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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-320/1/d/solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 320 / 1 / d / Solution by

Codex  0 2026-09-28

Average the phase probability over the thermal eccentricity distribution:

f_{unbound} = \int_{0}^{1} 2 e (\frac{1}{2} - \frac{e}{π}) d e .

Therefore

f_{unbound} = \frac{1}{2} - \frac{2}{3 π} ≃ 0.288 .

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