Transcript universal law of gravitation

Chapter 5
Circular Motion; Gravitation
The Force of Gravity
Our goals for learning:
• What is the universal law of gravitation?
• What types of orbits are possible according
to the law of gravitation?
• How can we determine the mass of distant
objects?
© 2004 Pearson
Education Inc.,
5-6 Newton’s Law of Universal Gravitation
If the force of gravity is being exerted on
objects on Earth, what is the origin of that
force?
Newton’s realization was
that the force must come
from the Earth.
He further realized that
this force must be what
keeps the Moon in its
orbit.
5-6 Newton’s Law of Universal Gravitation
The gravitational force on you is one-half of a
Third Law pair: the Earth exerts a downward force
on you, and you exert an upward force on the
Earth.
When there is such a disparity in masses, the
reaction force is undetectable, but for bodies
more equal in mass it can be significant.
Newton’s Universal Law of
Gravitation
Isaac Newton discovered that it is gravity which
plays the vital role of determining the motion of the
planets - concept of action at a distance
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Questions
• If the planets are orbiting the sun , what force is
keeping them in orbit?
• What force keeps the moon in its orbit?
• Could the force of gravity be universal?
Newton’s Law of Universal
Gravitation
• Any two objects attract each other with
a gravitational force, proportional to the
product of their masses and inversely
proportional to the square of the
distance between them.
• The force acts in the direction of the line
connecting the centers of the masses.
Newton’s Universal Law of
Gravitation
Between every two objects there is an attractive
force, the magnitude of which is directly
proportional to the mass of each object and
inversely proportional to the square of the
distance between the centers of the objects.
© 2004 Pearson Education Inc., publishing as Addison-Wesley
Change of
Gravitational
Force with
Distance

Law of universal
gravitation is
known as an
inverse square
law.
Newton’s Universal Law of
Gravitation
G=6.67 x 10-11 m3/(kg s2)
© 2004 Pearson Education Inc., publishing as Addison-Wesley
•How does the acceleration of gravity depend on the mass
of a falling object?
•It does not. All falling objects fall with the same
acceleration (on a particular planet).
•Now see why…
•F = ma and on Earth acceleration due to gravity
denoted “g” so F=mg or g=F/m
•If mass of earth is M1 then Fg=GM2/d2
© 2004 Pearson Education Inc., publishing as Addison-Wesley
5-6 Newton’s Law of Universal Gravitation
Therefore, the gravitational force must be
proportional to both masses.
By observing planetary orbits, Newton also
concluded that the gravitational force must decrease
as the inverse of the square of the distance between
the masses.
In its final form, the Law of Universal Gravitation
reads:
(5-4)
where
Henry
Cavendish’
s
experiment
determined the
proportionality
constant
G
in 1798.
http://www.newscientist.com/data/images/archive/1639/16390101.jpg
5-6 Newton’s Law of Universal Gravitation
The magnitude of the
gravitational constant G
can be measured in the
laboratory.
This is the Cavendish
experiment.
5-7 Gravity Near the Earth’s Surface;
Geophysical Applications
Now we can relate the gravitational constant to the
local acceleration of gravity. We know that, on the
surface of the Earth:
Solving for g gives:
(5-5)
Now, knowing g and the radius of the Earth, the
mass of the Earth can be calculated:
5-7 Gravity Near the Earth’s Surface;
Geophysical Applications
The acceleration due to
gravity varies over the
Earth’s surface due to
altitude, local geology,
and the shape of the
Earth, which is not quite
spherical.
Problem 1
•
Two spheres of mass 35kg are 30m apart.
A) What force does one exert on the other?
B) If the mass of one is tripled and the radius
is quadrupled how does the force change?
Problem 2
• Two spheres of equal mass have a force
of gravity of 7x10-9 N exerted on each
other. If the distance between them is 7m,
find the mass.
Problem 3
• Find the value of the gravitational
acceleration g. The mass of the Earth is
6.0 x 1024kg. The radius of the Earth is
6.38 x 106 m.
Homework – Chapter 5
• 28, 29, 30, 33, 36, 41
• Kahoot