# In this chapter you will:  Learn the nature of gravitational force.  Relate Kepler’s laws of planetary motion to Newton's laws of motion.  Describe.

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In this chapter you will:  Learn the nature of gravitational force.  Relate Kepler’s laws of planetary motion to Newton's laws of motion.  Describe the orbits of planets and satellites using the law of universal gravitation.

Chapter 7 Sections Section 7.1: Planetary Motion and Gravitation Section 7.2: Using the Law of Universal Gravitation

SECTION 7.1 PLANETARY MOTION AND GRAVITATION Objectives Relate Kepler’s laws to the law of universal gravitation. Calculate orbital speeds and periods. Describe the importance of Cavendish’s experiment.

INTRODUCTION Nicholas Copernicus – a Polish astronomer, that observed the movements of the planets revolved around the Sun, his book was published in 1543. Tycho Brahe – a Dutch astronomer. At the age of 14 saw an eclipse of the sun and vowed to become an astronomer. He believed the moon and Sun revolved around Earth and all other planets revolve around the Sun.

KEPLER’S LAWS Johannes Kepler – a German astronomer. He was an assistant of Brahe. When Brahe died he inherited 30 years’ worth of observations and from this data he was able to develop 3 laws of planetary motion. He believed in a Sun centered universe. Kepler’s First Law – states that the paths of the planets are ellipses with the Sun at one focus. Comets are divided into 2 groups. Long Period Comets (Orbital Period over 200 years.) Short Period Comets (Orbital Period under 200 years. Halley’s) Kepler noticed that the planets move faster when they are closer to the sun and slower when they are farther away from the sun.

KEPLER’S LAWS Kepler’s Second Law – states that an imaginary line from the Sun to a planet sweeps out equal areas in equal time intervals. (Fig. 7.3) Kepler’s Third Law – states that the square ratio of the periods of any 2 planets is equal to the cube of the ratio of their average distances from the sun. (T A / T B ) 2 = (r A / r B ) 3 Table 7.1 p. 173 will be used throughout this chapter.

KEPLER’S LAWS Do Example Problem 1 p. 174 (T C / T I ) 2 = (r C / r I ) 3 (16.7 / 1.8) 2 = (r C / 4.2) 3 (9.28) 2 = r C 3 / 74.088 86.1184(74.088) = r C 3 6380.34 = r C 3 18.55 units = r C Do Practice Problems p. 174 # 1-5

NEWTON’S LAW OF UNIVERSAL GRAVITATION Sir Isaac Newton – started studying planetary motion in 1666. He found that the Force varies inversely with the square of the distance between the centers of the planet and the sun. Force (F) is proportional to 1 / r 2. Gravitational Force – the attractive force between 2 objects that is directly proportional to the mass of the objects.

NEWTON’S LAW OF UNIVERSAL GRAVITATION Newton’s Law of Universal Gravitation – states that objects attract other objects with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. The Gravitational Force is equal to the Universal Gravitational Constant, times the mass of object 1, times the mass of object 2 divided by the distance between the centers of the objects squared. F = G(m 1 m 2 ) r 2 Go over the Connecting Math to Physics Table at bottom of p. 175.

UNIVERSAL GRAVITATION AND KEPLER’s THIRD LAW Period of a Planet Orbiting the Sun – equals 2Π times the square root of the orbital radius cubed divided by the product of the universal gravitational constant and the mass of the Sun. ______________ T = 2Π √ (r 3 / (G * m s ) )

MEASURING THE UNIVERSAL GRAVITATIONAL CONSTANT Henry Cavendish – an Englishman that calculated the attractive force between 2 objects (G). He found the value for G by substituting into the Law of Universal Gravitation. His experiment is called “Weighing Earth” because it helped determine Earth’s mass. The value of G is 6.67 x 10 -11 Nm 2 /kg 2 if you use m 1 and m 2 measured in kg and r in meters and F in Newtons. Read through p. 178 and go over example. Do 7.1 Section Review p. 178 # 6-11

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