The Gravitational Field Strength Concept Builder is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Concept Builder can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

Many Physics courses include a unit on Satellite Motion and Gravitation. Even those who don't often devote a small portion of the course discussing field forces such as the gravitational force. These forces are unique in terms of the dependency on distance between the two interacting objects. More recently there has been a renewed interest in the effort to understand the concept of a field surrounding both charged (electric field) and massive (gravitational field) objects. A massive object creates a gravitational field in the space that surrounds it, causing other masses that enter that space to interact with the field in such a manner as to be pulled towards the mass. The strength of this gravitational field at any given location is dependent upon the distance of that location from the center of mass and upon the amount of mass of the object creating the field.

Most physics courses spend considerable time using physics formulas to solve numerical word problems. Algebraic manipulation and substitution of known values into the formula is a typical activity. But we think that physics formulas are much more than recipes for solving problems for an unknown quantity. Physics formulas are tools to guide our thinking about how a variation in one quantity might affect another quantity in the formula. And that is what this activity is all about. Students think proportionally about the dependence of gravitational field strength (g) upon planet mass and the distance to the planet's center:

Most physics courses spend considerable time using physics formulas to solve numerical word problems. Algebraic manipulation and substitution of known values into the formula is a typical activity. But we think that physics formulas are much more than recipes for solving problems for an unknown quantity. Physics formulas are tools to guide our thinking about how a variation in one quantity might affect another quantity in the formula. And that is what this activity is all about. Students think proportionally about the dependence of gravitational field strength (g) upon planet mass and the distance to the planet's center:

In the process of completing this Concept Builder, students must ponder how an alteration in planet mass would effect the gravitational field strength. And they must ponder how an alteration in the distance between objects would effect the gravitational field strength. This task is much different than the algebraic manipulation of a formula and substitution of known values. This task will help students gain a better intuition for the relationship between g, the planet mass, and the distance.

This Concept Builder was intended as an in-class activity. After some discussion of gravitational field strength and proportional relationships, allow students an opportunity to interact with the questions. The Concept Builder includes three activities that include different types of thinking. Teachers using the Concept Builder with their classes should preview the Concept Builder (or view the Questions in the separate file) in order to judge which activities would be most appropriate for their students. There is no redundancy from one activity to another activity. That is, all the questions in the third activity are unique to that activity. And each activity stands alone; there is no need to do the first activity in order to do the second activity. Our summary of the three activities is as follows:

**Ranking Tasks**: Question Groups 1-6. Students are presented with three different locations having varying planet mass and distance and must rank the three locations according to their relative gravitational field strength.**Case Study: A vs. B**: Question Groups 7-12. Students are provided two locations with varying planet mass and distance and must determine which location has the greatest gravitational field strength and how many times greater it is.**The Value of g:**Question Groups 12-18. Students are provided the value of the gravitational field strength at one location and use the inverse square law to calculate the value at a second location.

In order to complete an activity, a student must correctly analyze each question in that activity. If a student's analysis is incorrect, then the student will have to correctly analyze the same or very similar question twice in order to successfully complete the level. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through an activity, a system of stars and other indicators are used to indicate progress on the level. A star is an indicator of correctly analyzing the question. Once a star is earned, that question is removed from the que of questions to be analyzed. Each situation is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly analyze it twice before earning a star. A yellow box is an indicator that the question must be correctly analyzed one time in order to earn a star. Once every question at a level has been analyzed, the student earns a medal which is displayed on the Main Menu. This system of stars and medals allows a teacher to easily check-off student progress or offer credit for completing assigned levels.

The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each question group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.

There are numerous resources at The Physics Classroom website that serve as very complementary supports for the Gravitational Field Strength Concept Builder. These include:

- Reading:

Most of Lesson 3 of the Circular and Satellite Motion Chapter of the Tutorial is a perfect accompaniment to this Concept Builder. The following pags will be particularly useful in the early stages of the learning cycle on Newton's Law of Universal Gravitation and Gravitational FIeld Strength. The Lesson includes the following five pages:

Gravity is More Than a Name

The Apple, the Moon, and the Inverse Square Law

Newton's Law of Universal Gravitation

Cavendish and the Value of g

The Value of g

- Minds On Physics Internet Modules:

The Minds On Physics Internet Modules include a collection of interactive questioning modules that help learners assess their understanding of physics concepts and solidify those understandings by answering questions that require higher-order thinking. Assignments CG6 and CG7 of the Circular Motion and Gravitation module provide great complements to this Concept Builder. They are best used in the middle to later stages of the learning cycle. Visit the Minds On Physics Internet Modules.

Users may find that the App version of Minds On Physics works best on their devices. The App Version can be found at the Minds On Physics the App section of our website. The Circular Motion and Gravitation module can be found on Part 2 of the six-part App series. Visit Minds On Physics the App.

- Physics Interactives: Our Physics Interactives section include interactive simulations that makes for a perfect pre-cursor to this Concept Builder. There are three in particulat that might make perfect supplements. The links are below.

Gravitational Fields

The Value of g

The Value of g on Other Planets

- Calculator Pad: For those teachers committed to the use of equations as tools for algebraic problem-solving, the section of our website that provides the best support is the Calculator Pad. There you will find a set of problems of varying difficulty and complexity on most topics of interest. Each problem is accompanied by an answer and an audio-guided help file. It's a great tool for students attempting to improve their problem-solving ability.

Visit the Circular Motion and Gravitation Problem Set at the Calculator Pad

- Curriculum/Practice: Several Concept Development think sheets at the Curriculum Corner will be very useful in assisting students in cultivating their understanding, most notably ...

Universal Gravitation

Inverse Square Law of Universal Gravitation

Visit the Curriculum Corner - Circular and Gravitation

Additional resources and ideas for incorporating Gravitational Field Strength into an instructional unit on Newton's Laws or Circular and Satellite Motion can be found at the Teacher Toolkits section of The Physics Classroom website. Visit Teacher Toolkits.