2. SUMMARY Kepler’s 3 laws (pages 3-4-5) Illustration of Kepler’s laws (page 6) Newton’s law of universal gravitation (pages 7-8)Newton’s law of universal gravitation (pages 7-8) Illustration of Newton’s law (page 9) Exercises (pages 11-12-13) Conclusion (page 14)

3. Kepler’s firt law: an orbiting body travels in an elliptical path around a central, massive body, wich is located at one of the ellipse’s foci.

4. Kepler’s second law: If a line is drawn between the central massive body and the orbiting satellite, area is swept out by the line at a costant rate.

5. Kepler’s third law: the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. where P is the orbital period of the planet and a is the semi-major axis of the orbit. The constant of proportionality is: P²/a³=K

6. Video: Illustration of Kepler’s laws

7. Newton’s law of universal gravitation: Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

8. where: F is the force between the masses, G is the gravitational constant, m 1 is the first mass, m 2 is the second mass, and r is the distance between the centers of the masses.

9. Video: Illustration of Newton’s law of universal gravitation

10. Now let’s have some practice! Turn the page for some exercises!

11. Exercise n.1 The planet trajectory around the Sun is described by: 1)a circumferencea circumference 2)an hyperbolean hyperbole 3)an epicyclean epicycle 4)an ellipsean ellipse

12. Exercise n.2 Calculate the force of attraction between the earth and the sun knowing that the mass of the Sun Ms = 1,98 · 10³⁰ kg, the mass of the Earth Me = 5,98 · 10²⁴ kg, and the average radius of the Earth orbit r = 1,50 · 10¹¹ m. [3,51 · 10²² N]

13. Exercise n.3 Calculate the force of attraction between two boys who weigh 60 kg at the distance of 1 m. [2,4 · 10¯⁷ N]

14. Thanks for watching! Brunetti P. Cipriano D. Siciliano M.

15. WRONG! 

16. RIGHT! 