A common question when you learn an equation in physics is “how is the value of one variable affected when a second variable is changed?” For example, “An astronaut has a weight of 200 N as she stands on the surface of a certain moon of Jupiter. How much would she weigh standing on a second moon that has three times the mass and twice the radius of the first moon?”

Many students find this a difficult problem to calculate, but it is actually something that you can solve quickly with just a bit of thought. The trick is to recognize that problems of this sort can be solved with a simple ratio. Let’s see how to solve the problem posed above. We will call the astronaut’s weight on the first moon F_{1} and on the second moon F_{2}. The masses of the two moons are M_{1} and M_{2} respectively and their radii are r_{1} and r_{2}. The mass of the astronaut is M_{A}. Then from the universal law of gravitation:

and

But we are told that the mass of the second moon is three times the mass of the first moon and its radius is twice the radius of the first moon. That means that M_{2 }= 3 M_{1} and r_{2 }= 2 r_{1}. We substitute these expressions into the equation for F_{2} above. This gives

Now divide this equation by the first equation and all the variables cancel out:

With some practice, you will find that you can do many of these problems in your head!