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05 October 2010

Universal Gravitation -- instructions and strategy

It's time to discuss universal gravitation.  Since quantitative demonstrations won't work here -- what, you want to hook a spring scale to the moon to verify the force the earth is exerting on it? -- I make some calculations with interesting results.

First, I calculate the gravitational field g, and show that g is still the same value at the top of Mount Everest. 

Next, I calculate the force of the earth on the moon using universal gravitation.  We get 1017 N.  As a check on that calculation, I use circular motion (which we have just finished covering):  I find the centripetal force required to keep the moon in its orbit.  We get the same answer... and then we discuss how the combination of circular motion and universal gravitation allows calculation of all sorts of astronomical quantities. 

A quiz a few days in asks to find the mass of the Milky Way galaxy, given the sun's orbital period around the center, assuming a two-body problem and circular motion. This calculation gives an accurate result, despite the crazy assumptions.

Throughout the unit I am modeling ORDER OF MAGNITUDE ESTIMATION.  I don't ever pound the calculator, and students are forbidden from having calculators on their desks.  Instead, I just write every calculation in scientific notation in standard units.  From that, I cancel powers of ten in my head, and write the answer to zero or one significant figures.  And, we check the reasonability of all answers where possible by direct comparison to known quantitites -- for example, if we calculate the mass of a star, we compare that to the mass of the sun.

Below are the instructions I write out on my problem sets for universal gravitation.  I follow through on my demands, too -- a problem without an order-of-magnitude estimate written out loses at least 3 out of 10 points.  The nebulous and meaningless statement "that's a really huge mass" rather than "that's 1/10 the mass of the sun, so reasonable for a star" loses 3 of 10 points. 

Topics to be discussed: Newton’s law of universal gravitation. I find that, amazingly, the biggest trouble that students have when solving universal gravitation problems is plugging correctly into their calculators. To be sure you don’t screw up, follow this advice:

• Solve in variables as far as possible in each problem. Only plug in values at the end.

• Do an order of magnitude estimate of your answer without the calculator, to be sure you’re not way, way off.

• Check the reasonability of the answer. When you’re asked to make a comparison, do this right – don’t just say “that’s a big mass”, say “that’s twice the mass of the earth” or “that’s close to the mass of the sun”. Astronomical data is easily available online, and there are astronomical tables in all physics texts.

• I will be looking at comparisons VERY CAREFULLY on gravitation problems. Do these right.

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