Inspired by this question.
The Martian day is 24 hours, 37 minutes long. After approximately 39 Martian days, 40 days have passed on Earth. As a Martian colonist, should I rest every seventh Martian day, and have my Shabbat differ from that of my brothers in Jerusalem?
Additionally, how would one synchronize the remaining Jewish holidays with my kin on Earth? Does the Halacha prescribe any method to determine the times to observe holidays and fasts when the local year differs from the Earth year?