Question #43555

A satellite is placed in a constrained, non-Keplerian circular equatorial orbit around a planet of mass $M$ (in $\text{kg}$). The planet's rotation period is $T$ (in $\text{s}$). By means of a radial propulsion system, the satellite's orbital period is forced to be $T/2$. Despite being in this constrained orbit, the satellite's areal velocity (the rate at which its radius vector sweeps out area) is maintained to be exactly equal to the areal velocity of a standard, unconstrained Keplerian satellite in a synchronous orbit (orbital period $T$) around the same planet. An onboard telescope operating at a wavelength $\lambda$ (in $\text{m}$) is used to observe the planet. Assume the planet's radius is negligible compared to the satellite's orbital radius. What is the minimum aperture diameter $D$ required for the telescope to resolve two point-like surface features on the planet separated by a distance $d$ (in $\text{m}$)? (Let $G$ be the universal gravitational constant in $\text{N}\cdot\text{m}^2/\text{kg}^2$).