In part one of this series, I discussed the common misconception that projectiles follow a parabolic path as they fall to earth, and hinted that I would undertake to debunk another common understanding of how gravity works, namely:
Before I begin my somewhat heretical attack on one of the more universally accepted "truths" in the world of science, let me make it clear that I will be talking about gravity and gravity alone. When I compare the falls of two different objects ‐ a hammer and a feather, for instance ‐ let it be understood that wind resistance has been eliminated from the experiment. Let me also state that I will be discussing gravity as formulated by Newton and not the more precise and subtle theory of Einstein. Milk before meat.
There is a mythology that accompanies the teaching of science, and the truth about one thing is often compromised for the purpose of making a point about another thing. One of the myths that I learned as a child was that long, long ago there was a wise man named Aristotle who asserted that heavier objects fall to earth faster than lighter ones. "It is obvious," he said, "how much more strongly a heavy object is pulled downward to the earth than a light object. Of course it will fall faster if released." And for hundreds of years, everyone believed him. Then along came our hero Galileo Galilei, who had the audacity to question Aristotle's authority, and actually carried out experiments to determine whether or not Aristotle was right. He dropped two balls of different weights from the Leaning Tower of Pisa, and they both hit the ground at the same time. The age of experimental science was born, hooray! Or so goes the myth. The version you learned in your youth may vary from mine. The moral of this story is that experimentation and the scientific method can uncover truth that armchair reasoning cannot. And a fine moral that is. But the conclusion of the story is that heavy objects fall to earth at the same rate as lighter ones. Period. And that is not entirely true, even though one is hard-pressed to find a science professional who will disagree in so many words. Part of the problem is that centuries ago, our theory of gravity surpassed in precision the limits of our ability to measure results in a laboratory environment. More on that subject will follow.
Isaac Newton gave us three laws of motion. One of them states that if you pull on something, you will be pulled in the opposite direction. This is why you lean away and dig your feet in when trying to drag something heavy on the end of a rope; otherwise you will end up tipping over as you pull. What this means for gravity is that as the Earth pulls downward on a ball, the ball pulls upward on the Earth. Furthermore, the heavier the ball and the Earth are, the more they will pull on each other. According to Newton, the force of gravity between the ball and the Earth is directly proportional to both the mass of the Earth and the mass of the ball.
Now to my point. Imagine two stones, one weighing 1 kilogram and the other weighing 10 kilograms. The lighter stone is raised up from the ground and the Earth pulls it down with a certain amount of force. When released, that force causes the stone to accelerate downward 9.8 meters per second faster and faster . . . per second. Got that? After one second, it falls 9.8 meters per second downward. After two seconds, 19.6 meters per second, and so on. The second stone is raised from the ground. It experiences a gravitational force that is ten times greater due to its mass being also ten times greater. But conversely, that greater force is acting on a greater mass, so it all balances out to a downward acceleration of 9.8 meters per second per second. Up to this point, Galileo is doing fine and things are not looking so good for Aristotle.
But look at the other side of the problem. The lighter stone is pulling the Earth upward just the tiniest bit, and when it is released, the Earth will be attracted upward, theoretically shortening the time it takes the stone to fall to earth. The heavier stone will pull the Earth upward ten times as much, and so the time it takes to fall to the Earth will theoretically be even shorter. Aristotle was not entirely wrong. If we follow this reasoning, then the two stones dropped together will in theory fall to earth at the same rate, but both of them would fall even faster than either of them would fall separately.
I say "in theory" because the difference is much too small to measure with the methods available to us. The upward acceleration of the Earth to meet the small stone is nearly nothing; and the ten-times-greater acceleration to meet the larger stone ‐ ten times nearly nothing ‐ is still nearly nothing. To measure this "nearly nothing," we would need equipment that could time the fall of the stone to an accuracy of dozens of decimal places. In the gravitational field of the Earth, the difference in mass between a sesame seed and a battleship is not very significant in determining the rate of fall of each. But there is an appreciable difference between the mass of the moon and the masses of man-made satellites. Whereas man-made satellites have no measurable effect as they circle the Earth, the moon pulls hard enough to make the Earth revolve in a measurable circle around the center of gravity (off-center but still within the Earth) that the Earth and moon define together.
If we were able to stop the moon in its orbit, weigh it, and then time its fall as we dropped it on the Earth, we would certainly have fewer science experts telling us that heavier objects fall no faster than lighter ones. But then there would be fewer of us left to hear them anyway.