2. Projectile and Satellite Motion

3. PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal motion at a constant speed.   Forces are at work in only the vertical motion

4. Parabola (approximately)

5. Monkey in a Tree Set to 48 minutes

6. For a particular range less than the maximum and for a particular launch velocity, two different launch angles will give that range. The two angles add to give 90 0. 45 0 gives the maximum range. Simulation

7. Free Fall Results Horizontal motion is constant   No force is acting Vertical Motion is accelerated   Gravity acts in this direction Rise time = Fall Time Final speed = Initial speed

8. Actual path and ideal path (free fall) are different.

9. FAST-MOVING PROJECTILES - SATELLITES Let’s throw stones horizontally with ever increasing velocity. The Earth’s curvature is 16 ft for every 5 miles (4.9 m for 8 km).

10. 16 ft Curvature of Earth 5 miles Throw an objectfaster,faster.faster, We draw in each trajectory for 1 second

11. Kepler’s Laws First Law First Law   Planets orbit the Sun in ellipses with the Sun at one focus of the ellipse Sun Planet

12. Ellipses Focus d1d1 d2d2 d 1 + d 2 = constant for any point on ellipse

13. Ellipses b a a = Semi-major axis b = Semi-minor axis

14. Eccentricity a c e = c/a

16. Kepler’s Laws Second Law   A line drawn from the planet to the Sun sweeps out equal areas in equal intervals of time

17. The Search for Order Perfect solids

18. The Search for Order Music of the Spheres

19. Kepler’s Laws Third Law   The orbital period of a planet squared is proportional to the length of the semi-major axis cubed. P 2  a 3

20. Using the Third Law P 2  a 3 P 2  constant  a 3 P 2  a 3 P measured in years, a in AU, object orbits Sun

21. Kepler’s Laws Empirical Kepler could not explain why the planets orbited the Sun (he thought it had something to do with magnetism) Universal

22. The Apple m M

23. The Earth and Moon F Earth Moon R

24. The free-fall motion of a projectile near the surface of the earth is very nearly parabolic. A parabola is one of the conic sections. Circle EllipseParabolaHyperbola

25. Ellipse Ellipse - Circle Ellipse Parabola V circle = 5 mi/s = 8 km/s V escape = 7 mi/s = 11 km/s Hyperbola

26. Orbiting Falling without getting closer to the ground. Force of Gravity = Centripetal Force