The feather will land first and please don t include this in the article Let s do a calculation The mass of the Earth is about 1024 times bigger than the mass of the hammer Therefore the acceleration of the Earth is 1024 times smaller than the acceleration of the hammer so if the hammer falls through 1 m the Earth will move 10 24 m during the same time Such short distances which correspond to an energy of 100000 TeV are not probed even by the most energetic particle accelerators Let s now do another calculation Suppose we re dropping the feather The hammer which is presumably on the ground attracts the feather with its gravity The additional acceleration of the feather is given by GM r2 where M is the mass of the hammer and r is the distance from the feather to the hammer This gives roughly 10 10 m s2 which is much bigger than the effect suggested by the Anonymous