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.

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 amoon = FG/mmoon
• For the Earth aEarth = FG/MEarth
• 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 MEarth

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 its mass and radius are less

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.