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m367 white pill - NBX Soluciones

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The James Webb Space Telescope images a galaxy cluster where the apparent angular separation between gravitational lenses is 0.8 arcseconds. If the cluster is 5 billion light-years away, and the lensing effect scales with mass and inverse distance, if a nearby cluster L tallies a separation of 1.6 arcseconds at equal distance, what is the ratio of the lensing mass of the distant cluster to the nearby one?

📌 Since apparent separation ∝ mass / distance, and distance is same (5 billion ly), then apparent separation ratio = mass ratio

📌 / 1.6 = 0.5 → mass ratio = 0.5

📌 But lensing strength increases with mass, so distant cluster has half the lensing mass. But question asks for ratio of distant to nearby: 0.5 = 1/2

📌 Wait — apparent separation is larger for more massive lens. So if 0.8 > 1.6? No — 0.8 < 1.6, so distant would appear smaller? Contradiction.

📌 Reinterpret: The lensing effect size is proportional to mass and inversely proportional to square of distance? But problem states: "apparent separation ∝ mass / distance" — assuming monochromatic approximation.

📌 But 0.8 < 1.6, so if distance is same, mass ratio = 0.8 / 1.6 = 0.5. But that would imply less mass, contradicting stronger lensing.

📌 Unless the formula is approximate and larger separation implies stronger lensing, so larger angular deflection corresponds to higher mass. But formula says separation ∝ mass / distance.

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