Newton's Law of Universal Gravitation
Activity on the dataset Gravity Force PhET Lab Sim
Students use graphical representations of relationships within Newton’s Universal Law of Gravitation to evaluate and derive the meaning of the constants they find.
Learning objectives: Essential understanding or skill: Students use mathematical representations of Newton’s Law of Gravitation to describe and predict the gravitational force of attraction between objects. (NGSS HS-PS2-4) Other information for teachers: Students need to have the algebra skills to rearrange or solve the equation for different variables and understand units associated with the slope of a line. For reference, the value of constant G, adjusted for the units used in this dataset, is 66.7 N m^2^/kg^2^. The formula for the New Attribute in the optional Step 6 should look something like this: "<Force of Attraction (N)> * <Distance (km)>^2 / <Mass 1 (billion kg)> * <Mass 2 (billion kg)>" Students will: Make a scatter plot with least squares line fit of mass vs force for modeled experiments changing Mass 1 and Mass 2. Identify the meaning of the slope of the linear relationship between mass and force. Fit an inverse square function to the relationship between distance and force. Derive meaning of the constant in the inverse square equation fit. Consider limitations of the modeled data by evaluating the spread of the value of G calculated from all of the simulation data.
After Johannes Kepler published his laws of planetary motion, Isaac Newton developed the idea that those laws must also apply to all objects on Earth. In 1687, Newton published his Philosophiæ Naturalis Principia Mathematica with mathematical analysis and the relationship: ![]320:l The measurements of Henry Cavendish (pub. 1798) later led to determination of the proportionality constant, G. The more familiar version of the equation looks like: ![]280:l In this activity, you will graph data pulled from the PhET Gravity Force Basics simulation to visualize and model the relationships between masses, distance, and force of attraction. Using the law's equation and some algebra skills, you will work to make sense of the constants found through line and function fits of the modeled data. Click Next to get started!
Topics and standards: Science, Physical Science, Forces & Motion, Grades 9-12, HSS-ID-C-7, HSS-ID-B-6-C, HS-PS2-4, Guided, Forces, TEKS Science PHY.5.B, TEKS Science PHY.5.H, TEKS Science PHY.6.A, TEKS Science PHY.6.C, TEKS Science IPC.5.D, TEKS Science IPC.5.E, PHYS1-PS2-9, 3.2.9-12.L