Gravity

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```					                                                         Overview
Gravity and Kepler’s
In this section:
Laws                                  What is gravity and how does it work?
How do objects move in the solar system?

PSC 203                       Pre-
Pre-lecture questions …

Theory of Gravity
Gravity is the force of attraction
Gravity                             between any two masses

Sir Isaac Newton
Albert Einstein

Law of Gravity                          Qualitative relationships
Force is:                                    Mass
directly proportional to product of masses     More mass, more force
inversely proportional to distance squared     Less mass, less force
Distance
Large distance, less force
Small distance, more force

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G                                Qualitative Example
Universal Gravitational Constant                                 G mA m2               G 2m A m 2
found by experiment                                        FA=          2
FB=             2
r                        r
assumed constant throughout universe

F B= 2F A
Don’t need to memorize this number

Example 2                                    Qualitative relationships

G m1m2                           G m 1m 2          Need to look at full equation
FA=                              FB=               2
You need to make sure that your units are
r2                               3r           the standard mks (meters, kilograms, and
seconds)
Then it is just plugging into the calculator
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FB=             F
9 A                           For astronomy, masses and distances are
often found in the tables in the book

Example: Earth and Moon

Nm 2                                           Surface Gravity
(6.7 x10 −11        )(6 x10 24 kg )(7 x10 22 kg )
kg 2
FG =
(4 x108 m) 2

FG = 1.75x1020 N

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Surface Gravity                Qualitative relationships
Measures the affect                      Mass
of gravity at the                          More mass, more gravity
surface of an object
GM              Less mass, less gravity

Depends on mass and

Give and take                         Example questions

The jovian planets have more mass than   From concept tests…
terrestrials
But they also have a larger radius…

So what is the result?
Table from other textbook

Kepler
Kepler's 1                1st                        (1571-
Johannes Kepler (1571-1630)
was trying to understand how planets
Law                               moved
used very precise data from Tycho Brahe

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1st observation                              Kepler's 1st Law
converted observations of positions of
planets against background stars to
“Each planet moves in an
positions relative to sun                    elliptical orbit with the sun
didn't fall on perfect circles as had been   at one focus of the ellipse.”
assumed

Ellipse                               Eccentricity
oval shape                                    eccentricity - a measure of the flattening
of an ellipse
2 focus points
e = 0 is circle
mathematical
equation                                      e > 0 means flattened
higher e means more flattened

Eccentricity of objects
most planets have low eccentricity (e <
0.1)
Kepler's 2nd
comets have high eccentricity
applet
Law

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2nd observation                           Kepler's 2nd Law
Planets didn't move at a constant speed    “The line from the sun to any planet
sweeps out equal areas in equal time
moved faster when closer to sun
intervals.”
moved slower when further from sun

Animation
Links to animation applets are on course
website
Kepler's 3rd
applet
Law

3rd observation                           Kepler's 3rd Law
planets did not orbit around sun at same    “The squares of the periods of
speed
the planets are proportional to
closest to sun orbited faster                  the cubes of the average
further out from sun orbited slower            distances from the sun.”
P2 ~ a3

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Animations                              Using the equation
Links to animation applets are on course   Most often use the ratio form of the equation
website
applet                                                   2           3
P   1
=   a1
2        3
P   2       a   2

Example: Planets around Sun                Example: Planets around Sun

For Earth:                                 For an object at, a = 2AU
P2 = 1 year
a2 = 1 AU                                 a 3 = ( 2) 3 = 2 ∗ 2 ∗ 2 = 8
For any other object:

P= (a∗a∗a)                        P = 8 = 2.83
P in years, a in AU

Example question

From concept tests….

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