Announcements

Quiz #1 is this Friday. Study guide being handed out

Readings: Chapters 1-7 in Ferris

Lectures 1-8 (don’t forget planetarium)

Planetarium EC show moved to next Monday, when we hope it will be easier to get to campus

Please turn off all electronic devices

Don’t forget to sign the attendance sheet

a) The Coriolis effect

b) The parallaxes of the stars

c) The North Star moves closer to the horizon as you go south

d) The phases of Venus

e) The 24 cycle of day and night

What is one piece of evidence that the Earth spins on its axis?

Coriolis wrote about waterwheels and spinning coordinate system, not specifically about the rotating Earth

Lecture 7: Forces

Astronomy 1143 – Spring 2014

Key IdeasUnits! (again)•Metric Units of meters, seconds, kilograms•Mass and weight are not the same

• Mass is how much stuff you have and does not depend on where you are

•Unit of force is the Newton

How do we see the unseen?•To look for the existence of dark matter and black holes, we need to discuss how forces affect objects.

Key Ideas Newton’s Laws of Motion

•Tell us how force affects motions

1st Law of Motion: •Objects in motion remain in motion unless acted upon by a force.

2nd Law of Motion: •Acceleration is proportional to the force & inversely proportional to the mass (F=ma)

3rd Law of Motion:•To every action there is an equal and opposite reaction.

The Metric SystemAstronomers use the Metric System:

Length in Meters

Mass in Kilograms

Time in Seconds

All scientists use Metric Units

Standard Prefixes

103 = kilo- (kilogram, kilometer)

106 = mega- (megawatt, megayear)

109 = giga- (gigabyte, gigayear)

1012 = tera- (terabyte, terawatt)

102 = centi- (centimeter)

103 = milli- (millimeter, millisecond)

106 = micro- (microsecond, micron)

109 = nano- (nanosecond, nanometer)

Units of Length

The basic unit of length is the meter (m)

Traditional Definition:• 1 ten-millionth the distance from the North Pole

to the Equator of the Earth.

Modern Definition:• The distance traveled by light in a vacuum in 1 /

299792458th of a second.

Commonly use meters and kilometers.

Units of Time

The basic unit of time is the second (s):

Traditional Definition:

• 1/86400th of the mean solar day. Modern Definition:

• 9,192,631,770 oscillations of a Cesium-133 atomic clock.

Common Uses:

seconds, minutes, hours, years

Units of Mass

The basic unit of mass is the kilogram (kg):

Traditional Definition:

• 1 kg = mass of 1 liter of pure water.

Modern Definition:

• 1 kg = mass of the international prototype of the kilogram

• A platinum-iridium alloy weight kept at the International Bureau of Weights & Measures in Sèvres, France.

Standard Kilogram(Sèvres, France)

Mass versus Weight

Mass & Weight are NOT the same!Mass:

The amount of matter in an object.

Weight:

The force of gravity on an object.

Of the two, Mass is more fundamental.• Mass is the same everywhere.• Weight depends on the local gravity.

Mass & Weight Units

Mass & Weight have different unitsMetric:

• Mass measured in kilograms• Weight measured in Newtons (unit of force)

English:• Mass measured in slugs• Weight measured in pounds

Don’t erroneously mix pounds & kilograms!

Weight of Elvis at the time of his death at various locations in the Solar System

Location Weight Mass

Earth 255 lbs 116 kg

Moon 42.2 lbs 116 kg

Mars 97.0 lbs 116 kg

Jupiter 597 lbs 116 kg

Sun 7144 lbs 116 kg

Principia Mathematica

In 1684, Newton was prevailed upon by Edmond Halley to publish his work on motion & gravitation.

• Newton took 3 years to reproduce his work• Halley paid the publication expenses out of his

own pocket, after wheedling, cajoling, & flattering Newton into finishing it in 1687.

Philosophiae Naturalis Principia Mathematica(Mathematical Principles of Natural Philosophy)

Isaac Newton

Edmund Halley

Newton’s Synthesis

The Principia is one of the most important books in history:

• Laid the foundations of modern physics.• Swept away the last vestiges of the Aristotelian

view of the World.• Replaced older, empirical descriptions with

quantifiable, physical explanations of the nature of the World.

Unified all motions into three simple laws.

What is the force on an object?

We all have a sense of what a force is – a push or pull, for example

In physics, force has a very specific meaning

A force changes the velocity of an object

Newton’s Three Laws of Motion describe the basic properties of forces

This is not what we mean by “force” in astrophysicsobject?

Forces

The four fundamental forces of Nature

Strong force• Binds quarks into nucleons

Electromagnetic force• Binds electrons and protons into atoms

Weak force• Causes radioactivity

Gravitational force• Attracts masses

How much mass is there?

How do we measure the mass (the amount of stuff) in an object?

We measure mass by observing the gravitational force

This works because of the basic nature of gravity

Mass exerts a gravitational force

No mass = no force

First Law of Motion

Every body will stay in a state of rest or uniform motion in a straight line unless that state is changed by forces impressed upon it.

Often called the Law of Inertia• Property of matter that it resists having its state

of motion changed.

Important property is the net force exerted.

Net Force is Zero, therefore No Net Motion

Speed versus VelocityAll motion is composed of two parts:

• Speed (how fast is it going)• Direction (where is it going)

The combination is called the velocity:• Velocity = how fast, and in what direction.

Change in motion is acceleration• Measures how fast the velocity changes.• Change can be in speed, or direction, or both!• Units of acceleration are meters per second per

second

Falling Apple is accelerating:Changing Speed

(gets faster as it falls)Same Direction

(always falls down)

Ball Swung around on a String is accelerating:

Same Speed,(in uniform circular motion)

Changing Direction(swinging around the circle)

Second Law of Motion

The size of an acceleration is directly proportional to the force applied, and inversely proportional to the mass of the body.

The resulting acceleration is in the same direction as the applied force.

The Second Law of Motion

Expressed Mathematically:

• Acceleration is proportional to force,

and inversely proportional to mass.

• Force is mass times acceleration.

Force, Mass, & AccelerationSecond law has two parts:1) Quantifies "force" in terms of its effects on

a massive body.• Forces produce accelerations.• The more mass a body has, the less it

can be accelerated by a given force.2) Forces and accelerations have directions

• Acceleration is in the same direction as the applied force.

Unit of Force: Newton

The metric unit of force is the Newton

1 Newton is the amount of force needed to accelerate a 1 kg object by 1 m/s in 1 second

In other words, Newtons can be written as

Teddy Bear swung around on a String

Acceleration=Forcemass

Force

Accelerating around a circle

The size of the acceleration needed to keep an object going around in a circle is

a = acceleration

v = speed

r = radius of circle

When we see objects moving in a circle, we know that the force on them has to provide that much acceleration

Preview of Dark Matter DiscussionWe can observe the motion of stars in galaxies.We can calculate how much force is being exerted on those starsWe can count up the amount of matter than we see.We can calculate how much gravitational force that matter has

Too little matter for the forces that we measure

Third Law of Motion

For every force applied to a body, there is an equal and oppositely directed force exerted in response.

Or,

"To every action there is an equal & opposite reaction."

Astronaut Dave Scott learns to appreciate Newton’s 3rd Law

Rocket Thrust

A Complete Description

Newton’s Laws of Motion provide a complete, quantitative explanation of the motions of objects.

• They are simple & easily stated in either words or mathematics.

• They are Universal Physical Laws applicable to all objects on the Earth or in the heavens.

• They unify phenomena, explaining all motions with the same set of self-consistent rules.