Newton and Gravity Newton and Gravity

State of PhysicsBy 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 (Kepler’s 1st law)

• The orbital speeds of the planets obeyed Kepler’s 2nd and 3rd laws

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

Newton’s Concepts

1) m (mass): How much stuff something 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 Motion1) A body’s velocity will remain constant, unless acted upon by

an outside force = inertia

Newton’s Laws of Motion

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

1) A body’s velocity will remain constant, unless acted upon by an outside force = inertia

3) For every force, there is an equal and opposite force.

F = m a

Newton’s 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.

Note that the word “separation” means the distance between the centers of the two bodies.

F = G m1 m2

r 2

Galileo found that objects with different masses feel same acceleration from the Earth. Why is that?

Newton’s 2nd law: F = m a

Newton’s law of gravity: F = G m M / r2

F = m a = G m M / r2

a = G M / r2

m

M = Earth’s mass

An object’s acceleration is independent of its mass, anddepends only on the mass of the other object

Example of Gravity – a Thrown Ball

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

The horizontal motion obeys Newton’s 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.

Example of Gravity – a Thrown Ball

Example of Gravity – 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.

Example of Gravity – Weightlessness

As an example, a sky diver is in free fall towards the earth, and therefore feels weightlessness.

gravity

Example of Gravity – 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).

gravity

inertia

Example of Gravity – 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.

gravity

inertia

Example of Gravity – Orbits

If the Earth had been born at rest relative to the Sun, it would have fallen immediately into the Sun.

Example of Gravity – Binary Stars

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.

Example of Gravity – Binary Stars

If the Sun was orbited by larger bodies, like other stars, it would move much more in its orbit.

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Summary• Newton’s concepts: mass, velocity, acceleration, force• Newton’s Laws of Motion

• inertia• Force = mass x acceleration• For every force, there is an equal and opposite force

• Newton’s Law of Gravity• Gravitational force = GM1M2/r2

• Explains trajectory of projectiles, planetary motion, tides, etc.• Corrected version of Kepler’s 3rd law: (M1+M2)P2=a3