Transcript Gravity
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