This resource features well-organized text explanations alongside algebraic equations and animations to help users form a better understanding of gravitational interactions. Multiple short problems and tables are employed to illustrate the universal nature of gravitational attraction. This item is part of Physics Classroom, a larger collection of tutorials for beginning high school physics students.

9-12: 4G/H1. 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.

10. Historical Perspectives

10B. Uniting the Heavens and Earth

9-12: 10B/H1. Isaac Newton, building on earlier descriptions of motion by Galileo, Kepler, and others, created a unified view of force and motion in which motion everywhere in the universe can be explained by the same few rules. Newton's system was based on the concepts of mass, force, and acceleration; his three laws of motion relating them; and a physical law stating that the force of gravity between any two objects in the universe depends only upon their masses and the distance between them.

9-12: 10B/H2. Newton's mathematical analysis of gravitational force and motion showed that planetary orbits had to be the very ellipses that Kepler had proposed two generations earlier.

11. Common Themes

11D. Scale

6-8: 11D/M3. Natural phenomena often involve sizes, durations, and speeds that are extremely small or extremely large. These phenomena may be difficult to appreciate because they involve magnitudes far outside human experience.

Next Generation Science Standards

Motion and Stability: Forces and Interactions (HS-PS2)

Students who demonstrate understanding can: (9-12)

Use mathematical representations of Newton's Law of Gravitation and Coulomb's Law to describe and predict the gravitational and electrostatic forces between objects. (HS-PS2-4)

Disciplinary Core Ideas (K-12)

Types of Interactions (PS2.B)

Newton's law of universal gravitation and Coulomb's law provide the mathematical models to describe and predict the effects of gravitational and electrostatic forces between distant objects. (9-12)

NGSS Science and Engineering Practices (K-12)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

Use mathematical representations of phenomena to describe explanations. (9-12)

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.2 Reason abstractly and quantitatively.

MP.7 Look for and make use of structure.

High School — Algebra (9-12)

Seeing Structure in Expressions (9-12)

A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

A-SSE.2 Use the structure of an expression to identify ways to rewrite it.

Creating Equations^{?} (9-12)

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

High School — Functions (9-12)

Linear, Quadratic, and Exponential Models^{?} (9-12)

F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Key Ideas and Details (6-12)

RST.9-10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

RST.11-12.2 Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms.

Range of Reading and Level of Text Complexity (6-12)

RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently.

NSES Content Standards

Con.B: Physical Science

9-12: Motions & Forces

This resource is part of a Physics Front Topical Unit.

Topic: Dynamics: Forces and Motion Unit Title: The Universal Law of Gravitation

This resource features well-organized text explanations alongside equations in a concept-building format for understanding gravitational interactions. Short problems and tables provide a concrete approach to helping learners grasp the universal nature of gravitational attraction so that formulas make sense.

<a href="http://www.compadre.org/precollege/items/detail.cfm?ID=4812">Henderson, Tom. Physics Classroom: Newton's Law of Universal Gravitation. December 12, 2004.</a>

Henderson, T. (2004, December 12). Physics Classroom: Newton's Law of Universal Gravitation. Retrieved October 22, 2014, from http://www.physicsclassroom.com/Class/circles/U6L3c.cfm

Henderson, Tom. Physics Classroom: Newton's Law of Universal Gravitation. December 12, 2004. http://www.physicsclassroom.com/Class/circles/U6L3c.cfm (accessed 22 October 2014).

%A Tom Henderson %T Physics Classroom: Newton's Law of Universal Gravitation %D December 12, 2004 %U http://www.physicsclassroom.com/Class/circles/U6L3c.cfm %O text/html

%0 Electronic Source %A Henderson, Tom %D December 12, 2004 %T Physics Classroom: Newton's Law of Universal Gravitation %V 2014 %N 22 October 2014 %8 December 12, 2004 %9 text/html %U http://www.physicsclassroom.com/Class/circles/U6L3c.cfm

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