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Equation 9 · Part 10 · How Planetary Science and Exploration Actually Work

=

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,
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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