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Why isn't the acceleration of an object in Earth's gravity related to the object's mass?

Please, try to explain this effect without physical formulas, but using only logical formulation.

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  • $\begingroup$ Comment but not an answer: Actually it is, but when one object is much larger than the other (like the Earth versus a book) then the effect is almost but not quite zero. Why? The force is certainly proportional to the object's mass, but the object's acceleration is also limited by the mass. Push a car and a bicycle with equal force and the bicycle will accelerate much faster. $\endgroup$ – uhoh Feb 13 at 16:32
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    $\begingroup$ This is more of a physics questions than an earth science one. $\endgroup$ – Fred Feb 13 at 18:53
  • $\begingroup$ It's impossible to explain without physical formulas. $a = F/m$, hence it is independent of mass. $\endgroup$ – AtmosphericPrisonEscape Feb 14 at 12:52
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This is clearly related to Newton's 2nd law, but since you have asked about the phenomenon rather than the formulas, a Physics SE user explained much better than I can possibly can:

(..) the gravitational force is different on different masses. Half the mass only has half the weight, so it is also only pulled in half as much by gravity.

What gravity does is to pull in every single "particle" equally. If there are double as many "particles", then the pull in each is still the same and each accelerates the same amount.

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