23
UNIVERSAL GRAVITION
UNIVERSAL GRAVITION
A Very Brief History of
Statics and Dynamics
The idea that a force causes motion
goes back to the 4th century B.C., when
the Greeks were developing ideas about
science.
Aristotle (384-332 BC) studied motion,
and believed that objects with more
mass fell to the earth faster because
they had a greater attraction to the earth.
Galileo Galilei
Galileo, the premier scientist of the 17th century, determined that moving objects eventually stop because of a force called frictionand that
all objects regardless of their mass will fall at the same rate.
Johanas KeplerAlso during the 17th
Century, a German
mathematician and
astronomer Johannes
Kepler developed three
laws of planetary motion
that accurately predicted
the location of the
planets but did not
explain why they change
speed throughout their
elliptical orbits.
Troubled by the lack of explanation for the planet's particular orbits, Newton eventually related the motion of the moon about the earth to the motion of an object falling on earth. He determined that both are acted on by the same force, Gravity.This realization led him to his Law ofUniversal Gravitation.
Youtubevideo
Enter Newton 18th century
Universal GravitationNewton recognized that the force of gravity between any
two objects with mass is directly proportional to the
product of the masses, and inversely proportional to the
square of the distance separating the masses.
2
21
r
mmGF
gravForce of Gravity
Mass of object 1 Mass of object 2
Gravitational Constant
Distance
between objects
(radius)
G - the universal gravitation constant
The value of G was experimentally determinednearly a century later by Lord Henry Cavendishusing a torsion balance.
G is 6.67 x 10-11 N·m2/kg2
The value of G is an extremely small numericalvalue because the force of gravitational attractionis only appreciable for objects with large mass.
The value for the gravitational force you exert onthe earth and it exerts on you are equal.
22
Earth
youEarth
Earth
Earthyou
gravr
mmG
r
mmGF
Where’d g Come From???Since an object’s weight on Earth is the
gravitational force that the earth exerts on the
object, we can say, near sea level:
WFg
26
24
2211
2)1037.6(
1098.5/1067.6
m
kgkgmN
r
mGg
Earth
Earth
g = 9.81 m/s2
gmobject2
Earth
Earthobject
r
mmG
Notice: The
acceleration
due to gravity is
only dependent
on the mass of
the Earth and
the distance
from the center
of Earth.
Universal Gravitation is an
inverse-square law
The gravitational force between two objects only
depends on:
2
21
r
mmGF
grav
Distance-Inverse Relationship
AND Squared
Mass- Direct Relationship
Which variable has
the greatest effect on
the gravitational
force—Mass or
Distance? Why?
Distance because it is squared
About the Inverse Square…
Implications of Universal Gravitation:
• If the mass of an object if doubled, then the force of gravity is ….
• Doubled
• If the distance between two objects is doubled, then the force of gravity is …
• One/fourth
• What happens to the force of gravity if there is half the original ….
• Mass?
• It is halved
• Distance?
• It is quadrupled
2
21
r
mmGF
grav
Universal Gravitation explains Satellite
motion
Why is a satellite a
projectile?
Because the only force
acting on it is gravity.
Newton proposed
that if you fired a
cannon ball fast
enough, it would
orbit the Earth.
Remember, Newton had
realized that the Moon
orbits the Earth because
the gravitational force of
the Earth, which pull’s all
object’s down, must be
balanced (net F=0) with
the Moon’s inertia.
Which cannon ball was fired
with the greatest velocity?
#4
Launch Speed less
than 8000 m/s
Launch Speed equal
to 8000 m/s
Launch Speed greater
than 8000 m/s
What happens if the projectile has a….
Projectile falls to Earth
Projectile orbits Earth –
Circular Path
Projectile orbits Earth - Elliptical Path
In an elliptical orbit, a satellites velocity changes as
it’s distance from the object it orbits changes. Why?
Force of gravity changes with the distance change.
How else could the
force of gravity on
the satellite be
changed?
Change Mass
Remember: Kepler had determined that
planetary orbits are elliptical.
Using Newton’s Law of Universal Gravitation,
how could the force of gravity on
a satellite be decreased?
1. Decrease the
mass
OR
2. Increase the
distance
Field Forces-Forces that affect
objects motion
without direct
physical contact
Example: Gravity
Contact Forces-Forces that affect
objects motion when
in direct physical
contact
Example: Weight
REMEMBER there are TWO types of force:
Fundamental Forces of Physics
All particles interact with each other and can be described by:
– Gravity - the attractive force that draws two masses
toward each other.
– Electromagnetism - the interaction of particles with an
electrical charge.
– Weak Nuclear Force -acts on the scale of the atomic
nucleus and is responsible for radioactive decay.
– Strong Nuclear Force - keeps nucleons (protons &
neutrons) bound together in the atomic nucleus.
Notice: The EM, Weak and Strong force all act across short
distances.
Gravity is the only force that acts across large distances.
• Just for comparison sake take two electrons 1m apart:
Fgrav=(6.67∗10−11Nm2/kg2)(9.11∗10−31kg)2/(1m)2
= 5.54∗10−71N
•
Felec=−(8.99∗109Nm2/C2)(1.60∗10−19C)2/(1m)2
= −2.30∗10−28N
The electromagnetic force is 4*10^42 times larger
Gravity is the weakest of the
fundamental forces since it’s
effects can only be seen by large
masses.
Fact of Gravity:
• Attractive force only
• Increases with a decrease of distance between objects
• All matter has gravity
• Increases with an increase of mass
• Gravity accelerates all objects at the same rate, regardless of their mass
• Gravity is a field force (exerts a force without contact)
• Gravity is the weakest of the four fundamental forces
Gravity Applet
