An astronaut on the Moon, where there is no atmosphere, simultaneously drops a feather of mass \(m\) and a hammer of mass \(M\) from the same height \(H\) above the lunar surface. The mass of the hammer is significantly greater than the mass of the feather (\(M \gg m\)). Which of the following correctly compares the time \(t_f\) it takes for the feather to hit the surface to the time \(t_h\) it takes for the hammer to hit the surface and provides a correct justification?