The TRAPPIST-1 system is the first transiting planet system found orbiting an ultracool dwarf star[SUP] 1 [/SUP]. At least seven planets similar in radius to Earth were previously found to transit this host star[SUP] 2 [/SUP]. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 day orbital period for the outermost transiting planet, TRAPPIST-1 h, which was previously unconstrained. This value matches our theoretical expectations based on Laplace relations[SUP] 3 [/SUP] and places TRAPPIST-1 h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1 h has a radius of 0.752 R [SUB]⊕[/SUB] and an equilibrium temperature of 173 K. We have also measured the rotational period of the star to be 3.3 days and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf.
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