The Grand Tharsis Lodge

In the not-too-distant future, the ambitious great great grand-clone of Bezos-Musk II has been proclaimed Archduke of Valles Marineris and Tharsis, and is pushing ahead with plans to develop the potentially lucrative Martian tourism industry. Key to the Archduke's plan is the construction of a state-of-the-art luxury tourist facility with ease of access to the so-called Grand Canyon of Mars and the massive volcanoes of the Tharsis plateau. As an astrospatial scientist in the royal retinue, you have been tasked with identifying candidate locations for the Archduke's Grand Lodge. Since efforts to terraform the red planet have so far proved ineffective, the ideal site must be situated in a Martian cave (in order to mitigate against harmful UV radiation) but with close proximity to the mountains and within striking distance of day trips to the canyon. Furthermore, this cave must be very close to the equator since it will serve as the de facto terminus for the space elevator currently in construction. The Archduke has decreed a Michelin 3.0-rated restaurant and lounge be built along the space elevator's tether, so you must also determine a suitable height for this establishment, so as to provide breathtaking views of both canyon and volcanoes for the billionaire class as they pause for refreshment on their way up or down the elevator.

An antiquated but surprisingly thorough old NASA Mars Cave Catalog from the 2010s was dusted off and a trio of candidate caves were found on the eastern slope of Tharsis within 0.3 degrees of the equator. Viewshed analysis was performed for each of the locations at heights of 10km, 50km, and 100km in order to find a threshold for where the restaurant ought to be situated along the space elevator's run. Its windows would of course feature augmented optics, but the Archduke wished for it to be as close to the surface as possible while still allowing a relatively comprehensive view, in case any of the lodge's guests desired a quick trip up for an evening of fine dining while gazing down upon the Aeolian landscape.

The analysis finds that a restaurant located 100km above the Martian datum would provide suitably sweeping views from any of the three candidate sites, which have been given the monikers "Skylight," "Channel," and "Tharsis Plain." However, this analysis was conducted using the standard Gaussian refractivity coefficient, which was derived through empirical observations on Earth. Due to the red planet's exceedingly thin air (less than 1% of the Earth's atmospheric pressure), this coefficient on Mars is very close to zero: light moves faster through the Martian skies than at home, and bends less, which translates into smaller relative viewsheds.

After taking into account the lack of refractivity, the crater of Arsia Mons is no longer visible from this height, so another viewshed was generated from a height of 150km. The modeled views from here looked to be comprehensive enough for the restaurant's patrons without being too far off the Martian ground.

Of the three candidate lodge locations, Skylight and Channel were favored over Tharsis Plain, which would lack a view of the crater of Arsia Mons from this height. It was also thought that since they were closer to the volcanoes these locations would be better able to exploit potential geothermal power sources. Skylight was ultimately chosen as the best candidate for its slightly closer proximity to the summit of Pavonis Mons (a mere 100km) and its huge, eponymous natural opening to the sky.

Tethering the elevator near the Tharsis Plain location would have afforded a better view of the canyon from the restaurant, but that site was deemed "in the middle of nowhere." Besides, plans had been made to locate a forward base facility at the interface of Noctis Labyrinthus and Valles Marineris as an anchor for tourists' day expeditions from the Grand Tharsis Lodge. You must now find an optimal location for this base camp, within a day's travel to the lodge but with a most magnificent view of the chasms and defiles of the canyon.

The candidate sites for the base camp were chosen prosaically, the old-fashioned way: maps were visually inspected and pins were dropped. Viewsheds were then analyzed from a height of 100m to account for a planned observation deck. Site 3, on an outcropping at the extreme east of the "Night Labyrinth" was ultimately designated for development after ascertaining its superior breadth of views, especially to the south.

The Archduke is pleased with the study and gives their imprimatur to the selected sites. Construction proceeds apace and a promotion seems likely. At the very least you have once more avoided incurring the prince's displeasure and allayed for the time being any fear of joining those less fortunate astrospatial scientists and former colleagues who now toil in exile, scattered among the cruel mining outposts of the asteroid belt.

Notes: There seems to be no way to set ArcGIS Pro's Geodesic Viewshed tool for extraterrestrial geodesy. Future studies would attempt to account for Mars' relatively extreme curvature in the analysis, perhaps using gdal or R instead of the GIS. The default refractivity coefficient for the viewshed tool is based on Gauss' 19th-century experiments and consistent with surveyor convention; my estimation of essentially zero refractivity due to the thin Martian atmosphere is somewhat speculative, since I lacked the data to compute an accurate atmospheric temperature gradient for the red planet. Additionally, some adjustment should be made to account for the incidence of solar radiation on the red planet (only 43.7% of the Earth's).