth

Scientific concepts & nature phenomena presented

Properties and structure of the Sun

• Sun’s composition and mass fraction in the solar system: ~99.68% of the solar system’s total mass.
• Rotational period: ~27 days at the equator; ~30 days near the poles.
• Extreme core conditions:
  • Central density: ~10⁵ kg/m³ (about 100× denser than water).
  • Central pressure: > 10⁹ atmospheres.
  • Central temperature: ~1.5×10⁷ K.

• Energy generation mechanism: continuous nuclear fusion

  • Mass difference between reactants and products leads to energy via Einstein’s relation [ E=\Delta m\,c^2 ]

• Energy generation region:

  • Most energy originates near the core; cited that ~90% is generated at about 0.23× solar radius, then transported outward.
• Energy transport inside the Sun:
  • Mention of a convective zone (outside the core region).
  • Temperature gradient: core ~very high; surface ~6000 K (temperature decreases outward).

Energy emission and Earth reception

• Solar irradiance (emitted power / solar power):
  • Sun’s total radiated power quoted: 3.8×10²⁶ W (as stated).
• Energy received by Earth (as stated):
  • Earth receives about 1.7×10¹⁸ W.
• Earth’s basics (as given):
  • Age: ~4.6 billion years
  • Orbit: elliptical, period 1 year
  • Axial tilt: 23.5°
  • Inner core: solid iron-nickel
  • Outer core/mantle description: solid rock (per subtitles)
  • Surface coverage: 70% water, 30% land
  • Blackbody temperature: ~288 K

Radiation theory used for propagation/emission

• Maxwell’s electromagnetic theory:
  • Radiation modeled as electromagnetic waves.
• Planck’s radiation theory:
  • Radiation modeled as photons / energy quanta.
• Claim (as presented): these theories underpin models of radiation emission and propagation from Sun to Earth.

Thermal radiation and heat transfer in vacuum

• Thermal radiation concept: Any body with T > 0 K emits thermal radiation.
• Radiative heat transfer only in vacuum: No medium ⇒ no convection/conduction, only radiation.
• Solar thermal radiation wavelength range (as stated):
  • Between 0.1 to 100 microns (μm), with “most” in 0.1–100 μm.

Electromagnetic spectrum bands and applications (wavelength ranges)

• Thermal/solar-related spectral range: 0.1–100 μm
• Solar blackbody temperature: ~5760 K (~6000 K)
• Solar shortwave spectral distribution (as stated):
  • Radiation peak range: 0.1–3 μm
  • Visible: 0.4–0.7 μm
  • Infrared: 0.7–1000 μm (as stated)
  • Ultraviolet: 0.4 to 10⁻² μm (as stated)
• Other bands listed with approximate ranges:
  • X-rays: 0.01–100 nm (radiography)
  • Ultraviolet: 10–400 nm (water purification)
  • Visible (day vision & photosynthesis): 400–800 nm
  • Near IR: 800 nm–10 μm (night vision)
  • Thermal IR: 10 μm–1 mm (heating/cooling)
  • Microwave: 1 mm–10 cm (microwave ovens)
  • Radar waves: 10 cm–1 m (speed detection/mobile comms)
  • Radio waves: >1 m (radio/TV/communications)

Sun–Earth geometry and orbital variability

• Earth–Sun distance changes due to elliptical orbit:
  • Using mean distance as baseline; distance varies by about ±1.7% (as stated).
• Earth’s apparent subtended angle: 0.53° (as stated).
• Mean Earth–Sun distance: 4.96×10¹¹ m (as stated).
• Earth’s revolution and rotation:
  • Rotation about own axis in 24 h
  • Revolution around Sun in ~4 weeks rotation of Sun mentioned (as stated in subtitles; likely mixing solar rotation and Earth revolution in wording).

Solar constant and extraterrestrial solar flux

• Solar constant (ISC):
  • Defined as radiant flux at the top of Earth’s atmosphere, perpendicular to solar rays at mean Sun–Earth distance
  • Value quoted: 1367 W/m²
• Seasonal/geometry variation due to Earth’s orbit:
  • Values quoted (as stated): around 1322 W/m² (June) to 1411 W/m² (Dec)
  • Variation magnitude quoted: ~0.33%

• Extraterrestrial irradiance formula (as presented): [ I_{EXT}=I_{SC}\left(1+0.033\cos\left(\frac{360n}{365}\right)\right) ]

  • n = day number of the year

Propagation through Earth’s atmosphere: absorption, scattering, and greenhouse effect

• Atmospheric constituents mentioned: particulate matter, O₂, O₃ (ozone), H₂O (water vapor), NO₂, CO₂, CO (as listed).
• Two main atmospheric processes reducing transmitted shortwave:
  • Absorption (dominant in wavelength-selective bands)
  • Scattering
• Longwave re-radiation from Earth:
  • Earth surface emits longwave (infrared) radiation.
  • Certain gases (especially CO₂, per subtitles) absorb and retain some longwave, contributing to atmospheric warming / greenhouse effect.
• Atmospheric thickness reference: ~30 km contains ~99% of atmosphere (as stated).

Extraterrestrial vs terrestrial spectral irradiance

• Spectral irradiance vs wavelength:
  • Extraterrestrial spectrum: dotted line (outside atmosphere)
  • Terrestrial spectrum: solid line (ground, clearest atmosphere)
• Attenuation reason: absorption and scattering in atmosphere cause reduced/shifted spectrum at the surface.
• Wavelength-specific absorption bands (as stated):
  • Ozone (O₃): strong UV absorption roughly 0.2–0.29 μm, and 0.29–0.34 μm
  • Oxygen (O₂): absorption near 0.76 μm (narrow line)
  • Water vapor (H₂O): absorption 0.7–2.2 μm
  • Carbon dioxide (CO₂): absorption for wavelengths > 2.2 μm
• Wavelength range emphasized for solar reaching ground: about 0.29–2.5 μm
• Hot vs cold blackbody idea:
  • Sun (~6000 K) emits more at shorter wavelengths
  • Earth (~288 K) re-radiates at longer wavelengths (peak near ~10 μm per subtitles)

Beam/direct vs diffuse vs global radiation (defined via absorption/scattering)

• Absorption mainly due to: ozone, water vapor, and to a lesser extent other gases and particulates.
• Scattering due to: molecules and particulates/aerosols.

• Radiation components:

  • Direct/Beam radiation (I_B): sunlight reaching surface without scattering
  • Diffuse radiation (I_D): scattered radiation arriving from many directions (lower intensity)
  • Global radiation (I_G): [ I_G = I_B + I_D ]

• Note (as stated): these definitions are tied to instrument measurements and device performance later.

Blackbody radiation, Planck’s law, and Stefan–Boltzmann law

• Blackbody principle:
  • For a given temperature and wavelength, no real body emits more than a blackbody.
• Planck’s law for spectral emissive power (as described):
  • Uses constants C1 and C2 with dependence on wavelength and temperature.
  • Constants quoted (with units in μm-based form):
    • ( C1 \approx 3.743\times 10^8 ) (stated as a value leading to 8 W·μm⁴/m² in their unit system)
    • ( C2 \approx 1.4387\times 10^4 ) (μm·K)

• Stefan–Boltzmann law via integration of Planck’s law:

  • Blackbody emissive power: [ E_B=\sigma T^4 ]

  • Stefan–Boltzmann constant: σ = 5.67×10⁻⁸ W/m²·K⁴

  • Sun as a blackbody (as argued):
  • Using solar constant and geometry relations to infer an equivalent blackbody temperature:
  • Substituting leads to ~5777 K (as stated), close to the Sun’s ~6000 K.

Air mass (AM) for solar testing

• Air mass (AM): measures the relative optical path length through Earth’s atmosphere.

• Geometry relation (as presented): [ AM = \frac{AB}{BC} \approx \frac{1}{\cos\theta} ]

  • θ = solar zenith angle
  • Key reference values (as stated):
  • AM = 1 when Sun is at zenith (θ = 0)
  • AM = 0 for extraterrestrial radiation (no atmospheric path)
  • AM = 1.5 is important because tests are typically done at ~48.2° solar zenith angle
  • Standard test conditions mentioned:
  • Irradiance: 1000 W/m²
  • Device ratings: “Watt peak (Wp)” under standard test conditions (as described).

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Researchers / sources featured

• James Clerk Maxwell (Maxwell’s electromagnetic theory)
• Max Planck (Planck’s radiation theory; photon/quanta concept)
• Albert Einstein (energy–mass relation (E=\Delta mc^2))
• Stefan–Boltzmann (Stefan–Boltzmann constant and law; referenced via σ)