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Thin disk

{title2=$\Phi\simeq-GM/R+\Omega_K^2z^2/2$}

At fixed <cylindrical radius> $R$ with $|z|\ll R$, the central <gravitational potential> is harmonic in height. The <vertical epicyclic frequency> equals $\Omega_K$ in this spherical potential.

Thin-disk expansion of the stellar gravitational potential

Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 321 / 2 / a / Solution

Thin-disk expansion of the stellar gravitational potential ( $Φ ≃ - GM / R + Ω_{K}^{2} z^{2} /2$ )

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Thin-disk expansion of the stellar gravitational potential (Φ≃−GM/R+ΩK2​z2/2)

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Thin-disk expansion of the stellar gravitational potential ( $Φ ≃ - GM / R + Ω_{K}^{2} z^{2} /2$ )

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