Two weeks ago, students in some of our classes began reading the latest and greatest elementary-school-level introduction to the astrophysical objects popularly known as black holes: Carolyn DeCristofano’s wonderful A Black Hole Is NOT a Hole, a book that has managed a seemingly impossible feat: delighting clued-up reviewers like physicist and children’s space science author Marianne Dyson *and* garnering praise from readers (see, for example, ABHINaH‘s 3.88 score on Goodreads).

Early in the book, DeCristofano explains that the force of gravity between two objects is greater when the masses of one or both are greater and/or when they are closer together. That’s true, but we want our students to have a bit of a better handle on Newtonian gravity so we went a step further and introduced the equation for Newton’s law of universal gravitation, a prime example of what is known in science as an inverse-square law.

We enjoyed walking our classes through the effects, in terms of the “pull” of gravity, of dialing the masses of two objects up and down and changing the distance between their centers of mass. Since it can be described by an equation in which the value for distance lives in the denominator and is squared, halving the distance separating two things causes the force of gravity to increase fourfold. Likewise, doubling the distance between two things diminishes their mutual attraction to a quarter of its former strength.

We included a question in the next lesson’s quiz that challenged our students to demonstrate a qualitative understanding of Newtonian gravity. Some quiz-takers aced it (see the question and Ryan H.’s answer above) but others were stumped, so we’ve put together some additional exercises and will be revisiting the topic.