There is talk in the scientific community of a manned Mars mission: sending an elderly couple to slingshot past Mars and return to Earth as a trial mission, toward eventual other missions that will land there in the future. The mission would last around 300 days.
What would be the halachic challenges that the couple could face on a day-to-day basis? (This question doesn't ask whether space exploration/travel is halachically desirable.)
These questions can be summarized as follows: For those Halakhot which depend on astronomical \ planetary variables, do we follow Earth or local (Martian) values?
Calendar. A day on Mars is about 40 minutes longer than an Earth day. Does one go based on the the Mars day or the Earth day?
If we do go by the Martian day, then Mars will fall behind at a rate of about 1 day per (Earth) month. The Martian calendar will need to be re-calculated (subtract one day per month, etc) to stay in sync with the Earth calendar.
Kiddush Levana. Mars has two moons, Phobos and Deimos. When would one say Kiddush Levana? Would one say it once per orbit for each of these moons, once per Martian "month" (which would probably be divorced from the lunar cycles), or follow the Earth tradition? Perhaps one wouldn't say Kiddush Levana at all.
Zmanim. Seems pretty straight-forward, as Halakhic time is based on location and length of daylight anyways.