Transcript Gravitational Forces

Gravitational Forces
What is Gravity?

Gravity is the tendency of all objects (with
mass) to attract one another.
 We often refer to this as a gravitational
force. Which is the attractive force one
mass places on another.
 The idea of a gravitational force came from
Sir Isaac Newton.
Developing the Idea of
Gravitational Forces

Newton’s did not discover that when you let
go of a object held above the ground, it falls
to the floor.
– Mankind knew that back since its beginning

Newton did make this following piece of
logic that united the Earth with the universe,
and establish the means to unravel the
mysteries of space.
The Logic
If you drop an object it
falls because of a
gravitational force.
If you fire a cannon ball it
Arcs its path because it is
Accelerated at same way as the
dropped. It too is falling because
of a gravitational force.
But the faster the ball is fired
The large the ball’s range.
On Top of The World

Now lets say we have a cannon on the top
of the world and it fires a series of balls
horizontally. With each shot being faster
then the previous one.
At some speed the ball will
never reach the ground
because it out runs the curve
of the Earth. It is however
still falling because of the
Gravitational Force.
Expanding to the universe

The Moon orbits the Earth in this manner.
 All the planets of our solar system orbit the Sun in
this manner.
 All objects in space are falling towards one
another. Gravitational Forces are everywhere (just
like on earth)
 The universe must object the same physical laws
as objects on earth do.
– Until this point people believed the laws for the
universe and life on earth were different.
The factors that influence
gravitational Forces

Newton realized that the gravitational force acting
on an object just did not depend on it’s mass, but
the mass of the object pulling it.
 Also the mass of at least one of the two objects
must be very large for the force to be noticed.
– You don’t often see a person stuck to a wall because of
the gravitational force between them.

He also realized that the distance of separation has
a huge affect (inverse squared) on the gravitational
force between the objects.
Newton’s Gravitational Law
Is often shown as the equation:
(Universal Gravitational Constant)* (Mass1)*(Mass2)
Fg =
(Distance of separation)2
G m1m2
Fg =
r2
Newton’s only problem is the fact he did not know what the
universal gravitational constant was equal to.
Enter Henry Cavendish
By placing
masses used
inside the
and measuring
Henrydifferent
Cavendish
an device
enclosed
device the
Deflection
of the suspend
lead balls, he lead
was able
to find the value of G
consisting
of suspended
balls.
Newton’s Gravitational Law
Is often shown as the equation:
(Universal Gravitational Constant)* (Mass1)*(Mass2)
Fg =
(Distance of separation)2
G m1m2
Fg =
r2
G = 6.67*10-11 Nm2/kg2
Orbital speeds
SFsatellite = (m satellite)ac
Fg
(Vorbit)2
Fg = (m satellite)*----------R
Vorbit
R
G(m planet)(m satellite)
(Vorbit)2
--------------------------- = (m satellite)*----------R2
R
Vorbit
G(mplanet)
= -------------R
Period and radius
Circumference of 1 orbit
Period = -------------------------------Orbital speed
2pR
T = -----------------G(mplanet)
-------------R
2pR
T = ---------V orbital
4p2R2
T2 = -----------------G(mplanet)
------------R
[ ]
[ ]
[ ][ ]
4p2R2
T2 = -----------------G(mplanet)
------------R
T2
4p2
--------- = -----------------R3
G(mplanet)
4p2R3
T2 = -----------------G(mplanet)
R
------------G(mplanet)
R
------------G(mplanet)
T2
---- = Constant
R3
TA2
TB 2
---- = ------RA3
RB3
Gravitational Fields

Because gravitational forces do not required
contact, but act over a distance of separation
gravitational forces are a field force
 A gravitational field is simply how much
gravitational force acts one 1 kg of mass
Gravitational Field = Fg/m
g = Fg/m
The gravitational field and
gravitational acceleration
have the same equation so the are
numerically equal. But they are
not the same thing.
Gm
g =
r2
The unit for a gravitational field is a N/kg
Gravitational Field Vectors

Because gravitational forces are always
attractive all gravitational field vectors point
toward the object who is making them.