= Solution
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A <geostationary orbit> provides continuous viewing of approximately the same terrestrial region, favouring fast <cloud> evolution, storm tracking and the diurnal cycle. The large range makes fine spatial resolution demanding, high latitudes have poor viewing geometry, and a single platform has no global coverage. A <polar orbit> gives much smaller range and broad latitude coverage as <Earth> rotates beneath it, favouring detailed global mapping; any one location is sampled intermittently. A <Sun-synchronous orbit> can hold approximately fixed local solar time for comparing observations, but that sampling can miss much of the diurnal evolution. The science therefore sets a trade between spatial coverage, spatial resolution and temporal sampling.
The <Moon>'s very slow, tidally locked rotation makes a lunar stationary <orbit> fundamentally problematic. Let its <orbital angular velocity> around <Earth> be $n$, approximately also its spin rate. For lunar <mass> $m$, terrestrial <mass> $M$, and separation $a$, the two-body estimates give
$$
n^2\simeq\frac{GM}{a^3},\qquad r_{\rm sync}=\left(\frac{Gm}{n^2}\right)^{1/3}\simeq a\left(\frac mM\right)^{1/3},\qquad
r_H\simeq a\left(\frac m{3M}\right)^{1/3}.
$$
Thus $r_{\rm sync}\simeq3^{1/3}r_H$ lies outside the lunar <Hill sphere>. Earth's tidal perturbations prevent the desired simple stable, lunar-centred stationary <orbit>. This is stronger than merely saying that the required <orbit> is high; specially maintained <three-body orbits> are a different construction.
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