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4. The Law of Universal Gravitation Gravitational Attraction of Spherical Bodies: A Uniform Sphere Weight of the Earth Newton's Law of Universal Gravitation Uniform Circular Motion and Gravitation > Newton's Law of Universal Gravitation Free to share, print, make copies and changes. Get yours at www.boundless.com www.www/boundless.com/physics?campaign_content=book_624_section_55&campaign_term=Physics&utm_campaign=powerpoint&utm_mediu m=direct&utm_source=boundless

5. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

6. Key terms center of mass The center of mass (COM) is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. gravitational force A very long-range, but relatively weak fundamental force of attraction that acts between all particles that have mass; believed to be mediated by gravitons. induction Use inductive reasoning to generalize and interpret results from applying Newton's Law of Gravitation. inverse Opposite in effect or nature or order. point mass A theoretical point with mass assigned to it. weight The force on an object due to the gravitational attraction between it and the Earth (or whatever astronomical object it is primarily influenced by). Free to share, print, make copies and changes. Get yours at www.boundless.com Uniform Circular Motion and Gravitation

7. Diagram used in the proof of the Shell Theorem This diagram outlines the geometry considered when proving The Shell Theorem. In particular, in this case a spherical shell of mass M (left side of figure) exerts a force on mass m (right side of the figure) outside of it. The surface area of a thin slice of the sphere is shown in color. (Note: The proof of the theorem is not presented here. Interested readers can explore further using the sources listed at the bottom of this article.) Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia Commons. "Shell-diag-1." CC BY-SA 2.5 https://commons.wikimedia.org/wiki/File:Shell-diag-1.png View on Boundless.comCC BY-SA 2.5https://commons.wikimedia.org/wiki/File:Shell-diag-1.pngView on Boundless.com Uniform Circular Motion and Gravitation

8. Gravitational Field of Earth Diagram of the gravitational field strength within the Earth. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. CC BY-SA http://upload.wikimedia.org/wikipedia/commons/4/43/Earth-G-force.png View on Boundless.comCC BY-SAhttp://upload.wikimedia.org/wikipedia/commons/4/43/Earth-G-force.pngView on Boundless.com Uniform Circular Motion and Gravitation

9. Newton's Law of Universal Gravitation A brief introduction to Newton's Law of Universal Gravitation for high school students. Free to share, print, make copies and changes. Get yours at www.boundless.com View on Boundless.com Uniform Circular Motion and Gravitation

10. Forces on two masses All masses are attracted to each other. The force is proportional to the masses and inversely proportional to the square of the distance. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Universal gravitation." GNU FDL http://en.wikipedia.org/wiki/Universal_gravitation View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Universal_gravitationView on Boundless.com Uniform Circular Motion and Gravitation

11. Free to share, print, make copies and changes. Get yours at www.boundless.com Uniform Circular Motion and Gravitation The Shell Theorem states that a spherically symmetric object affects other objects as if A) all of its mass were uniformly spread through the volume B) all of its mass were concentrated at its center C) it had zero mass D) it had infinite mass

12. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Uniform Circular Motion and Gravitation The Shell Theorem states that a spherically symmetric object affects other objects as if A) all of its mass were uniformly spread through the volume B) all of its mass were concentrated at its center C) it had zero mass D) it had infinite mass

13. Free to share, print, make copies and changes. Get yours at www.boundless.com Uniform Circular Motion and Gravitation When the bodies have spatial extent, gravitational force is calculated by A) assuming that all the mass is concentrated in the center B) summing the contributions of three largest point masses C) summing the contributions of point masses which constitute them D) assuming that the object has a zero volume

14. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Uniform Circular Motion and Gravitation When the bodies have spatial extent, gravitational force is calculated by A) assuming that all the mass is concentrated in the center B) summing the contributions of three largest point masses C) summing the contributions of point masses which constitute them D) assuming that the object has a zero volume

15. Attribution Wikipedia. "Newton's law of universal gravitation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitationCC BY-SA 3.0 http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation Wikipedia. "Shell theorem." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Shell_theoremCC BY-SA 3.0http://en.wikipedia.org/wiki/Shell_theorem Wikipedia. "Center of mass." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Center_of_massCC BY-SA 3.0http://en.wikipedia.org/wiki/Center_of_mass Light and Matter. CC BY http://lightandmatter.com/mef.pdfCC BYhttp://lightandmatter.com/mef.pdf Wikipedia. "center of mass." CC BY-SA 3.0 http://en.wikipedia.org/wiki/center%20of%20massCC BY-SA 3.0http://en.wikipedia.org/wiki/center%20of%20mass OpenStax CNX. "OpenStax College, College Physics. September 17, 2013." CC BY 3.0 http://cnx.org/content/m42073/latest/?collection=col11406/1.7CC BY 3.0 http://cnx.org/content/m42073/latest/?collection=col11406/1.7 Wikipedia. "Law of universal gravitation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Law_of_universal_gravitationCC BY-SA 3.0http://en.wikipedia.org/wiki/Law_of_universal_gravitation Wikipedia. "Gravitational constant." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Gravitational_constantCC BY-SA 3.0http://en.wikipedia.org/wiki/Gravitational_constant Wikipedia. "Law of universal gravitation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Law_of_universal_gravitationCC BY-SA 3.0http://en.wikipedia.org/wiki/Law_of_universal_gravitation Wiktionary. "point mass." CC BY-SA 3.0 http://en.wiktionary.org/wiki/point+massCC BY-SA 3.0http://en.wiktionary.org/wiki/point+mass Wiktionary. "gravitational force." CC BY-SA 3.0 http://en.wiktionary.org/wiki/gravitational+forceCC BY-SA 3.0http://en.wiktionary.org/wiki/gravitational+force Wiktionary. "weight." CC BY-SA 3.0 http://en.wiktionary.org/wiki/weightCC BY-SA 3.0http://en.wiktionary.org/wiki/weight Wiktionary. "inverse." CC BY-SA 3.0 http://en.wiktionary.org/wiki/inverseCC BY-SA 3.0http://en.wiktionary.org/wiki/inverse Wiktionary. "induction." CC BY-SA 3.0 http://en.wiktionary.org/wiki/inductionCC BY-SA 3.0http://en.wiktionary.org/wiki/induction MONTEREY BAY INSTITUTE. CC BY http://www.montereyinstitute.org/courses/Introductory%2520Physics%2520I/nroc%2520prototype%2520files/coursestartc.htmlCC BY http://www.montereyinstitute.org/courses/Introductory%2520Physics%2520I/nroc%2520prototype%2520files/coursestartc.html MONTEREY BAY INSTITUTE. CC BY http://www.montereyinstitute.org/courses/Introductory%2520Physics%2520I/nroc%2520prototype%2520files/coursestartc.htmlCC BY http://www.montereyinstitute.org/courses/Introductory%2520Physics%2520I/nroc%2520prototype%2520files/coursestartc.html WIKIPEDIA. "Isaac Newton." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Isaac_Newton#Apple_incidentCC BY-SA 3.0http://en.wikipedia.org/wiki/Isaac_Newton#Apple_incident Free to share, print, make copies and changes. Get yours at www.boundless.com Uniform Circular Motion and Gravitation

16. WIKIPEDIA. "Newton's law of universal gravitation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Newton%2527s_law_of_universal_gravitationCC BY-SA 3.0 http://en.wikipedia.org/wiki/Newton%2527s_law_of_universal_gravitation Free to share, print, make copies and changes. Get yours at www.boundless.com Uniform Circular Motion and Gravitation