= Solution
{c}
A calibrated multispectral filter <radiometer> is a natural choice for rapid thermal mapping: a few selected bands provide higher photon throughput and faster imaging than spreading the light over many <spectrometer> channels. Several bands can help separate <temperature>, dust <emissivity> and atmospheric effects. A <spectrometer> would be justified if identifying composition or resolving spectral structure were a central additional objective; one broadband <radiance> alone cannot generally determine both <temperature> and unknown <emissivity>.
Thermal <infrared> radiation is preferable to reflected visible light for measuring <temperature>. The <Rayleigh criterion> sets
$$
1.22\frac\lambda D\lesssim\frac{500}{h},\qquad
\boxed{\lambda\lesssim12.0\,\mathrm{\mu m}.}
$$
A band near $10\,\mathrm{\mu m}$ is therefore a reasonable compromise between useful planetary thermal emission and the required <diffraction-limited resolution>. At that <wavelength>, the nominal surface <Rayleigh criterion> separation is about $415\,\mathrm m$; at $15\,\mathrm{\mu m}$ it is about $623\,\mathrm m$ and fails the target. The exact bands must avoid or model strong atmospheric absorption and account for the dust spectrum. The $500\,\mathrm m$ sampling pitch is still not a guarantee of faithful reconstruction of arbitrary $500\,\mathrm m$ features: detector sampling and the <point spread function> must be considered together.
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