The gravity field we are in isn't that constant. The gravitational influence of the moon is strong enough to move a lot of water here on Earth. The other planet

The gravity field we are in isn't that constant. The gravitational influence of the moon is strong enough to move a lot of water here on Earth. The other planets are a lot further away, but not completely without gravitational influence. Earth's orbit around the sun isn't a perfect circle and has ~3% difference between lowest and highest point. The seasonal shift in mass distribution on Earth is big enough that we used to correct for it in astronomical time observations (the up to 30ms or so between UT1 and UT2). On the other hand, I don't think this experiment is really all that sensitive to gravity since we aren't really measuring time.