Yes - I was making a mistake. I was trying to describe the effect of both masses. When one is much smaller than the other, then the movement is mostly in one direction. When they are closer in mass or even equal, they move toward each other. For example, if you have a 1 liter water bottle filled with a material that gives it the same mass as the earth, then the two bodies will move toward each other, and the water bottle will seem to move toward the earth much faster that the 1 filled with water (1kg). If it is filled with a material, that gives it much grater mass than the earth, the earth will move toward it.
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