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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 3

Write
$$
y=y_0+\Delta y,
\qquad
y_0=\frac{\sin\phi}{b},
$$
where $\Delta y$ is first order in $M$. Substitution into $y''+y=3My^2$ and omission of terms of order $M\Delta y$ and $(\Delta y)^2$ gives
$$
\boxed{
\Delta y''+\Delta y
=3M y_0^2
=\frac{3M}{2b^2}(1-\cos2\phi).}
$$
This is the linearized orbit equation used in the <perturbative derivation of Schwarzschild light deflection>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 37B / a / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 37B / a / iii / Solution

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 37B / a / iii / Solution

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