Satellite = projectile in free-fall
y Projectile : free fall from launch to landing.
Satellite = projectile in free-fall
Projectile and Satellite Motion
PH 104 w/ dr. g
Lec 11
y Satellites = projectiles too fast to land.
y Kepler’s Laws of Planetary Motion
y Energy conservation: determines escape speed
Satellite = projectile in free‐fall
Satellite = projectile in free‐fall
Projectile : free fall from launch to landing.
Projectile : free fall from launch to landing.
Snapshots of a Trajectory: every 0.1 seconds
Snapshots of a Trajectory: every 0.1 seconds
Satellite = projectile in free‐fall
Satellite = projectile in free‐fall
Projectile : free fall from launch to landing.
Projectile : free fall from launch to landing.
y Trajectory is always a
y Trajectory is always a PARABOLA
y Velocity has two components: horizontal & vertical
y Result : a parabolic trajectory!
y Horizontal : constant: equal distance per unit time
y Horizontally launched: half a parabola
y Vertical : free-fall (gains 9.8 m/s per sec down)
y Any launch angle: more or less than half
: 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
Satellites = projectiles too fast to land.
Horizontal launch at 8 km/s = circular orbit!
y Projectile always about
below the zero-g path
y Zero-g : path always a straight line (no force!)
y First second: about 5 m below this ideal path
yCurvature of Earth: 5-m “drop” for every 8 km !
yHorizontal line = tangent to sphere at observer
y8 km away: Earth curve is 5 m below
yHorizontal launch @ 8 km/s : falls with Earth curvature!
8 km
5 km
Satellite = projectile in free‐fall
Satellite = projectile in free‐fall
Kepler’s Laws of Planetary Motion
Kepler’s Laws of Planetary Motion
y Launch > 8 km/s: “overshoots” : orbit is an ELLIPSE.
y Ellipse: has two FOCI (plural of FOCUS) I.F. 10.25
y Each point: distance to F1 + distance to F2 = CONSTANT
y Circle:
special case: zero separation between foci
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 2nd & 3rd Laws: Planet moves faster when closer to Sun
y 3rd Law: farther orbit takes longer for one period
Satellite = projectile in free‐fall
Energy conservation: determines escape speed
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
y To escape Sun (launch from Earth): need 42.5 km/s
y Kepler’s observations : Laws of Planetary Motion
y