• 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)

• 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)

• 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)

• 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.

• 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.

• 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.

• 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.

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

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

• 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.

• 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.

• 9-12: Motions & Forces

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.

• Physical Sciences K-8 The Universal Law of Gravitation Unit
• Physics First The Universal Law of Gravitation Unit
• Conceptual Physics The Universal Law of Gravitation Unit
• Algebra-Based Physics The Universal Law of Gravitation Unit
• AP/Calculus-Based Physics The Universal Law of Gravitation Unit