The Mulvey Method helps students see what happens how something like the force of gravity changes when other quantities change. It's great for questions where all the answers look like F, 2F, 4F, F/4, etc. It's named after Hillary Mulvey, Brown '14, who came up with this technique.
Let's try it on an easy relationship. If the kinetic energy of an object is doubled, what happens to its velocity? Start by writing the equation twice that describes the relationship you're studying, once under a column labeled NEW and once under a column labeled OLD. Then, under the OLD column, plug 1 in for everything, and I mean everything, that isn't the dependent variable in the situation. So your work should look like this:
Yes, even replace the 1/2 with a 1. You're looking for the ratio between quantities before the change and after the change, so we set all the quantities, including constants, equal to 1.
Then, it's time to figure out the values for the NEW column. The kinetic energy doubles, so it goes from 1 to 2. The 1/2 factor didn't change, it was "multiplied by 1", so it's a 1 in the next line, and, since the mass didn't change, it also was multiplied by 1. So that leaves me with:
Now you can solve for v to be the square root of 2, and so the velocity is multiplied by the square root of 2. Now this technique isn't the most mathematically rigorous, but I've found it can help students figure out what these types of questions are asking, and, over time, they start seeing the relationships without having to resort to the Mulvey Method. I also found that when I try to do it a more mathematically rigorous way at the beginning, my students get confused by all the variables, but when I show why the Mulvey Method works in March or April, it makes perfect sense.
We also got to play with PHeT's Solar System simulation, using a lab I think I've done since 1998 in some form or another, starting with Interactive Physics software on the old fruit-colored iMacs.