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Equation 9 · Part 6 · How Planetary Science and Exploration Actually Work

Symbol n

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,
nn

What this part means

n is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

n is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…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 wavelength-dependent optical depth, n(z) the number density of an absorbing species at altitude z , and σ(λ,z)\sigma(\lambda, z) its absorption cross-section, which itself depends on temperature and pressure. The instrument records I(λ\lambda) ; the abundance profile n(z) is recovered by inverting this relation against a model atmosphere,…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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