 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-4/37b/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Use the total mass

M ≃ 60 M_{⊙} ≃ 1.2 \times 1 0^{32} kg .

With the stated last-orbit estimate,

r = \frac{6 GM}{c ^{2}} ≃ 5 \times 1 0^{5} m .

T = 2 π \frac{r ^{3}}{GM} = 12 π 6 \frac{GM}{c ^{3}} ≃ 3 \times 1 0^{- 2} s .

f_{GW} ≃ \frac{2}{T} ≃ 7 \times 1 0^{1} Hz .

Only one significant figure is meaningful under the approximations.

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