Weight: Gravitational forces

Prerequisites

From the time we were toddlers in a high chair dropping a spoon thirty times to irritate our parents, we learned that unsupported objects fall.  In our Newtonian framework, whenever we see an object changing its velocity we look for an interaction with some other object to cause that change. When things fall, it's not directly obvious that an interaction with some other object is responsible.  Indeed, for thousands of years it was assumed otherwise.

Without the Newtonian framework, there are other ways of interpreting the (apparently) universal fact that unsupported objects fall.  Aristotle simple said it was the natural state of all things to seek the central point of the universe: which he identified as the center of the earth. Interestingly enough, in Aristotle's view, the earth doesn't cause gravity. Gravity — the attraction of everything towards the center of the universe — causes the earth to be where it is. Most of the matter of the universe fell to the center, building up to create the earth.

The fundamental Newtonian principle — that objects act on each other to change each other's velocity — leads us to look for an object causing every velocity change.  So when we discover that on a round earth, objects on any side of it tend to accelerate toward the center, it's natural to assume that the earth is responsible for that attraction. Then we can begin to see that other objects might attract the earth and the earth might not be the center of the universe after all. This is logically sensible, but it is not the way it happened historically.  The Copernican revolution, placing the sun at the center of the universe, came before the Newtonian revolution of learning to see motion in a new, non-Aristotelian way. I suspect it really arose because Copernicus felt that the sun was more important than the earth, and that it would make more sense to put it at the center. Of course, we came to accept it because many other things then fell into place.

One of the difficult things for us to deal with conceptually is that ONLY the earth seems to "do" gravity. Newton showed that having the moon, sun, and planets also exert gravitational forces on each other also allowed us to make sense of the solar system, but it still seems strange for our everyday experiences. The way Newton made sense of this is to say that EVERYTHING exerts forces of gravity on each other (see Newton's Universal Gravitation), but the force is proportional to the product of the objects' masses AND it falls off like the square of the distance between the centers of the objects. Furthermore, gravity is an extremely weak force. According to modern measurements, it's forty orders of magnitude weaker than electricity.  (That's not a factor of 40, it's a factor of 1040!) Because it's such a weak force, the only time we can actually feel gravity as significant is when at least one of the objects is of planetary size. Particle physicists are fond of saying "gravity is such a weak force we can always ignore it." We can usually ignore it when we are doing cell biology, too. But animals on the scale of humans or larger ignore gravity at their peril!

In this class we will not be doing much planetary astronomy, so almost all of the examples we consider will be ones that can be done in a room over distances small compared to the radius of the earth. As a result, we will typically make the approximation that the gravitational force on an object — its weight — always points straight down and is independent of the object's position. This is the result we would get if the earth were flat, so we refer to this as the flat-earth gravity model. The distances we rise and fall in our everyday motions are typically small compared to our distance from the center of the earth (the earth's radius — about 6400 km) so we can ignore Newton's 1/r2 fall off of gravity.

Making sense of gravity is challenging since it's really one of our invisible forces — and we have to disentangle it from another invisible force, air resistance (drag). For a discussion of this, see the page, The effect of air resistance

Joe Redish 10/1/11

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Article 369
Last Modified: February 8, 2019