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Chapter 9 & 10
Gravity
Pythagoras
(550 BC)

Claimed that natural
phenomena could be
described by
mathematics
Aristotle
(350 BC)

Asserted that the
universe is governed
by physical laws

The ancient Greeks believed that the earth
was at the center of a revolving sphere with
stars on it.

The Geocentric Model implies Earth-Centered
Universe.
Copernicus
(1500's)

Developed a
mathematical model
for a Sun-centered
solar system
Tycho Brahe
(1500's)

Made precise
measurements of the
positions of the
planets
Kepler
(1600's)

Described the shape of
planetary orbits
as well as their orbital
speeds
Kepler’s First Law

The orbit of a planet
about the Sun is an
ellipse with the Sun at
one focus.
Kepler’s Second Law

A line joining a
planet and the Sun
sweeps out equal
areas in equal
intervals of time.
Kepler’s Third Law

The square of a planet's orbital period is
proportional to the cube of the length of its
orbit's semimajor axis.

Or simply… T2 = R3
if T is measured
in years and R is measured in astronomical
units.
An Astronomical Unit...

…is the average distance of the Earth from
the Sun.

1 AU = 93,000,000 miles = 8.3 lightminutes
Kepler’s Laws

These are three laws of physics that
relate to planetary orbits.

These were empirical laws.

Kepler could not explain them.
Kepler’s Laws...Simply
(See page 192.)

Law 1: Elliptical orbits…

Law 2: Equal areas in equal times…

Law 3: T2 = R3
Newton’s Law of Universal
Gravitation

From Kepler's 3rd Law, Newton deduced
inverse square law of attraction.
Gm1m 2
F
2
d

G=6.67  10-11 N m2/kg2
Gravity Questions

Did the Moon exert a gravitational force on the
Apollo astronauts?

What kind of objects can exert a gravitational
force on other objects?

The constant G is a rather small number. What
kind of objects can exert strong gravitational
forces?
Gravity Questions

If the distance between two objects in space is
doubled, then what happens to the gravitational
force between them?

What is the distance is tripled?
…is quadrupled?




What if the mass of one of the object is doubled?
…tripled?
…quadrupled?
Weight and Weightlessness

Weight
» the force due to gravity on an object
» Weight = Mass  Acceleration of Gravity
»W=mg

Weightlessness - a conditions wherein
gravitational pull appears to be lacking
– Examples:
» Astronauts
» Falling in an Elevator
» Skydiving
» Underwater
Ocean Tides

The Moon is primarily responsible for ocean
tides on Earth.

The Sun contributes to tides also.

What are spring tides and neap tides?
Spring Tides
Full Moon
Earth
New Moon
Sun
Neap Tides
First Quarter
Earth
Last Quarter
Sun
End of Section…
Einstein’s Theory of Gravitation

Einstein perceived a gravitational field as a
geometrical warping of 4-D space and time.
BLACK HOLES
Let’s observe a star that is shrinking but
whose mass is remaining the same.
What happens to the force acting on an
indestructible mass at the surface of the
star?
SFA
F
F
F
m
m
1
2
m1m2
F

G
2
G
Remember that the force between
R
2
the
two
masses
is
given
by
R
G
G
m1m2
R2
R
m1m2
R2
R
R
R
F
G
m1m2
R2
BLACK HOLES
If a massive star shrinks enough so that the
escape velocity is equal to or greater than the
speed of light, then it has become a black hole.
Light cannot escape from a black hole.
Near a Black Hole