 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2023

Paper 321

A satellite on a circular orbit is stationary in the corotating sheet. Write its tidal forcing and the response as
$$
\Psi=\psi(x)e^{ik_yy},
\qquad
v_y=v(x)e^{ik_yy}.
$$
Since $D=-iSk_yx$, the forced wave equation becomes
$$
\boxed{
-v_s^2v''+
[\kappa_r^2+v_s^2k_y^2-S^2k_y^2x^2]v
=(2\Omega-S)\psi'-Sxk_y^2\psi}.
$$
This ordinary differential equation describes a <satellite-forced density wave in an astrophysical disk>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 321 / 2 / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 321 / 2 / d / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 321 / 2 / d / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)