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Lecture series from Conceptual Physics, 8 th Ed. The Falling Apple p166. Newton new that inertia kept the moon moving around the Earth. So, there must be a force that pulled it into an elliptical orbit. The same force that pulled the apple to the ground must extend to the moon.

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Lecture series from Conceptual Physics, 8 th Ed.

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Lecture series from Conceptual Physics, 8th Ed.


The Falling Apple p166

Newton new that inertia kept the moon moving around the Earth.

So, there must be a force that pulled it into an elliptical orbit.

The same force that pulled the apple to the ground must extend to the moon.

The Falling Moon p167

Falls 1.4mm during one sec.

Falls 4.9m the first sec.


Gmemm

(6.67x10-11)(5.98x1024)(7.36x1022)

F =

=

d2

(3.84x108)2

F = 1.99x1020N

F

1.99x1020N

And then, a =

=

m

7.36x1022kg

a = 0.0027 m/s2

And, finally…d = ½ at2

d = ½ (0.0027)(1)2 = 0.0014 m

d = 1.4 mm in the 1st second.

The apple falls 4.9 m in the 1st second.

d = ½ g t2 = (0.5)(9.8)(1)2 = 4.9 m


Circular Orbits p168

Without tangential velocity, the Earth would fall into the sun.

Fig 9.5- No work is done on bowling ball because force is perpendicular to motion of ball.

We can see the curvature but the force is still perpendicular.

At 8 km/s the bb doesn’t need the track.


Elliptical Orbits p170

Fig 9-8 Satellite is moving faster than 8 km/s.

a) Goes outside circle and slows down.

b) Falls back to Earth gaining speed.

c) Does it over again.


8 km/s

Initial thrust gets rocket off the ground.

The trajectory of a cannon ball is part of an ellipse that would occur if the Earth didn’t get in the way.

Sideways thrust gets it to orbital speed.

Both up and sideways are done together.


Energy Conservation and Satellite Motion p172

For a circular orbit the energy is constant.

Satellite is slow at apogee. Has small KE.

Satellite is faster at perigee. Has large KE.

Conservation of energy: KE + PE = k.


In an ellipse the force is not always perpendicular to the motion.

Here a component of the force is speeding up the satellite.

Recall: work = delta KE.

This component of the force is doing work on the satellite.

The other component doesn’t do work. It changes the direction of the satellite.


vesc =

2GM

d

Escape Speed p176

vesc =

2(6.67x10-11)(5.98x1024)

6.37x106

vesc =

11,200 m/s

However, you could escape at any speed, 2 m/s, if you kept the motor turned on all the way.

d won’t fall back.

The end


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