Why Do All Objects Fall at the Same Rate?

Gravity causes an object to accelerate. Near the Earth, objects accelerate towards the center of the Earth. (The ground, of course, stops them.) The magnitude of this acceleration can be determined from the equation g = (Gm)/r² , which says the acceleration, g, is equal to G (which is a universal constant) times m, the mass of the Earth, divided by r squared, where r is the distance between the object and the Earth's center. For objects near the Earth's surface, r is approximately the radius of the Earth. Regardless of one's location on Earth, G and m do not vary, and r varies very little. We can therefore say that this acceleration due to gravity is about 9.81 meters per second squared anywhere on Earth. (The units indicate that the accelerating object increases its speed by 9.81 meters per second each second; starting from rest, an object speeds up to 9.81 m/s after one second, finds itself at 19.62 m/s after two seconds, 29.43 m/s after three seconds, etc.)

We have just defined the acceleration of an object due to gravity. The force of gravity on an object is a little different. Remember the famous Newtonian equation, F=ma. This tells us that the force (F) on an object (i.e. the strength of the push or pull) is equal to the object's mass (m) times its acceleration (a). Therefore, the force of gravity on an object is equal to 9.81 m/s² times the mass (m) of the object. Force is proportional to mass. This tells us that the force of gravity on a very massive object will be greater than the force of gravity on a light object. In other words, if I were to drop both a bowling bowl and a ping-pong ball from the balcony of my apartment, the pull of gravity would be stronger on the more massive bowling ball. So why doesn't it hit the ground first?

The answer entails the concept of inertia, so let me define it. Inertia is the tendency of a body to maintain its state of rest or of uniform motion in a straight line. All objects are subject to inertia. This means that an object, traveling through space at 10 m/s, will not speed up or slow down but will continue traveling forever, in a straight line, at that 10 m/s, given that nothing pushes or pulls on it. (Also, an object at rest won't spontaneously start moving unless something pushes or pulls on it.) This isn't obvious when observing objects moving about on Earth, because there is almost always some pushing or pulling on these objects. Usually some form of friction or drag. We slide a book across a table and it comes to a stop. Friction stops it. We can get a sense for unadulterated inertia, though, when we observe an ice skater gliding across a frozen pond (better yet if the ice is just starting to melt). There is little friction between the skates and ice, and, given one little push, the skater will travel a very long time before slowing down. If there was absolutely no friction, and no air resistance, she would maintain her speed forever, or until she hit an obstacle or reached the edge of the pond. She wouldn't need someone constantly pushing her to keep her moving. Inertia is one of the most important ideas in the laws of the mechanical universe.

So what does inertia have to do with falling objects and gravity? Falling objects, like all objects, are subject to inertia. When you hold a ball over your balcony railing and release it, it begins at rest. And because of inertia, it wants to stay at rest. It doesn't want to move downwards. When gravity begins pulling on it, it fights back. It resists acceleration. And that resistance is proportional to the mass of the object. Heavy object, large resistance. Light object, small resistance. This should make sense. Isn't it much harder to push a car (in neutral) and get it up to a speed of 10 mph than to do the same with a bicycle. The car, being much more massive, fights the acceleration you are trying to give it much more than the light bicycle does.

Perhaps now you can begin to see why all objects fall at the same rate. A falling object is subject to not only the force of gravity (which accelerates an object towards the ground), but the opposing resistance-to-acceleration that comes about because of inertia. These two battle it out. A bowling ball wants to fall faster than a ping pong ball, because gravity is pulling on it harder, but its larger mass gives it more inertia and slows it down. The ping pong ball is not being pulled downwards as hard as the bowling ball, but the ping pong ball, light as it is, offers little resistance to the downward acceleration. For all objects, the downwards acceleration and the resistance to that acceleration happen to balance in such a way that the objects, regardless of mass, fall at the same steady 9.81 m/s².

P.S. I'll also mention that a falling object exerts a gravitational force (or pull) on the Earth. While the object (say, a ball) is falling, its pulling on the Earth with the same force that the Earth is pulling on it. However, because the Earth is so massive (i.e. it has so much mass) relative to the falling object, it barely moves. You could calculate the Earth's acceleration towards the falling object by using the equation F=ma. The ball is being pulled towards the center of the Earth with a force of, say, 50 [units]. The Earth, likewise, is being pulled towards the ball with a force of 50. However, given a fixed F (or force), and using the equation F=ma, if m (or mass) is HUGE, then a (or acceleration) must be tiny. The mass of the Earth is indeed huge, so its acceleration towards any of a million balls being thrown about near its surface is miniscule, undetectable.