Chapter 3: Inertia and Newton's Law of Motion

Inertia

Galileo developed the idea of inertia.
Newton used it as his 1st law of motion.
Net force = The sum of all forces pulling in various directions.
If the net force = 0, inertia is constant.
A body that is not moving will remain motionless = constant velocity.
A moving body’s motion will remain constant at the same speed and in the same direction = constant velocity.

Newton understood that orbiting objects, such as the Moon and Earth, have constantly changing velocity because of the changing direction.
Newton realized that a force causes this changing velocity.

When an object accelerates, its velocity changes.
Its speed may increase in some length of time.
Its speed may decrease in some time = a deceleration or a negative acceleration.
If an object’s direction of motion changes its velocity changes even though its speed may remain constant = acceleration.
Units are $m/s^{\Lambda }2$

Mass - amount of matter in a body.
Impossible to count the number of atoms and molecules in a body.
Express the mass in kilograms (kg).
Mass is NOT the same as weight.
Weight is the force of gravity on a mass.
Confusion is caused when people use the kg for both mass and weight - wrong.
The unit of weight is the Newton.

With the quantities we have defined, we can state Newton’s 2nd law of motion.
A net force causes of body with a mass to accelerate and the relationship is acceleration = net force/mass (a=F/m)
It is a simple equation, but it explains the motions of all objects on Earth, in the solar system, and throughout the Universe.

When two objects interact with each other the force of object 1 on object 2 is equal to the force of object 2 on object 1.
Action = Reaction

Newton needed to develop a law for the force of gravity for his laws of motion.
Force of gravity depends on all masses: for two objects these are M for the larger mass and m for the smaller mass.
Force of gravity depends on the separation.
Greater separation $\rightarrow$ weaker force.
Weakens as (1/separation) = “inverse square law”
Force of gravity never goes to zero, no matter how far away.
Newton’s equation:
$F(G) = G*(Mm/(d^{\Lambda }2))$
G = universal gravitational force constant.
M = the mass (kg) of the larger object.
m = the mass (kg) of the smaller object.
d = the separation (m) between the two objects.

The force of Earth’s gravity on the Moon is $F_{G}=G(M_{Earch}\cdot m_{moon}/d^{\Lambda }2)$
However, the Earth and Moon respond differently to the same force because they have different masses.
For the Moon a_moon = F_G/m_moon
For the Earth a_Earth = F_G/M_Earth
NOTE: The force of gravity causes both the Moon and Earth to accelerate.

Measuring orbits is the fundamental way of measuring masses in astronomy.
To make things simple, assume M>>m.
Combine Newton’s 2nd law of motion and his law of gravity to get M = dV^2/G.
The mass equation can be rewritten as a modified version of Kepler’s 3rd law $(P^{\Lambda }2 = a^{\Lambda }3).$
Newton’s version: $M = (4\cdot pi^{\Lambda }2\cdot d^{\Lambda }3)/(GP^{\Lambda }2)$
This can be used for any planet.

We experience “surface gravity” here on Earth every day, and that would also be true on the Moon or another planet.
Surface gravity is the acceleration caused by a planet’s (such as Earth) gravity.

The surface gravity determines how fast an object must travel to escape into space.
The equation can be found from Newton’s laws of motion and gravity.
Earth’s escape velocity is found using its mass and radius.
The moon’s escape velocity is much less because its mass and radius are less

A planet’s ability to have an atmosphere depends on two things:
Distance from the Sun, which determines the temperature of the atmospheric gas: closer to the Sun the gas is hotter and moves faster (molecules in hot temperature are more active).
The escape velocity of the planet.
If the gas speed > escape speed, the planet cannot hold an atmosphere.

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