The Newtonian Synthesis

2. Week of 11/ 06 /2006 The Newtonian Synthesis • Nicolaus Copernicus 1473 – 1543 • Frame of Reference • Tycho Brahe 1546- 1601 • Accurate Data • Johannes Kepler 1571-1630 • Emperical Laws • Isaac Newton 1642 – 1727 • Universal Law

3. Kepler’s Laws of Planetary Motion • Law of Ellipses • Each planet orbits the sun on an elliptical path with the sun at one focus. • Law of Equal Areas • The radius vector drawn from the sun to each planet sweeps out equal areas during equal time intervals. • Harmonic Law • The period of a planetary orbit is directly proportiopnal to the cube of its semimajor axis.

4. Newton’s Universal Law of Gravitation • Every body in the universe attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of their separation F = G M1M2 r2

5. F = Gravitational Force (N) m1 = Mass of body 1 (kg) m2 = Mass of a body 2 (kg) G =Universal Gravitational Constant d = Distance between the centers of the objects (m)

6. 60 kgKatie and 80 kg Evan are sitting at opposite ends of the Physics classroom 6 meters apart. • Find the gravitational force that one exerts on the other. • Who is attracted to the other more? Physics F = ma

7. The Force is: Directly proportional to the product of the masses. Inversely proportional to the square of the distance More Mass More Force More distance much Less Force

8. Hyperbolic

9. Intensity of force diminishes as 1/d2

10. Forces are equal in magnitude and opposite in direction FAE FEA Earth pulls apple down and apple pulls earth up

11. Find the Gravitational force of attraction between the following Where

12. Two objects attract each other with a force of 16 N, what • is the new force if: • The distance is doubled? • The distance is tripled • The distance is quadrupled • The distance is reduced in half • The mass of one is doubled • The mass of both is doubled • The mass of one is halved • The mass of both is halved • The mass of both is tripled • One mass is doubled the other halved

13. Tougher Ones: • The mass of both is doubled, and the distance is doubled • The mass of both is tripled, and if the distance is doubled • The mass of one is doubled, and if the distance is tripled

14. Our solar system is in the Milky Way galaxy. The nearest galaxy is Andromeda, 2 x 1022 m away. The masses of the Milky Way and Andromeda galaxies are 7 x 1011 and 6 x 1011 kg respectively. Find the magnitude of the gravitational force exerted on the Milky Way by the Andromeda galaxy.

15. Using an apple to weigh the earth! The gravitational force on an apple: G = Universal gravity constant = 6.67 x 10 -11 N m2 / kg2 M = mass of earth = (?) R = radius of earth = 6.4 x 10 6 m

16. Weighing the Earth Solve equation for M • To find the Mass of a planet, you have to know: • “g” on the planet • Radius of planet

17. Conversely: Finding “g” • To find the acceleration due to gravity on a planet in the above • equation you have to know: • Mass of planet • Radius of planet

18. Earth’s Gravitational field diminishes as 1/r2

19. Summary: The forces are equal in magnitude and opposite in direction

21. The gravitational force due to the Earth on a 1 kg mass at one • Earth radius above the surface of the Earth is equal to_______ • the force on the same mass on the surface of the Earth. • 1/2 of • 1/4 of • 1/8 of • 1/16 of