Past exam of the physics of atmospheres and oceans course of the University of Oxford / 2019 / 3 / c / Solution

Assume a circular orbit, nadir viewing, negligible planetary rotation and a fixed camera relative to the orbital ground track. If $R_V$ is the planet's radius and $h$ the orbital altitude, the orbital angular speed isThe nadir footprint moves across the surface at $v_g=n{R}_V\simeq 6.88\times 10^3\mathrm{m}{\mathrm{s}}^{-1}$, rather than the slightly larger satellite speed $n(R_V+h)$. HenceThis is an upper integration time for approximately one $200\mathrm{m}$ along-track sample without motion compensation. Using satellite speed directly changes it by only about four per cent; the expression above keeps the projection onto the planetary surface.