Newton and Gravity

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Newton and Gravity
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State of Physics

• By now the world knew
• Bodies of different weights fall at the same
  speed
• Bodies in motion did not necessarily come to rest
• Moons could orbit different planets
• Planets moved around the Sun in ellipses with the
  Sun at one focus (Keplers 1st law)
• The orbital speeds of the planets obeyed Keplers
  2nd and 3rd laws

But why??? Isaac Newton put it all together.
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Newtons Concepts

• m (mass) How much stuff something contains
• v (velocity) A bodys speed and direction
• 3) a (acceleration) The change in a bodys
  velocity
• 4) F (force) What is needed to change a bodys
  velocity

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Newtons Laws of Motion

• A bodys velocity will remain constant, unless
  acted upon by an outside force inertia

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Newtons Laws of Motion

• A bodys velocity will remain constant, unless
  acted upon by an outside force inertia

• A bodys 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 m a

• For every force, there is an equal and opposite
  force.

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Newtons Law of Gravity

• There is an attractive force between two bodies
  called gravity. The force of gravity depends on
  the masses of the two bodies, and their
  separation (squared) the larger the mass, the
  greater the attraction the larger the
  separation, the smaller the attraction.

G m1 m2
Note that the word separation means the
distance between the centers of the two bodies.
F ????
r 2
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Example of Gravity a Thrown Ball

• When you throw a ball, there are 2 motions
  horizontal vertical.

The horizontal motion obeys Newtons first law
(bodies in motion will stay in motion). The
attractive force of gravity causes the upward
motion to decelerate, and then change direction.
You see the composite of the two behaviors.
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Example of Gravity a Thrown Ball
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Example of Gravity Weightlessness

• You feel weight because of Newtons 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.
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Example of Gravity Weightlessness

• You feel weight because of Newtons 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.

As an example, a sky diver is in free fall
towards the earth, and therefore feels
weightlessness.
gravity
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Example of Gravity Weightlessness

• If an object is dropped from rest, it will
  free-fall until it reaches the Earth.
• However, if the object is given a velocity
  parallel to the ground, the compromise between
  Newtons 1st law of motion and gravity will be a
  free-fall that always misses the Earth, which is
  an orbit. Because astronauts orbit the Earth in
  free-fall, they feel weightlessness.

velocity
gravity
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Example of Gravity a Planetary Orbit

• Imagine a planet moving sideways with respect to
  the Sun. Newtons first law says that it will
  continue to move sideways. But the law of
  gravity says that it will also be pulled towards
  the Sun. The result is a combination motion, in
  which the planet falls towards the Sun, but
  misses. This is an orbit.

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Example of Gravity a Planetary Orbit

• Imagine a planet moving sideways with respect to
  the Sun. Newtons first law says that it will
  continue to move sideways. But the law of
  gravity says that it will also be pulled towards
  the Sun. The result is a combination motion, in
  which the planet falls towards the Sun, but
  misses. This is an orbit.

If the Earth had been born at rest relative to
the Sun, it would have fallen immediately into
the Sun.
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Example of Gravity Binary Stars

• According to Newtons third law, just as the Sun
  exerts a force on the Earth, the Earth exerts a
  force on the Sun. However, since the Sun is so
  much more massive, it doesnt move much. But if
  the Earth were more massive, the Sun would move.

Thus, Keplers 3rd law is not quite complete.
The true law is (M1 M2) P2 a3
where the orbital period (P) is in years, the
semi-major axis (a) is in A.U.s, and the masses
(M) are in solar units.
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Example of Gravity Binary Stars

• According to Newtons third law, just as the Sun
  exerts a force on the Earth, the Earth exerts a
  force on the Sun. However, since the Sun is so
  much more massive, it doesnt move much. But if
  the Earth were more massive, the Sun would move.

Thus, Keplers 3rd law is not quite complete.
The true law is (M1 M2) P2 a3
where the orbital period (P) is in years, the
semi-major axis (a) is in A.U.s, and the masses
(M) are in solar units.
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Example of Gravity Tides

• The effects of gravity do not depend on the
  composition of a body, just its mass and
  distance. The Moon exerts a force on the Earth,
  but since the Earth has a finite size, this force
  is different from one side of the Earth to the
  other. The side of the Earth near the Moon gets
  pulled most, the center of the Earth less, and
  the backside least of all. Since most of the
  Earth is solid, it doesnt move much, but water
  reacts to this difference. So we have tides.

d
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Summary

• Newtons concepts mass, velocity, acceleration,
  force
• Newtons Laws of Motion
• inertia
• Force mass x acceleration
• For every force, there is an equal and opposite
  force
• Newtons Law of Gravity
• Gravitational force GM1M2/r2
• Explains trajectory of projectiles, planetary
  motion, tides, etc.
• Corrected version of Keplers 3rd law
  (M1M2)P2a3
• Homework 2 due tomorrow morning