Universal Gravitation

1. Universal Gravitation Newton’s Law of Universal Gravitation Cavendish and the value of G Kepler’s Laws

2. A. Newton’s Law of Universal Gravitation • “What goes up, must come down” • Force of Gravity • Force which exists between the earth and the objects which are near it • Fgrav • Acceleration of Gravity • Acceleration of an object when the only force acting upon it is the force of gravity • g = 9.8 m/s2

3. A. Newton’s Law of Universal Gravitation • Isaac Newton • Compared the acceleration of the moon to the acceleration of objects on earth • Concluded that the force of gravitational attraction between the earth and other objects is inversely proportional to the distance separating the earth’s center from the objects center • Force also depends on the mass of the earth

4. A. Newton’s Law of Universal Gravitation • The force of gravity acting between the earth and any other object is: • Directly proportional to the mass of the earth • Directly proportional to the mass of the object • Inversely proportional to the square of the distance which separates the centers of the earth and the object

5. A. Newton’s Law of Universal Gravitation • Gravitation is Universal!

6. A. Newton’s Law of Universal Gravitation • What happens if the mass of an object is doubled? • Gravitational force is doubled • As distance increases what happens to the gravitational force? • Decreases

7. A. Newton’s Law of Universal Gravitation • Universal Gravitational Equation

8. A. Newton’s Law of Universal Gravitation • Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.37 x 106 m from earth's center.

9. A. Newton’s Law of Universal Gravitation

10. A. Newton’s Law of Universal Gravitation • Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above earth's surface. This would place the student a distance of 6.38 x 106 m from earth's center.

11. A. Newton’s Law of Universal Gravitation

13. B. Cavendish and the Value of G • Lord Henry Cavendish experimentally determined the value of G using a torsion balance • Torsion Balance • 6 ft long – light rigid rod • Two metal spheres were attached to each end • Rod was suspended by wire

14. B. Cavendish and the Value of G • Determined the relationship between the angle of rotation and the amount of tensional force

15. B. Cavendish and the Value of G • Large spheres exerted a gravitational force upon the smaller spheres and twisted the rod

16. B. Cavendish and the Value of G • Once the torsional force balanced the gravitational force, the rod a spheres came to rest and Cavendish was able to determine the gravitational force of attraction between the masses and calculate G

17. B. Cavendish and the Value of G • Suppose that you have a mass of 70 kg (equivalent to a 154-pound person). How much mass would another object have to have in order for your body and the object to attract each other with a force of 1-Newton when separated by 10 meters?

18. B. Cavendish and the Value of G • Suppose that you have a mass of 70 kg (equivalent to a 154-pound person). How much mass would another object have to have in order for your body and the object to attract each other with a force of 1-Newton when separated by 10 meters? • 2.14 x 1010 kg

19. C. Kepler’s Laws • Johannes Kepler • German mathematician and astronomer • 1600’s • Analyzed astronomical data • Developed three laws to describe motion of the planets around the sun

20. C. Kepler’s Laws • Kepler’s First Law • Law of Ellipses • The path of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus

21. C. Kepler’s LawsFirst Law

22. C. Kepler’s Laws • Kepler’s Second Law • Law of Equal Areas • An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time

23. C. Kepler’s LawsSecond Law

24. C. Kepler’s Laws • Kepler’s Third Law • The Law of Harmonies • The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun.

25. C. Kepler’s LawsThird Law

26. C. Kepler’s LawsThird Law • Galileo discovered four moons of Jupiter. One moon - Io - which he measured to be 4.2 units from the center of Jupiter and had an orbital period of 1.8 days. Galileo measured the radius of Ganymede to be 10.7 units from the center of Jupiter. Use Kepler's third law to predict the orbital period of Ganymede.

27. C. Kepler’s LawsThird Law • Galileo discovered four moons of Jupiter. One moon - Io - which he measured to be 4.2 units from the center of Jupiter and had an orbital period of 1.8 days. Galileo measured the radius of Ganymede to be 10.7 units from the center of Jupiter. Use Kepler's third law to predict the orbital period of Ganymede. • T = 7.32 days

28. C. Kepler’s LawsThird Law • If a small planet were located eight times as far from the sun as the Earth's distance from the sun (1.5 x 1011 m), how many years would it take the planet to orbit the sun. GIVEN: T2/R3 = 2.97 x 10-19 s2/m3

29. C. Kepler’s LawsThird Law • If a small planet were located eight times as far from the sun as the Earth's distance from the sun (1.5 x 1011 m), how many years would it take the planet to orbit the sun. GIVEN: T2/R3 = 2.97 x 10-19 s2/m3 • Tplanet = 22.6 years

30. C. Kepler’s LawsThird Law • On average, the planet Mars is 1.52 times further from the sun as is Earth. Given that the Earth orbits the sun in approximately 365 earth days, predict the time required for Mars to orbit the sun.

31. C. Kepler’s LawsThird Law • On average, the planet Mars is 1.52 times further from the sun as is Earth. Given that the Earth orbits the sun in approximately 365 earth days, predict the time required for Mars to orbit the sun. • 684 days