Topic 9: Universal Gravitation

Standard 8PC2.g. Students know the role of gravity in forming and maintaining the shapes of planets, stars, and the solar system.
Classroom discussion: Bring together two facts that the students either already know or can confirm for themselves: (1) Nothing accelerates unless it is acted on by a force. (They just learned this over the past several weeks.) (2) Everything falls faster and faster (accelerates downward) unless it is supported by something. Putting these two things together, it's clear that everything has a downward force exerted on it. That's not going to be a big surprise -- the students already know that there is such a force: they can feel it when they pick something up -- it's called the "weight" of the object. So far, so good. Now bring up another "fact": the moon doesn't move in a straight line at a constant speed, instead it travels around the earth. The student can't easily verify this, but with the help of a globe and a baseball and a flashlight you can show them how the orbital motion of the moon explains the phases of the moon. And anyway, they've heard this "fact" often enough that they probably believe it. So, if the m1on doesn't travel in a straight line at constant speed, in other words if it accelerates, it must be acted on by a force, just like the rock at the end of the string (week 7). Enter Newton: everything attracts everything else. Pretty clever! It explains why things fall and why the moon goes around the earth (and the earth and the other planets go around the sun) all at once. A really simple, if surprising, explanation for an incredible range of seemingly disconnected phenomena!

Note: it's not important, at this stage, to teach the kids the formula for gravity. That can come later.

Investigations: Students play around with a model in which every massive object attracts every other massive with a force proportional to the product of the two masses and inversely proportional to the square of the distance between them (strictly, between their centers of mass). Challenge: try to make a model of the earth-moon system in which the moon travels around the earth in a roughly circular orbit. Once you have that working, try to send a rocket from the earth to the moon with the least amount of fuel. The challenge could be to put the rocket into orbit around the moon or (harder!) to have it make a "soft" landing on the moon.
Extensions: Ask the students why, if everything attracts everything else, we don't notice the effect. Why, in other words, don't every day objects stick to each other like magnets?
Ask them to make a model consisting of two satellites orbiting the earth, attracted to the earth but not (appreciably) attracted to each other. Once they have that model running, challenge them to get the two satellites to rendezvous together by manipulating one of them. (The icons for this exercise might look roughly like the space shuttle and the international space station, to  lend verisimilitude.)
Suggested lab: Gravity is too small a force for the students to measure directly but ferromagnetisim is many orders of magnitude bigger. Can we set up a lab (e.g., with an instrumented torsion pendulum) in which 8th graders could measure the spatial dependence of the force between two bar magnets? (It wouldn't be exactly 1/R^2 but so what -- the point would be to show that the force falls off with increasing distance in a predictable way.)
Assessments: There are loads of things to assess here; here are some obvious examples. We keep track of how closely the student's model of the earth-moon system resembles the real thing (e.g., by reporting the eccentricity of the orbit and the changes to the orbital velocity that the kid makes to reduce it). We keep track of the mid-course corrections the kid makes in order to achieve lunar orbit or the soft landing objective. We have the kid describe in words what his strategy was in achieving either of these goals.