Transcript Universal Gravitation

Specific Forces
Fundamental Forces
Universal Gravitation
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Objectives
• Calculate the gravitational force given two masses
and the distance between them.
· Calculate the change in gravitational force when
the mass or distance is changed.
· Add gravitational force vectors
· Explain how a person's weight is related to the
Law of Universal Gravitation.
· Define 'gravitational field strength' and relate it
to the acceleration due to gravity
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SPECIFIC FORCES
Fundamental Forces
Gravitational Force
Centripetal Force
Restoring force
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What Are The Fundamental Forces?
Gravitational
Force
Electromagnetic
force
Strong Nuclear
Force
Weak Nuclear
Force
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Gravitational Force
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•
•
•
•
•
An attractive force that exists between all masses.
It is the basis of planetary motion.
It is the weakest force.
It acts over long distances
Is universal
We experience it as
– Weight
– Planetary orbits
– Satellite motion
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Comparing the Gravitational and
Electromagnetic Forces
The gravitational force, which only attracts,
is much weaker than the electric force.
electric force = 1035 gravitational force
Just as the space around a planet and every other
mass is filled with a gravitational field, the space
around every electric charge is filled with an
electric field.
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Sir Isaac Newton
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THE LAW OF UNIVERSAL GRAVITATION
• Newton proposed that an attraction between
bodies is universal.
• Gravitational force is extremely weak between
ordinary objects.
• Objects with enormous mass have significant
gravitational force.
Creates orbits
Creates tides
Is known as weight for objects on the surface.
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According to Newton's law of gravity, her weight
(not mass) decreases as she increases her distance
from the Earth's center (not surface).
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Equal and Opposite Forces
m1
-F
+F
m2
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r
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Newton’s Correlations!
He hypothesized that the net force on a planet must
vary inversely with the square of its distance from
the sun.
F 1/d2
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WEIGHT ON A PLANET
Weight is dependent upon the acceleration due to
gravity where the weight is measured.
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WEIGHT GRAPH
Universal Gravitation, and therefore weight, follow
the inverse square law.
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Variation of g with Altitude
typical space
shuttle altitude
2 altitude of
communication
satellites
3 distance to the
moon
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Altitude (km)
0
5
10
50
100
4001
35,7002
380,0003
G (m/s2)
9.83
9.81
9.80
9.68
9.53
8.70
0.225
0.0027
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The math…
F = (G m1 m2)/ d2
Newton’s Inverse Square Law.
G = 6.67  10-11 N·m2/kg2
– It is the Universal Gravitation Constant.
– Discovered later by Cavendish.
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Elmira
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Force
Changes
with the
Inverse of
the Distance
Squared
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Force Changes with
Mass
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A Gravity Concept
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How Can I be Weightless on Earth?
The sensation of weight (your apparent weight)
equals the force with which you press against the
supporting floor. If the floor accelerates up or
down, your apparent weight varies.
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Both are "weightless".
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If a star collapses to half its radius and there is no
change in its mass, gravitation at its surface would
increase by a factor of four.
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Which falls toward the other, A or B? Do
the accelerations of each relate to their
relative masses?
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Gravitational Field Strength
• Is the gravitational force per unit of mass
acting at a point
g = Fg / m
Units for gravitational field strength are N/kg
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Field lines represent the gravitational field about the
Earth. Where the field lines are closer together, the
field is stronger. Farther away, where the field lines
are farther apart, the field is weaker.
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Calculations about Satellites
We can calculate the velocity of a satellite using the
equation
_________
v = (Gme ) / r
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ESCAPE VELOCITY
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What is Escape Velocity?
• It is the slowest speed with which we can launch a
projectile so that it will never fall back to the
earth.
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What kinds of orbits?
• A launch speed of
–
–
–
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8 km/s will give a circular orbit
8 to 11.2 km/s will give an elliptical orbit
11.2 km/s orbit is parabolic, it escapes
Above 11.2 km/s, the orbit is hyperbolic
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What about the Period of the Satellite?
We use the equation
___________
T = 2  (r3 ) / (Gme )
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Geosynchronous Orbits
• The satellite remains stationary above one place
on the earth.
• Characteristics
– Must have the same period as the earth’s period of
rotation
• Which is 24 hours.
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The Astronomical Unit
• This is a unit of measure equal to the average
distance between the earth and the sun.
• It is designated as 1 A.U.
• 1 A.U. = 93 million miles.
• 1 A.U. = 1.5 X 10^11 m.
• The A.U. is used to measure astronomical
distances.
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