The Gravity of the Situation

Friday was my last day doing astronomy with the 3-4 graders at Peregrine School. The one standard I hadn't yet covered was gravity, so we did gravity before the break (this post) and after the break we discussed nuclear fusion in the Sun's core (next post).

I reviewed some ideas about motion we had discussed last year.  If you roll a marble, you expect it to go in a straight line unless something (another kid, perhaps, or a wall) interferes by pushing (exerting a force) on the marble. That's Newton's first law of motion. I then put a donut on a string and spun the donut in a circle over my head.   What will happen if the string is cut? Will the donut continue in a circle, fly off in a straight line, or fly off in a curve? We took a vote. I always clarify that the question is about what happens immediately, not about what happens eventually, like the donut falling due to the gravity in the room. This means that when we do the experiment, they have to really pay attention!

In reality I don't cut the string, but the string pulls through the soft donut, and it flies off in a straight line---Newton's first law again.  This is a pretty vivid demonstration that the Moon wouldn't keep going  around the Earth, nor the planets around the Sun, unless there was a force keeping them from flying off in a straight line.  Kids this age already know that we call that force gravity, but gravity is also the force that makes things fall when I drop them.  Why do we call these two forces by the same name?

I also have a tennis ball on a string so I can demonstrate circular motion as much as needed.  I do this and ask the kids what direction the force must be in.  It must be towards the center of the circle, where my fist is holding the string.  That's clear because the only direction a string can exert a force is pulling along the string! So whatever force is pulling on the Moon, it must be pointed toward the center of the Earth.  And that's exactly what we observe about gravity on Earth! (It helps to draw an Earth and how the arrow of gravity points in your location vs in, say, Australia.)  So it's quite plausible that these two forces are really the same force.

To bolster the argument that these are the same force, we should look not just at the direction, but also the strength.  I had the kids whirl the tennis ball on a string at various speeds, and feel whether the higher speed requires more force, less force, or the same force (the answer is more).  So let's look at the planets' speeds around the Sun and see if we can relate that to the force of gravity.  I asked the kids for suggestions as to what would affect the planet speed.  The two main suggestions were planet size, and planet distance from the Sun.  It would have been great to investigate both of these possibilities, but we were running short on time so we just did planet distance from the Sun.  I had the kids make graphs of planet speed vs planet distance from the Sun.  We took our time doing this right, figuring out how to draw the axes with reasonable scales, and adding planets one by one, starting with the most familiar ones.

A pattern did emerge: more distant planets are slower, as the graph below shows.

By our tennis ball experiment, slower circular motion implies a weaker pull (less acceleration). Therefore this graph implies that more distant planets feel a weaker pull, and planets closer to the Sun feel a stronger pull.  Does this make sense if the Sun's gravity is what keeps the planets from flying off in straight-line paths?  The kids agreed that it did.

[If we had also made the graph of speed vs planet size, we would not have seen such a clear pattern.  It happens that the outer planets tend to be bigger, so that there would be a tendency for bigger planets to be slower, but it would only be a tendency, not a law, because the biggest planet happens to be the nearest (fastest) of the outer four.  And the pattern would really be broken if we also included Pluto, which is a very distant (hence very slow), small object, providing a counterexample to the fast inner planets which happen to be small and which therefore might give someone the false impression that small means fast.]

I liked this 40-minute activity and I think it worked well.  I did simplify some details to avoid getting bogged down (eg the distinction between force and acceleration), but I think it was appropriate for 3-4 graders who wanted to focus on astronomy rather than physics. We also got in some more practice with graphs, which is important.  And we learned something which in Newton's time was revolutionary: the same laws of physics which we can deduce here on Earth also apply to objects in the sky.   This was one of the most wonderful discoveries in the history of science, and it's what allows us to understand the universe.