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Equation 9 · Part 1 · How Planetary Science and Exploration Actually Work

Symbol I

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,
II

What this part means

I is part of the quantity the equation computes from the expression on the right.

Its job in the formula

I is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…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, which means every composition result carries the assumptions of that model — cloud and haze opacity, temperature structure, and the line-list data used for σ(λ,z)\sigma(\lambda,z) — bundled in with…

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

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Sources cited in the article section

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