Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a...

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Projectile and Satellite Motion

Transcript of Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a...

Page 1: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Projectile and Satellite Motion

Page 2: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

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

Page 3: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Parabola (approximately)

Page 4: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Monkey in a Tree

Set to 48 minutes

Page 5: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

For a particular range less than the maximumand 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

Page 6: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

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

Page 7: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

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

Page 8: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

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).

Page 9: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

16 ft

16 ftCurvature of Earth

5 miles

Throw an object faster, faster.faster,

We draw in each trajectory for 1 second

Page 10: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Kepler’s Laws

•First LawFirst LawPlanets orbit the Sun in ellipses with the Sun at one focus of the ellipse

Sun

Planet

Page 11: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Ellipses

Focus Focus

d1d2

d1 + d2 = constant for any point on ellipse

Page 12: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Ellipses

a = Semi-major axis

b = Semi-minor axis

Page 13: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Eccentricity

a

c

e = c/a

Page 14: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.
Page 15: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Kepler’s Laws

•Second LawA line drawn from the planet to

the Sun sweeps out equal areas in equal intervals of time

Page 16: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

The Search for Order

•Perfect solids

Page 17: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

The Search for Order

•Music of the Spheres

Page 18: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Kepler’s Laws

•Third LawThe orbital period of a planet squared is proportional to the length of the semi-major axis cubed.

P2 a3

Page 19: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Using the Third Law

P2 a3

P2 constanta3

P2 a3

P measured in years, a in AU, object orbits Sun

Page 20: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Kepler’s Laws

•Empirical

•Kepler could not explain why the planets orbited the Sun (he thought it had something to do with magnetism)

•Universal

Page 21: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

The Apple

2

R

mGMF

m

M

mgR

mGM

2

2

R

GMg

Page 22: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

The Earth and Moon

F

2R

mGMF

Earth

Moon

R

maR

mGM

2

G

aRM

2

Page 23: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

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 Ellipse Parabola Hyperbola

Page 24: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Ellipse

Ellipse

Ellipse - Circle

Ellipse

Ellipse

Parabola

Vcircle = 5 mi/s = 8 km/s Vescape = 7 mi/s = 11 km/s

Hyperbola

Page 25: Projectile and Satellite Motion PROJECTILE MOTION We choose to break up Projectile Motion as a combination of vertical free-fall motion and horizontal.

Orbiting

•Falling without getting closer to the ground.

•Force of Gravity = Centripetal Force

d

GMv

vd

GMd

mv

d

GMm

orb

2

2

2