Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 354 / 2 / a / i

Table of contents
- Solution i

Solution

The horizon is the largest positive root of

f (r_{H}) = 0

. With

x = r_{H}^{2}

,

0 = 1 + \frac{x}{L ^{2}} - \frac{μ}{x} ⟺ x^{2} + L^{2} x - μ L^{2} = 0.

Choosing the positive root gives

r_{H}^{2} = \frac{L ^{2}}{2} (1 + \frac{4 μ}{L ^{2}} - 1) .

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