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The relationship between projectile motion and satellite motion, focusing on the concept of parabolic trajectories and kepler's laws of planetary motion. Students will learn about the differences between projectiles that fall to the ground and satellites that remain in orbit, as well as the significance of energy conservation in determining escape speed. The document also covers the curvature of earth and the impact of launch velocity on the shape of an orbit.
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Projectile and Satellite Motion PH 104 w/ dr. g Lec 11
Satellite = projectile in free‐fall
Snapshots of a Trajectory: every 0.1 seconds
Snapshots of a Trajectory: every 0.1 seconds
y Trajectory is always a PARABOLA y Velocity has two components : horizontal & vertical y Horizontal : constant: equal distance per unit time y Vertical : free-fall (gains 9.8 m/s per sec down ) : distance gets larger and larger y Components DO NOT AFFECT EACH OTHER! y Result : a parabolic trajectory! y Horizontally launched: half a parabola y Any launch angle: more or less than half
Satellite = projectile in free‐fall
y Trajectory is always a PARABOLA y Result : a parabolic trajectory! y Horizontally launched: half a parabola y Any launch angle: more or less than half
Satellite = projectile in free‐fall
y Kepler’s observations : Laws of Planetary Motion y 1st Law: Planetary orbit is ELLIPSE , Sun at one focus y Planet’s closest approach to sun = perigee y Planet’s farthest distance from sun = apogee
y 2 nd^ & 3 rd^ Laws: Planet moves faster when closer to Sun y 3rd Law: farther orbit takes longer for one period
Satellite = projectile in free‐fall
Johannes KeplerJohannesKepler 15711571 –– 1630 1630 Isaac Newton 1642-
D’oh! Gravity?? Of course!
Just gravity, son.
y PE + KE = constant y Projectile on Earth: PE increases with height, KE decreases y Planet around Sun: PE increases with distance, KE decreases y Escape speed = threshold speed for “breaking orbit” y PE: increases with distance (altitude): less and less y At certain distance, no more increase y KE needed to reach this distance: v = escape speed y To escape Earth: need 11.2 km/s y To escape Sun (launch from Earth): need 42.5 km/s
Satellite = projectile in free‐fall
