Download Newton`s Law of Universal Gravitation

Newton’s Law of Universal
Gravitation
Review:
Kepler’s
Laws
Newton’s Law of
Universal Gravitation
In 1666, some 45 years after Kepler did his
work, 24-year-old Isaac Newton used
mathematics to show that if the path of a planet
were an ellipse, which was in agreement with
Kepler’s first law of planetary motion, then
the magnitude of the force, F, on the planet
must vary inversely with the square of the
distance between the center of the planet
and the center of the sun.
The Apple and the Moon?
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Legend has it that Newton was struck by
this idea while sitting under an apple tree,
and he wondered whether the force that
brought the apple to the Earth when it falls
was the same as the force that held the
moon in its orbit.
The amazing thing about Newton’s law is
that he asserted, back in 1666, that it
applied to ALL objects, EVERYWHERE in
the universe. So far as we know, he was
right!! (well, almost right…)
Newton’s Law of Universal
Gravitation
The symbol a means is
proportional to, and r is the
distance between the centers of
the two bodies.
Newton’s Law of Universal
Gravitation
Every body in the universe attracts every other body with
a force that is directly proportional to the product of the
masses of the bodies and inversely proportional to the
square of the distance between the bodies. (INVERSE
SQUARE LAW)
Universal Gravitational Constant
m1m2
F G 2
r
G  6.67  10
11
N m
2
kg
2
Universal Gravitational Constant
m1m2
11
F  G 2 ; G  6.67 10
r
The proportionality constant, G is called the universal
gravitational constant. Its value in the SI system of units is,
G = 6.67  10-11N.m2/kg2.
The law of gravitation is UNIVERSAL and
FUNDAMENTAL. It can be used to understand the motions
of planets and moons, determine the surface gravity of planets,
and the orbital motion of artificial satellites around any central
body.
Cavendish experiment
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The constant G was measured by Henry Cavendish
in about 1797.
Amazingly accurate, yet simple, apparatus
Physics involved: Torque, simple harmonic motion,
Hooke’s law, gravitation
http://en.wikipedia.org/wiki/Cavendish_experiment
He thought he was “weighing the world”, really he
was also determining a fundamental constant of the
universe.
Video: the Cavendish experiment
Weight
Weight = Mass x Gravity
W  m g
The weight of an object is the gravitational force that the
planet exerts on the object. The weight always acts
downward, toward the center of the planet.
SI Unit of Weight: : newton (N)
Acceleration Due to Gravity
Calculate g for planet Earth at sea level.
The Hubble Space
Telescope
Practice problem
The mass of the Hubble Space Telescope is 11 600 kg.
Determine the weight of the telescope
(a) when it was resting on the earth and
(b) as it is in its orbit 598 km above the earth's surface.
Deriving Kepler’s Third Law
from Newton’s Universal Law
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In orbit, the centripetal force on a
planet is provided by the gravity of its
sun.
Mechanical Universe video: The Apple and the Moon
The Elegant Universe videos: Newton’s Secret, General
Theory of Relativity
Homework questions
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P. 138 Question 7
P. 141 Problems
25, 27, 29, 31, 35, 59b