Computer requirements: Vensim, STELLA, IP physics, Excel or Internet access
Prior content covered: Newton's Laws of Motion
Estimated time for computer portion of lesson: 60 min

Essential Questions or Ideas to address:

• How does the mass of each object affect the gravitational force between them?
• How is the gravitational force affected by the distance between the masses?

The lesson: (90-min block)
Students work in the computer lab in groups of two to construct a model in Interactive Physics and/or Vensim/STELLA^TM which will illustrate the gravitational force.

In the Interactive Physics version of the lesson, students place two objects of large mass a small distance apart and watch them move toward each other. They measure the force at various distances of separation and graph the force vs. distance to determine the value of the universal gravitation constant.

In the Vensim/STELLA^TM version, they already know the constant and use it to create a model where they can easily manipulate the distances between the two masses as well as the size of the two masses. They can observe the graphs generated by the model. For companion activities, see the Universal Gravitation Activity Packet.

Common misconception addressed: Large objects pull smaller objects toward them.

Evaluation of lesson effectiveness: While the Interactive Physics model is easier for the students to build, setting up all the meters to take data takes some time. Also, masses and distances need to be chosen carefully to keep the objects on the screen and moving at a reasonable acceleration. Since the students are focused on “discovering” the constant through data collection and graphing, it is easy for the students and the instructor to forget to draw attention to the graphs generated and thus the common misconception.

The Vensim/STELLA^TM model is difficult to build, but once it is built, the students can easily change the masses and initial positions and observe a variety of situations in a short time. This application can easily be used to address the misconception.

Either model can be used later to explore the electrical force.

Alternate presentation: Present the students with pre-built models that they manipulate. A web version of the Vensim/STELLA^TM model is available at the Universal Gravitation WebSim.

Math topics: Direct and inverse proportions, graph interpretation

Extensions:

• The Vensim/STELLA^TM model has been modified to answer a variety of questions about the behavior of gravity. For some of these questions and the models, see Universal Gravitation Model Extensions.

• To modify the Interactive Physics model to illustrate orbits, give one of the objects a sufficient velocity tangent to the gravitational force.

Standards:

MSDE (from the website as of 9/05):

National Science Standards (9-12):

Physical Science: Motion and Forces:

Gravitation is a universal force that each mass exerts on any other mass. The strength of the gravitational attractive force between two masses is proportional to the masses and inversely proportional to the square of the distance between them.

AAAS Benchmarks (9-12):

The Physical Setting: Forces of Nature:

Gravitational force is an attraction between masses. The strength of the force is proportional to the masses and weakens rapidly with increasing distance between them.