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Projectile and Satellite Motion

Projectile and Satellite Motion. 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. Parabola (approximately). Monkey in a Tree. Set to 48 minutes.

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Projectile and Satellite Motion

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  1. Projectile and Satellite Motion

  2. 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

  3. Parabola (approximately)

  4. Monkey in a Tree Set to 48 minutes

  5. 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 900. 450 gives the maximum range. Simulation

  6. 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

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

  8. 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).

  9. 5 miles 16 ft 16 ft Throw an object faster, faster, faster. Curvature of Earth We draw in each trajectory for 1 second

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

  11. Ellipses d1 d2 Focus Focus d1 + d2 = constant for any point on ellipse

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

  13. Eccentricity c a e = c/a

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

  15. The Search for Order • Perfect solids

  16. The Search for Order • Music of the Spheres

  17. Kepler’s Laws • Third Law • The orbital period of a planet squared is proportional to the length of the semi-major axis cubed. P2µ a3

  18. Using the Third Law P2µ a3 P2= (constant)a3 P2= a3 P measured in years, a in AU, object orbits Sun

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

  20. m M The Apple

  21. Moon F R Earth The Earth and Moon

  22. 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. Ellipse Parabola Hyperbola Circle

  23. Vescape = 7 mi/s = 11 km/s Vcircle = 5 mi/s = 8 km/s Ellipse Hyperbola Parabola Ellipse Ellipse - Circle Ellipse Ellipse

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

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