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Equation 3 · Part 4 · Comparing the Main Approaches to Planetary Science and Exploration

fraction

θ≈1.22 λD.\theta \approx 1.22\,\frac{\lambda}{D}.
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

The passage around this formula

This reach is the approach’s defining strength and its defining limitation is spatial resolution, which is fixed by the physics of diffraction rather than by mission budget. For a telescope with aperture diameter D observing light of wavelength λ\lambda , the smallest angular separation it can resolve is approximately θ≈1.22 λD\theta \approx 1.22\,\frac{\lambda}{D}. This relation is why an exoplanet studied by transmission spectroscopy is a single point of light with no visible surface at all — the target subtends an angle far smaller than θ\theta for any existing telescope, so every observation is necessarily a disk-integrated average over the whole illuminated hemisphere. Even for solar-system bodies, where θ\theta is…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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