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Chapter 7 Gravitation. 7.1 Planetary Motion. Planets move through the sky with More complicated paths than Stars do. . We begin with Kepler’s Laws in Order to find out how. Kepler’s Laws of planetary motion Are stated as… . The paths of planets are ellipses, With the sun at one focus.

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Presentation Transcript
slide1

Chapter 7

Gravitation

slide2

7.1 Planetary Motion

Planets move through the sky with

More complicated paths than

Stars do.

We begin with Kepler’s Laws in

Order to find out how.

slide3

Kepler’s Laws of planetary motion

Are stated as…

  • The paths of planets are ellipses,
  • With the sun at one focus.

2) An imaginary line from the sun

To a planet sweeps out equal

Areas in equal time intervals.

Thus planets move faster when

They are closer to the sun, and

Vise-versa.

slide4

3) The square of the ratio of the

Periods of any two planets

Revolving about the sun is

Equal to the cube of the ratio

Of their average distances

From the sun.

2

3

TA

TB

rA

rB

=

slide5

2

3

TA

TB

rA

rB

=

T = the planets’ periods

Of revolution

r = the average distance

From the sun (or another focus)

slide6

The first 2 laws apply to each

Individual planet, moon, or

Satellite.

The 3rd law relates to the motion

Of several satellites about a

Single body.

slide7

Problem...

Io has a period of 1.8 days and is

4.2 units away from Jupiter.

Callisto has a period of 16.7 days.

What is the distance away

From Jupiter?

rc = 19 units

slide8

Problem...

The moon has a period of 27.3

Days and a mean distance from

Earth of 3.9 X 105 km. Find the

Period of a satellite that is in

Orbit 6.7 X 103 km.

88.6 mins

slide9

Newton also played around

With a few formulas for gravitation.

Newton said that there was an

Attractive force between

All objects, this is called the

Gravitational force.

slide10

Newton was so confidant that

He came up with a law to find

The quantity of gravity.

The Law of Universal Gravitation

mAmB

d2

F = G

slide11

mAmB

d2

F = G

m = mass

d = distance between

The center of the objects

G = 6.67 X 10-11 Nm2 / kg2

slide12

Without showing all the math,

The force equals something else.

mp4π2r

T2

msmp

d2

F =

= G

And rearranged again…

4π2

Gms

T2 =

r3

slide13

Problem...

Jeff (75 kg) and Racheal (60 kg)

sit about 4 Meters away

from each other.

Racheal looks up and feels an

Attraction. Find the gravitational

Force between them.

F = 1.87 X 10-8 N

slide14

7.2 Using the Law of

Universal Gravitation

An object that is falling at the

Same rate at which the earth is

Curved is said to be in orbit.

slide15

Use Newton’s thought experiment

On page 179 to see how.

For an object to be in orbit,

air resistance Must be taken away,

which Means that it must

be at least 150 km

above the earth.

slide16

We can continuously derive

New formulas to find out things.

GmE

r

v =

r3

GmE

T = 2π

These formulas only

Work for the earth.

slide17

Problem...

A satellite orbits Earth 225 km

Above its surface. What is its

Speed in orbit and its period?

v = 7760 m/s T = 1.5 hr

slide18

As you move farther from Earth’s

Center, the acceleration due

To gravity changes.

2

rE

d

a = g

slide19

There are 2 kinds of mass…

Inertial mass

And

Gravitational mass

slide20

Inertial mass is a measure of an

Object’s resistance to an type

Of force.

Fnet

a

minertial =

slide21

The gravitational mass is the size

Of the gravitational force

Between the objects.

r2Fgrav

Gm

mgrav =

slide22

Einstein proposed that gravity

Is not a force, but an effect

Of space itself.

According to Einstein, mass

Changes space itself,

Making it curved.

slide23

Bodies are thus accelerated

Because they follow this

Curved space toward the center.

This is Einstein’s Special

Theory of Relativity.