What is the least gravity needed for human health on a one year space trip?
An excellent question. Finding minimum gravity to keep humans healthy should be a high priority. Maybe lunar or Mars gravity isn't sufficient. In which case efforts to colonize these places would be unproductive. If it turns out only a small amount is needed, it becomes much more doable to build orbital habs and workplaces for asteroid mines.
At this time it remains an open question. We really have only two data points: the weightlessness of someone in orbit and the full g on earth's surface.
Russian astronaut Valeri Polyakov spent 438 days in orbit without excessive bone loss.
However Valeri had a great deal of self discipline and had a very rigorous exercise regimen. We can't expect everyone to do as well.
I look at this question in my blog post What is Minimum Spin Hab?
Zero. None. Nada. Zip. 0.0
Artificial gravity is not necessary to stay healthy for one year.
OK it's 340 days, but it's probably safe to assume another 25 days wouldn't change the outcome too much.