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Lecture series from Conceptual Physics, 8 th Ed. Copernicus, Brahe, and Kepler p142. Used Brahe’s data to develop mathematical models of the motions of the planets.

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Copernicus, Brahe, and Kepler p142

Used Brahe’s data to develop mathematical models of the motions of the planets.

Thought he would gather some data before shooting off his mouth about his heliocentric ideas. Which was probably a good idea seeing as how his nose had already been cut off in a duel. (He was rich and threw really gnarly parties so he got away with a lot.)

Speculated that the sun was the center of the solar system.


Kepler’s Laws p143

First he translated Brahe’s data from Earth based reference to what would be seen by a stationary observer outside the solar system.

His laws of planetary motion are:

1. Planets move in ellipses.

2. The “equal areas” thing.

3. T2 proportional to R3

Fantastic stuff, but he didn’t know about gravity, didn’t apply “inertia”, didn’t know why ellipses…

BUT, he was right because he had good data.


Newton’s Law of Universal Gravitation p144

-knew that inertia kept the planets moving.

-the force acting on the planets caused them to curve.

-from looking at Kepler’s stuff, he knew the force emanated from the sun. (He deduced gravity.)

-he also deduced that the forced decreased with the square of the distance.

-the apple thing reminded him that gravity acts between masses and therefore objects in orbit are falling around their primaries.

Here it is gang!!

Gm1m2

Fg =

d2


The Universal Gravitational Constant, G p145

F d2

G =

= 6.67x10-11 Nm2/kg2

m1m2

An interesting example:

How much does the earth mass?

Imagine an object on the surface of the earth.

From F=Gmemo/d2

mog = Gmemo/d2

g d2

(9.8)

(6.4x106)2

= 6.0x1024kg

So, me =

=

G

(6.67x10-11)


Gravity and Distance: The Inverse-Square Law p147

Weight decreases as person climbs.


Weight and Weightlessness p149

Fig. 8.7 Your weight equals the force with which you press against the floor.


More Weightlessness

Both people are in a gravitational field.

In fact. Gravity does not produce weight! The floor produces weight.


Ocean Tides p150

Equal forces to the right means Jell-O ball stays spherical.

Forces shown here cause left side to lag behind.

The left side is further from moon and is not pulled as strongly toward moon.


More on Tides

F = G m m / d2

This planet has bigger tides because “delta” F is greater.

Smaller “delta” F means smaller tides.

“Delta” F refers to the difference in forces at the front and back of the planet.


Spring tides:

Neap tides:

The earth’s tilt means that this person has a lower high tide than this person.

Tides in the Earth and the atmosphere work the same way.


Why does the moon always face us?

Tides on the Moon p154

The key thing is that the moon acts like a pendulum.

This part of the moon

swings back and forth

trying to line up with the Earth.


The Gravitational Field Inside a Planet p155

First, the outside field lines:

Now, the inside:

Last, the in and the out -side


Einstein’s Theory of Gravitation p157

Albert says that the moon is NOT pulled to the Earth.

The moon curves because the surface it travels on is tilted toward the Earth.


Black Holes p157

Their gravitational field is so strong that even light can not escape!

Because of F=Gmm/d2

When the star collapses to ½ its radius, Supy’s weight quadruples.

When the star crushes its matter to a few hundred kilometers, that may be the last we see of it.

A collapsing star with Superman standing on its surface.

Things orbit it and spiral inward.

Only gravity, charge and angular momentum remain.


Universal Gravitation p 159

As far out as we can see, matter seems to obey Newton’s law of gravitation: F=Gmm/d2.

Neptune and Pluto were discovered by using the law.

The activities of distant galaxies seem to obey the law.

BUT, the universe is expanding too fast!!

To be continued.


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