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Published equation contexts

I(λ)=I0(λ) e−τ(λ),τ(λ)=∫n(z) σ(λ,z) dzI(\lambda) = I_0(\lambda)\, e^{-\tau(\lambda)}, \qquad \tau(\lambda) = \int n(z)\,\sigma(\lambda, z)\, dz

Why this formula appears here

Atmospheric composition is inferred the same way interiors are — from a signal, not from the substance itself — but the physics is radiative transfer rather than mechanics. The workhorse technique is transmission spectroscopy : as a planet with an atmosphere passes in front of its star (for an exoplanet) or as sunlight grazes a planet’s limb (for a solar-system body observed from orbit), starlight is filtered through the atmosphere’s outer layers before reaching the detector. Each gas absorbs a characteristic set of wavelengths, governed to first approximation by the Beer–Lambert relation, I(λ)=I0(λ) e−τ(λ),τ(λ)=∫n(z) σ(λ,z) dzI(\lambda) = I_0(\lambda)\, e^{-\tau(\lambda)}, \qquad \tau(\lambda) = \int n(z)\,\sigma(\lambda, z)\, dz. where I0(λ)I_0(\lambda) is the incident spectrum, τ(λ)\tau(\lambda) the…

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λ\lambda

Symbol λ

λ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

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I0I_0

Symbol I_0

the incident spectrum, τ(λ)\tau(\lambda) the wavelength-dependent optical depth, n(z) the number density of an absorbing species at altitude z.

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e−τ(λ)e^{-\tau(\lambda)}

Symbol e^-τ(λ)

e−e^-τ(λ) is one of the signed contributions combined to compute the quantity on the left.

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How to interpret it

The result depends on every term or point included by the summation or integral. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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I(λ)=I0(λ) e−τ(λ),τ(λ)=∫n(z) σ(λ,z) dz,I(\lambda) = I_0(\lambda)\, e^{-\tau(\lambda)}, \qquad \tau(\lambda) = \int n(z)\,\sigma(\lambda, z)\, dz,

Equation 9 · Space Science

How Planetary Science and Exploration Actually Work

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Atmospheric composition is inferred the same way interiors are — from a signal, not from the substance itself — but the physics is radiative transfer rather than mechanics. The workhorse technique is transmission spectroscopy : as a planet with an atmosphere passes in front of its star (for an exoplanet) or as sunlight grazes a planet’s limb (for a solar-system body observed from orbit), starlight is filtered through the atmosphere’s outer layers before reaching the detector. Each gas absorbs a characteristic set of wavelengths, governed to first approximation by the Beer–Lambert relation, I(λ)=I0(λ) e−τ(λ),τ(λ)=∫n(z) σ(λ,z) dzI(\lambda) = I_0(\lambda)\, e^{-\tau(\lambda)}, \qquad \tau(\lambda) = \int n(z)\,\sigma(\lambda, z)\, dz. where I0(λ)I_0(\lambda) is the incident spectrum, τ(λ)\tau(\lambda) the…

Meanings in this article

  • I0I_0: the incident spectrum, τ(λ)\tau(\lambda) the wavelength-dependent optical depth, n(z) the number density of an absorbing species at altitude z.
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