Today, students learn about the dramatic impact that Sir Isaac Newton had on our way of thinking about the universe. Before Newton's universal law of gravity, Aristotle's widely-held model of the universe stated that there existed a set of laws that governed the behavior of objects on Earth and a separate set of laws that governed the motion of "heavenly" bodies. After students learn about how Newton's the universal nature of gravity challenged and eventually replaced this view, they learn and apply the mathematical form of the Law of Gravity.
This lesson is aligned with NGSS performance standard HS-PS2-4, where students use mathematical representations of Newton’s Law of Gravitation to describe and predict the gravitational forces between two objects. Students use CCSS Math Practice 2: Reason abstractly and quantitatively, Science Practice 5: Using mathematics and computational thinking and Science Practice 4: Analyzing and interpreting data as they apply Newton's law of gravity to understand the force of gravity on us from the sun or between small, nearby objects.
At the beginning of class, the I display today's objectives on the whiteboard, found in the Newtons Universal Law of Gravity power point. With a big smile on my face, I am very animated as I tell students about an exciting revelation they are about to have, but I don't tell them what it is yet. I keep it a mystery and try to work up the suspense. With the second slide, I justify what they are about to learn by stating: "There are moments in history where a single event changes the course of everything that follows! A moment where people look back and say that marks the time when everything changed." I provide examples such as the American Revolution, the creation of the atomic bomb, the 9/11 terrorist attack, the cure for cancer (this hasn't happened, but I challenge students to imagine how things change if or when it does). Each of these events mark a moment after which the world would never be the same.
The publication of Newton's Principia marks one of those moments: the future of human civilization was put on a different course. Before Newton, Aristotle's way of thinking dominated for thousands of years. His widely-believed model of the universe was that there was a set of laws that governed the behavior of objects on Earth and a separate set of laws that governed the behavior of "heavenly" bodies. Then Newton, in his desire to understand the behavior of nature, performed a thought experiment that is now called "Newton's Mountain". Newton’s thought experiment led him to realize that the force that pulls an apple to the ground is the same force that keeps the moon in its orbit. This is an idea that scientist still embrace today. We believe that the laws of nature here on Earth are the same on the moons of Jupiter, in the center of our sun and with a super nova exploding a billion light years away. The rules that we discover here in a laboratory apply EVERYWHERE in the universe!
I then display on the board the formula for Newton's Law of Gravity and I define the variables. I explain that the gravitational constant, called "big G", is simply a constant, like pi, that makes the equality true. It turns out that Newton's did not know the value of G and it was not determined until a generations later with a clever experiment performed by the brilliant scientist, Henry Cavendish.
For slide 10, the formula is simplified by temporarily excluding "big G". I have students make a table in their notebooks and plug in a series of values for the masses and distance. The purpose here is to develop their mathematical thinking as they explore what happens if one of the masses is doubled or the distance between them is changed.
Then the students practice a series of gravity calculations such as the force of gravity between two people, the force of gravity between them and the Earth (gives the same result as F=mg), and if they are heavier at midnight verses noontime because the sun is pulling them down into the Earth rather than being overhead. With each problem, I expect students to write the problem in their notebook and calculate the answer. The problems are shown and after a few minutes, I reveal the answers so that students can check their work.
Now that students have practiced applying the gravity formula for a few situations, we switch focus to the inverse-square law as students graph force versus distance.
Once the lecture is over, I hand out to students the Force vs Distance Plot (original MS-Excel format if wanted; Force vs Distance Plot) and I ask them to complete it right away. The purpose of this sheet is to reinforce the concept of how dramatically forces change with distance. This is the students first exposure to the inverse square law, but it won't be their last, so it is beneficial for them to plot it out.
Once the students finish the graph they bring it to me and I check it. I ask for their observations and again reinforce this concept of how much force decreases with small changes in distance. Then I give them the Gravity and Circular Motion - Questions worksheet where they have a series of problems to complete. Students are expected to complete their own sheets and show all their work. However, while they are in class, they can collaborate and help each other or ask me questions. Any problems not finished in class are to be completed for homework. Here is the Gravity and Circular Motion - Solutions to be reviewed in the next day's class.
I close the class with a review. I call on random students to define the variables in the equation and to explain the meaning and possible applications of Newton's Universal Law of Gravity. I also ask students to explain why Newton's Universal Law of Gravity is called an inverse square law and project a Gravity Graph Exemplar with a document camera.