I'd recommend showing this + the time zone (e.g. "browser local time, UTC+2"). My guess was that it's the local time of the location entered, which can matter when telling someone "hey, you'll be able to see a cool satellite looking out your northward window at 9 pm!". If you're worried about keeping a clean look, at least add a tooltip.

(I've also been trained to distrust any time that doesn't specify a time zone, because I've seen sites that default to some random US timezone, use your local time, use UTC, ...)