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Newton and Gravity
Isaac Newton (1642-1727)
• Galileo found that bodies with
different masses experienced the
same acceleration when dropped to
the ground. But he didn’t know why.
• Kepler discovered that the motions
of the planets were perfectly
reproduced by 3 mathematical
relations. Like Galileo, Kepler didn’t
know why these relations worked.
• Isaac Newton was able to explain
the results of Galileo and Kepler,
and many other phenomena in
nature, with a few general principles
Newton’s Concepts
1) m (mass): the amount of matter an object contains
2) v (velocity): a body’s speed and direction
3) a (acceleration): the change in a body’s velocity
4) F (force): what is needed to change a body’s velocity
Newton’s Laws of Motion
1)
A body’s velocity will remain constant, unless acted upon by
an outside force = inertia
Newton’s Laws of Motion
1)
A body’s velocity will remain constant, unless acted upon by
an outside force = inertia
2)
A body’s acceleration depends on the force acting
upon it, and will be in the direction of that force.
Its resistance to acceleration depends on its mass.
In equation form, this is
F=ma
3)
For every force, there is an equal and opposite force.
Newton’s Law of Gravity
Any two objects with mass
experience an attractive force from
gravity that tries to pull them
towards each other. The strength of
this force depends on the masses of
the two bodies, and the distance
between their centers (squared). The
attractive force is greater for larger
masses and smaller distances.
Both objects feel the same force of
gravity, even if they have different
masses.
G m1 m2
F = 
d2
Explaining Galileo’s Experiment
m
M = Earth’s mass
Newton’s 2nd law:
F=ma
Newton’s law of gravity:
F = G m M / d2
F = m a = G m M / d2
a = G M / d2
An object’s acceleration does
not depend on its own mass. It
depends on the mass of the
other object (the Earth, in this
case).
Explaining Projectile Motion
The motion of a projectile can be
separated into two components:
horizontal & vertical.
Due to Newton’s 1st Law, the horizontal
motion remains unchanged because
there is no force acting on the ball in
that direction (ignoring air resistance).
The ball does experience a force in the
vertical direction (gravity), so the
vertical motion undergoes acceleration
downward (Newton’s 2nd law)
Explaining Projectile Motion
Explaining Weight and Weightlessness
You feel weight because of Newton’s third law. Gravity is pulling you
down, but the ground is not allowing you to fall. It must therefore be
exerting a force on you to keep you from falling. That force is the
weight that you feel.
If you were allowed
to fall, you would
not feel any weight.
So when you are in
free-fall, you feel
weightlessness.
Explaining Weight and Weightlessness
As an example, a sky diver is in free fall towards the earth, and
therefore feels weightlessness.
gravity
Explaining Weight and Weightlessness
If an additional force is applied to the sky diver that is not in the
direction of gravity, he will fall on a curved path because of inertia
(Newton’s 1st law).
inertia
gravity
Explaining Orbits
If the size of the force is just right, the sky diver falls on a curved
path that never reaches the ground and loops back on itself. This is
an orbit. The sky diver (or astronaut) experiences weightlessness
indefinitely.
inertia
gravity
Explaining Orbits
An orbit is a compromise between gravity and inertia.
Earth coalesced from gas and dust orbiting around the Sun, so it
was born with the inertia that maintains an orbit. If Earth had
been born stationary relative to the Sun (no inertia), it would have
fallen immediately into the Sun.
Explaining Orbits
Because planets are much less massive than the Sun, they induce
very little acceleration in the Sun, so the Sun barely moves and has
a very small “orbit”, while the planets are move a lot and have large
orbits because of the strong acceleration induced by the Sun.
Explaining Orbits
If the Sun was orbited by larger bodies, like other stars, it would
move much more in its orbit.
http://astro.unl.edu/naap/esp/animations/radialVelocitySimulator.html
https://phet.colorado.edu/en/simulation/gravity-and-orbits