# Chapter 9: Newton's Universal Law of Gravity

Difficulty Level:

**At Grade**Created by: CK-12Turn In

We know gravity as the force pulling downwards on everyday objects. The principles of gravity, however, apply on a much larger scale, and were discovered from study of the solar system. This chapter will cover Kepler's Laws of Planetary Motion, Newton's Universal Law of Gravity, and the mechanics of circular orbits.

Chapter Outline

### Chapter Summary

- Kepler’s Three Laws of Planetary Motion are:
- The orbital paths of the planets about the sun are ellipses with the sun at one focus.
- If an imaginary line is drawn from the sun to a planet as the planet orbits the sun, this line will sweep out equal areas in equal times. (A planet moves faster when it is closer to the sun and slower when it is farther away from the sun.)
- The square of the time
T2 for the orbital period of a planet about the sun is proportional to the cube of the average distancer3 between the sun and the planet. That is,T2∝r3 orT2=kr3 wherek equals4π2GM andM is the mass of the central body(T2=4π2Gmr3) . IfT is expressed in years andr in astronomical units thank=1 andT2=r3

**The Universal Law of Gravity**The forceF between two objects is directly proportional to the product of their masses,m1m2 , and inversely proportional to the square of the distance,r2 between their centers:F=Gm1m2r2 whereG is*the universal gravitational constant*equal toG=6.67×10−11N⋅m2kg2 .- The gravitational acceleration near a massive body of mass
m isg=Gmr2 wherem is the mass that creates the gravitational acceleration andr is the distance from the center of the planet to a point outside the planet. - The electrostatic force between two charged bodies is
F=kq1q2r2 .

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Covers Kepler's Laws of Planetary Motion, Newton's Universal Law of Gravity, and the mechanics of circular orbits.

Difficulty Level:

At Grade
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Date Created:

Jun 10, 2014
Last Modified:

Oct 20, 2016
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