# Chapter 3: Inertia and Newton's Law of Motion

Latest Version

Published 2 years ago

Latest Version

Published 2 years ago

## 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**.

### Speed and Velocity

**Speed**is a change of position in some amount of time, such as m/s or km/h.**Velocity**is a speed in a particular**direction**.- NOTE: The units, m/s, are still the same, which can cause confusion.
- If the speed remains constant, but the direction changes, the velocity changes.

### Orbital Motion and Gravity

- 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.

### Acceleration

- 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

- 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.

## Newton's Laws

### Newton’s 2nd Law of Motion

- 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.

### Newton’s 3rd Law of Motion

- 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’s Law of Gravitational Force

- 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.

### Gravity is important for Astronomy

- Astronomical objects have:
- Huge masses $\rightarrow$ huge force of gravity.
- Huge separations $\rightarrow$ weak force of gravity.
- Small separations $\rightarrow$ huge force of gravity.
- Mass is only a positive quantity.
- Gravity cannot cancel out.
- Gravity never stops, even at the largest distances.

### Earth and Moon

- 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 Masses

- 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.

## The Sun, Surface Gravity, Escape Velocity and Planets

### The Mass of the Sun

- To measure the Sun’s mass we can use Earth’s orbit.
- d = 1 AU
- P = 1 year
- G = $6.67 \cdot 10^{\Lambda }-11$
- This results in about 300,000 M
_{Earth}

### Surface Gravity

- 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.

### Escape Velocity

- 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**

### Atmospheres of Planets

- 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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