Q:
So Galileo couldn't figure out why objects fall at the same rate. What did Newton figure out to prove Galileo's theory?
- Layton M. (age 16)
Van, TX USA
A:

Newton obviously added a lot to Galileo's ideas about gravity but I don't think he added a proof of that particular observation. Here's what Newton added:

1. It's not just the Earth that makes all nearby things accelerate toward it. Every object has the same sort of effect.

2. The effect each object has falls off as the inverse of the square of the distance from the object.
(For a big spread-out object like the Earth, the effect is gotten by adding up effects from all the different parts, each at its own distance and own direction. Newton invented integral calculus to add the effects up.)

3, Here's where  Newton added more than just a more complete description but also a logical tie-in with more general ideas. His third law says that momentum is conserved. Momentum is the product of an object's velocity and something called its mass. If you say what the mass of one object is, you can figure out the mass of other objects by bouncing them off each other and seeing how much the different velocities change. Then you can check that the law actually works by using different pairs of objects and making sure you don't have to change what you say their masses are to get their momentum to still be conserved. What does that have to do with gravity? The basic property that Galileo found is the each object accelerates the same way, regardless of any of its properties, including M. That means the other object, the one that pulls on M, must accelerate toward it by an amount proportional to M. Otherwise, momentum wouldn't be conserved.  So the combination of Galileo's observation that gravity causes each thing to accelerate the same way and Newton's third law implies that the gravitational accelerations caused by something with mass M are proportional to M. This shows that the same mass that goes into an object's momentum and gives its inertia is also the source of gravity. That is a big deal.

Anyway, you can see that most of the content of the theory of gravity came from Newton, but the part about equal accelerations came straight from Galileo. Newton used it, he didn't prove it.

I suspect that if you ask this same question to other physics teachers you might sometimes get a different answer. Maybe they'll talk about "forces" and write out a force law. Sometimes that just amounts to multiplying the basic gravitational acceleration law by M, then dividing by M to get back to the observed acceleration. It doesn't add much. (What little is added by that procedure turns out, in the light of General Relativity, to be wrong. )

Mike W.

(published on 08/22/2013)