Universal Gravitation
Sir Isaac Newton: The
Universal Law of Gravitation
The Falling Apple

Newton reasoned the moon is falling for
the same reason the apple falls – they are
both pulled by the Earth’s gravity.
Newton’s Excellent Idea

Now came Newton's truly brilliant insight: if
the force of gravity reaches to the top of the
highest tree, might it not reach even further; in
particular, might it not reach all the way to the
orbit of the Moon! Then, the orbit of the Moon
about the Earth could be a consequence of the
gravitational force, because the acceleration
due to gravity could change the velocity of the
Moon in just such a way that it followed an
orbit around the earth.
Source: http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html
The Falling Moon

Newton’s First law:
– An object (the moon)
will remain in motion in
a straight line unless
acted on by an outside
unbalanced force
(gravitational attraction)

The force that pulls an
apple to the ground also
keeps the moon in
orbit.
The Falling Earth


Newton’s theory of gravitation confirmed
the Copernican theory of the solar system.
A planets tangential speed allows the
planets to orbit the sun without being pulled
into it.
Newton’s law of Universal
Gravitation
The Gravitational Constant
Henry Cavendish 1798
He used a device with two
objects on a rod that was
hung on a wire. These
masses were attracted to
two larger objects,
twisting the rod slightly.
The measurement of the
masses, distance between
them and the torque on
the wire allowed G to be
determined.
The Universal Gravitational
Constant – A G-thing



G is a constant of proportionality.
The magnitude is the force exerted by two
1-kg masses 1 meter apart.
G = 6.67 x 10-11 Nm2/kg2
Weight and Mass
Gravity and Distance: The
Inverse Square Law


A quantity varies as the inverse square
of its distance from its source
A localized source spreads evenly
throughout the surrounding space.
The Weight of an Apple?
Gravity and Orbits

Centripetal acceleration
– ac= v2/r

Centripetal Force
– Fc= mac

The force in circular motion is directed
towards the center - centripetal
Why is the Earth round?


Because of gravitation – earth attracted
itself together.
The deviation of a planet from its normal
orbit is called a perturbation. It is caused by
other planets.
Reviewing
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
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Objects orbiting around the Earth are actually
falling toward Earth but have great enough
tangential velocity to avoid hitting the earth.
Everything pulls on everything else with a force
that depends on the mass of the objects and
distances between them.
Gravitation decreases according to the inverse
square law.
Geosynchronous Orbits
GPS