Copyright © 2015, W. W. Norton & Company

Lecture SlidesCHAPTER 3: Laws of Motion

Prepared by Lisa M. Will, San Diego City College

Understanding Our UniverseSECOND EDITION

Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal

Laws of Motion

Describe planetary orbits.

Understand laws of motion and gravity.

Planetary Orbits

Copernicus realized the Solar System was heliocentric—centered on the Sun.

Planets exhibit apparent retrograde motion due to their distances from Earth and orbits around the Sun.

Kepler’s 1st Law: Planetary orbits are ellipses.

Each ellipse has two foci. The Sun is at one focus

of a planet’s elliptical orbit.

Planetary Orbits: Ellipses

Planetary Orbits: Semimajor Axis

An ellipse has a size, described by the semimajor axis.

The longest length (major axis) is twice the length of the semimajor axis.

Planetary Orbits: Eccentricity

Each orbit has a shape as well as a size.

The eccentricity describes the shape - how elongated the ellipse is and how far the foci are separated.

Class Question

Does Kepler’s 1st Law allow for a circular

planetary orbit?

A. Yes

B. No

Planetary Orbits: Remember

A circle is an ellipse with an eccentricity of zero.

Most planetary orbits are very close to circular.

The slight deviations from circular are why Kepler’s Laws are needed to explain orbits!

Planetary Orbits: Remember (Cont.)

Planetary Orbits: Remember (Cont.)

Planetary Orbits: Kepler’s 2nd Law

Kepler’s 2nd Law: the Law of Equal Areas.

The line between the Sun and the planet “sweeps” out equal areas in equal times.

Planetary Orbits: What is Kepler’s 2nd Law

What does Kepler’s 2nd law mean?• A planet will go fastest

when closest to the Sun.

• It will go slowest when farthest from the Sun.

Class Question

The Earth is closest to the Sun in January and

furthest from the Sun in July. When is the Earth

moving the fastest In its orbit?

A. January

B. July

Planetary Orbits: Kepler’s 3rd Law

Kepler’s 3rd Law: Distant planets

take longer to orbit the Sun.

Distant planets travel at slower speeds.

For P = orbital period in years and a = semimajor axis in AU

P2 = a3

Class Question

The semimajor axis of Earth’s orbit is 1 AU. The

semimajor axis of Saturn’s orbit is 9.5 AU. What Saturn’s orbital period in Earth years?

Use Kepler’s 3rd law!

P2 = a3

So P = a3/2

Answer: Ps/PE = (aS/aE)3/2 = (9.5/1)1.5= 29. So 1 year on Saturn is about 29 Earth years!

Galileo

Galileo Galilei was the first to use a telescope for astronomical observations, around the year 1609.

He made important discoveries (you could have, too, if you were the first to look at the night sky with the newly invented telescope!)

Galileo discovered Jupiter’s four largest moons, observing them to orbit Jupiter over several nights. He also observed phases of Venus.

Both discoveries were controversial. => Contradicted the widely held geocentric view of the universe and were consistent with a heliocentric view

Galileo: Model of Motion

He experimented with falling and moving objects and crafted a model of motion.

=>An object in motion will continue moving along a straight line with a constant speed until an unbalanced force acts on it.

He also came up with formulas for distance, velocity and acceleration as a function of time. For constant (uniform) acceleration, such as for falling bodies, starting from rest, the distance travelled is proportional to the time squared. (d ~ t2 )

Laws of Motion

Sir Isaac Newton discovered laws that explain why objects in the universe move the way they do.

Newton’s Laws of Motion and Law of Gravity explain why planets orbit the Sun, following Kepler’s observationally-derived Laws.

Laws of Motion: Newton’s First Law of Motion

Newton’s First Law of Motion: Galileo’s result

(also called the law of Inertia) A moving object will stay in constant motion.

• “Constant” motion means at a constant speed and in a constant direction.

• An object at rest stays at rest.

Laws of Motion: Newton’s Second Law

Newton’s Second Law: Net forces cause changes in motion => acceleration.

Laws of Motion: Example

In this example, the coffee cup is at rest with respect to the car that it is in.

As long as the car travels at a constant speed and direction, the coffee will be level.

Laws of Motion: Acceleration

A change in speed and/or direction is called acceleration.

Acceleration measures how quickly a change in motion takes place.

Acceleration = (change in velocity)/time

a = (vfinal- vinitial)/time interval

Laws of Motion: Acceleration – Force Vs. Mass

A net force causes acceleration. Mass resists changes in motion.

• More mass => less acceleration for a given force.

• Greater forces => greater accelerations.

• F = ma (or a = F/m)

Laws of Motion: Acceleration – Force Vs. Mass (Cont.)

•Blue arrow is applied force , green arrow is

acceleration

Laws of Motion: Acceleration – Force Vs. Mass (Cont.)

Laws of Motion: Acceleration – Force Vs. Mass (Cont.)

Laws of Motion: Summary Newton’s Third Law: forces occur in action-reaction

pairs. The two forces are equal in strength. The two forces have opposite directions. Note that the strengths of the forces between the Earth

and Moon are equal, but the accelerations are not!

Law of Gravity

All objects on Earth have been experimentally shown to fall with the same acceleration, g = 9.8 m/s2.

Experiments on the Moon have shown the same phenomenon but with a different value of the acceleration (about 1/6 of Earth’s) due to the Moon’s different mass and radius.

Weight is the product of your mass and the acceleration due to gravity:

Because different worlds have different gravitational accelerations, you would weigh a different amount elsewhere!

Law of Gravity: Weight

weightF m g

The acceleration due to gravity on the Moon is 1/6 g.

The acceleration due to gravity on Mars is 1/3 g. On

which of these worlds would you weigh more?

A. Mars

B. Moon

Class Question

Law of Gravity: Definition

Gravity is an attractive, mutual force between any two objects with mass.

It depends on the objects’ masses. It depends on the distance between them.

Law of Gravity: Mass Vs. Force

The greater the mass, the greater the gravitational force they experience.

The force of gravity includes the product of both masses.

Law of Gravity: Distance Vs. Force

The greater the distance between the objects, the weaker the gravitational force.

The gravitational force is dependent on the inverse square of the distance between the two objects.

Putting the pieces together:• G is the universal gravitational constant.

• The m terms are the two masses.

• The r is the separation distance.

This form is known as an inverse square law.

Law of Gravity: Inverse Square Law

221

grav r

mmGF

Object A and Object B initially have the same mass.

If Object A’s mass increased, what would happen to

the gravitational force between the two masses?

A. The force would decrease.

B. The force would increase.

Class Question

Object A and Object B have the same mass. If the

distance between the two objects increased, what

would happen to the gravitational force between the

two masses?

A. The force would decrease.

B. The force would increase.

Class Question

Law of Gravity: Orbits and Satellite

Orbits are one body falling around another.

The less massive object is considered a satellite of the more massive object.

Law of Gravity: Orbits and Satellite (Cont.)

Law of Gravity: Orbits and Satellite (Cont.)

Law of Gravity: Orbits and Satellite (Cont.)

Law of Gravity: Orbits and Satellite (Cont.)

Law of Gravity: Centripetal Force

Gravity provides the centripetal force that holds a satellite in its orbit.

If moving too fast or too slow, orbit will not be circular.

Law of Gravity: Centripetal Force (Cont.)

Law of Gravity: Centripetal Force (Cont.)

Law of Gravity: Astronauts

Astronauts float freely in the space station because they and the station are both falling at the same rate around Earth.

Gravity is acting on the astronauts!

Law of Gravity: Relation to Planetary Orbits

How does this relate

to planetary orbits? Gravity changes both the direction

and the speed of the planet. Explains Kepler’s

Second Law.

Law of Gravity: Relation to Planetary Orbits (Cont.)

Law of Gravity: Relation to Planetary Orbits (Cont.)

Law of Gravity: Bound or Unbound Orbit

An object’s speed at its closest approach will determine the shape of the orbit and if the orbit will be bound or unbound.

For example, an comet with an unbound orbit will orbit the Sun once and never return.

Newton and Kepler

Newton derived Kepler’s Laws from his law of gravity.• Physical laws explain Kepler’s results!

Newton’s laws were tested by Kepler’s observations.• Their agreement showed that Newton’s law of gravitation

was correct.

Chapter Summary

Kepler’s Laws describe planetary orbits.• Planetary orbits are ellipses.

• Planets sweep out equal areas in their orbits in equal times.

• The larger the orbit of a planet, the longer the orbital period of the planet.

Newton’s Laws of Motion and Gravitation explain why Kepler’s Laws work.

Astronomy in Action

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Velocity, Force and Acceleration

AstroTour

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Elliptical Orbits

AstroTour

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Newton’s Laws and Universal Gravitation

AstroTourVelocity, Acceleration, Inertia

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Nebraska Applet

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Ptolemaic Orbit of Mars

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Ptolemaic Phases of Venus

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Retrograde Motion

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Eccentricity Demonstrator

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Planetary Configurations Simulator

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Planetary Orbit Simulator

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Synodic Period Calculator

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Kepler’s Third Law

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Phases of Venus

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Newton’s Law of Gravity Calculator

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Gravity Algebra

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Planetary Orbit Simulator

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Earth Orbit Plot

Copyright © 2015, W. W. Norton & Company

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CHAPTER 3: Laws of Motion

This concludes the Lecture slides for

Understanding Our UniverseSECOND EDITION

Stacy Palen, Laura Kay, Brad Smith, and George Blumenthal

Prepared by Lisa M. Will, San Diego City College