Transcript Universal Gravitation

Universal Gravitation
Applied Science
Mr. Kuffer
The Fundamental Force!
• The gravitational force is
weak, but very long ranged.
Furthermore, it is always
attractive, and acts between
any two pieces of matter in the
Universe since mass is its
source.
The Tortoise and the Hare:
Gravity Always Wins
• Why Gravity is the Most Important force:
– it is long-ranged and thus can act over
cosmological distances, and
– it always supplies an attractive force between
any two pieces of matter in the Universe.
• Thus, although gravitation is extremely
weak, it always wins over cosmological
distances and therefore is important to
understanding our Universe.
Universal Gravitation
• We’ve all heard the story… An apple falls
on Isaac Newton’s head
• He understands Galileo’s idea of inertia…
Objects at rest will…
• Therefore there must be some force acting
on the apple…
• The problem he runs into is…
– What is causing the force?
What is causing the force?
• This led to the “most far-reaching
generalization of the human mind”
• Newton applied what he knew about the
apple to attempt (successfully) to
explain the motion of the moon around
the Earth.
The Falling Moon?
• Why doesn’t the moon just remain in
motion?
• A: Something is pulling it in… Fc!
• The moon is “falling around the Earth
just as the apple…okay, not quite “just
as” the apple… but similar.
Visualize it!
• Newton says “Object
in motion…
• Can you see that the
force exerted by the
Earth causes the
moon to fall “below”
the straight line that it
would have traveled?
The Falling Moon!
• The moon “falling” is a bit different then
the apple falling. The moon falls beneath
that straight line. We say it falls “around”
the earth.
• Let me explain…
• What are the odds?
• Gotta get it just right, Wow!
You See?
• The moon is just a projectile that wants to
stay in motion but ends up circling the
earth b/c of gravity (which provides the Fc).
• Likewise, the earth is just a projectile
circling the sun b/c of gravity. (confirming
the Copernican theory that the sun, not the
earth was the center of the solar system)
Newton’s Law of Universal
Gravitation.
• Every object attracts every other object with a
force that for any two objects is directly
proportional to the mass of each object. (that
means it depends on the masses involved)
• He also noted that it depends on the separation
between the masses. The further away, the less
attraction
F~ m1 m2 / d2
Newton’s Law of Universal
Gravitation.
• If this is true, then isn’t there an attraction
between all object? After all, all objects
have mass.
• A: YES, but the forces between these
masses are often negligible, b/c their
masses are so small in comparison to the
earth.
The BIG bang or the BIG crunch?
Food for Thought?!
• According to gravitational concepts, what
goes up….
• Apply this to the universe and…
The presently expanding universe (like a
stone thrown upward) will eventually
collapse (like the stone returning, due to
gravity), or will it?
Hmmmmm?
In Summary
• Gravitational concepts are present not only on
earth, but throughout the universe.
• Orbiting objects (like the moon) are actually
falling around another object (like the earth).
• Everything pulls on everything else with a force
that depends on the masses and the distance
between the masses.
– The greater the mass, the greater the force
– The greater the distance, the smaller the force
F = G (m1 m2 / d2)