RemindersReminders

Answering cell phones during class Answering cell phones during class shaves a little off your grade each time.shaves a little off your grade each time.

You will be dropped after six hours of You will be dropped after six hours of absence.absence.

The attendance requirement applies not The attendance requirement applies not only to students who only to students who cancan attend class, but attend class, but also to students whoalso to students who cannot cannot attend class. attend class.

CHAPTER 2:CHAPTER 2:Gravitation and the Waltz of the Planets

For the QuizFor the Quiz Know the basics of the Know the basics of the

Geocentric and Geocentric and Heliocentric theories, and Heliocentric theories, and be able to explain be able to explain planetary motion in terms planetary motion in terms of each.of each.

Be able to state Kepler’s Be able to state Kepler’s laws and understand their laws and understand their meaning.meaning.

Be able to define Be able to define “aphelion” and “aphelion” and “perihelion.”“perihelion.”

Be able to state Newton’s Be able to state Newton’s laws of motion, and laws of motion, and understand their understand their meaning.meaning.

Be able to state Newton’s Be able to state Newton’s law of gravitation and law of gravitation and understand its meaning.understand its meaning.

Define synodic and Define synodic and siderial period of a planet.siderial period of a planet.

Know the important Know the important observations Galileo observations Galileo made with his telescope, made with his telescope, and why those and why those observations were observations were important.important.

WHAT DO YOU THINK?WHAT DO YOU THINK?

What makes a theory scientific?What makes a theory scientific? What is the shape of the Earth’s orbit around the What is the shape of the Earth’s orbit around the

Sun?Sun? Do the planets orbit the Sun at constant speeds?Do the planets orbit the Sun at constant speeds? Do all the planets orbit the Sun at the same Do all the planets orbit the Sun at the same

speed?speed? How much force does it take to keep an object How much force does it take to keep an object

moving in a straight line at a constant speed?moving in a straight line at a constant speed? How does an object’s mass differ when How does an object’s mass differ when

measured on the Earth and on the Moon?measured on the Earth and on the Moon?

The scientific method is used to develop new scientific The scientific method is used to develop new scientific theories. Scientific theories are accepted when they theories. Scientific theories are accepted when they make testable predictions that can be verified using make testable predictions that can be verified using new observations and experiments.new observations and experiments.

Early models of the universe attempted to explain the Early models of the universe attempted to explain the motion of the five visible planets against the motion of the five visible planets against the background of “fixed” stars. The main problem was background of “fixed” stars. The main problem was that the planets do not move uniformly against the that the planets do not move uniformly against the background of stars, but instead appear to stop, move background of stars, but instead appear to stop, move backward, then move forward again. This backward backward, then move forward again. This backward motion is referred to as motion is referred to as retrograde retrograde motion.motion.

Ptolemy explained this motion using a Ptolemy explained this motion using a geocentric geocentric (Earth-(Earth-centered) model of the solar system in which the planets centered) model of the solar system in which the planets orbited the Earth indirectly, by moving on epicycles orbited the Earth indirectly, by moving on epicycles which in turn orbited the Earth.which in turn orbited the Earth.

In the geocentric model of the solar system developed by Ptolemy, A) the planets move with varying speeds in elliptical orbits around the

Earth. B) the planets move at constant speeds in circular orbits around the Earth. C) the planets move in circular epicycles around the Sun while the Sun

moves in a circular orbit around the Earth. D) the planets move in circular epicycles while the centers of the epicycles

move in circular orbits around the Earth.

When observing planetary motions from the Earth, the phrase “retrograde motion” refers to

A) the apparent westward motion of the planet (and the Sun, the Moon, and stars) across the sky due to the rotation of the Earth.

B) motion of the planet away from the Earth during part of its orbit. C) a slow eastward motion of the planet from night to night compared to

the background stars. D) a slow westward motion of the planet from night to night compared to

the background stars.

Nicolaus Copernicus developed the Nicolaus Copernicus developed the first heliocentricfirst heliocentric (sun-centered) model (sun-centered) model of the solar system. In this model, the of the solar system. In this model, the retrograde motion of Mars is seen retrograde motion of Mars is seen when the Earth passes Mars in its orbit when the Earth passes Mars in its orbit around the Sun. around the Sun.

1473-1543

We define special positions of the planets in their orbits depending We define special positions of the planets in their orbits depending where they appear in our sky. For example, while at a conjunction,where they appear in our sky. For example, while at a conjunction, a a planet will appear in the same part of the sky as the Sun, while at planet will appear in the same part of the sky as the Sun, while at opposition,opposition, a planet will appear opposite the Sun in our sky.a planet will appear opposite the Sun in our sky.

However, the cycle of these positions (a synodic However, the cycle of these positions (a synodic period) is different from the actual orbital period of the period) is different from the actual orbital period of the planet around the Sun (a sidereal period) because planet around the Sun (a sidereal period) because both the Earth and the planet orbit around the Sun.both the Earth and the planet orbit around the Sun.

The Copernican system for planetary motions is A) Earth-centered, with the planets, the Sun, and the stars mounted on

crystal spheres, pivoted to allow the correct motions around the Earth. B) Earth-centered, with the planets moving in epicycles around the Earth. C) Sun-centered, with the planets moving in elliptical orbits, the Sun being

at one focus of the ellipse. D) Sun-centered, with the planets moving in perfect circles around the Sun.

When Venus is at superior conjunction, A) it is at its smallest distance from the Earth. B) it is at its greatest angle from the Sun as seen from the Earth. C) its speed in its orbit has its greatest value. D) it is at its greatest distance from the Earth.

When Mars is at opposition, it is A) high in the sky at midnight. B) high in the sky at sunset. C) high in the sky at noon. D) rising at about midnight.

When a planet is seen at opposition, it is always A) at its most distant point from the Sun. B) at its closest point to the Sun. C) at its most distant point from the Earth. D) at its closest point to the Earth.

When a new “star” appeared in the sky during the 16th century, a Danish astronomer named Tycho Brahe (1546-1601) reasoned that the distance of the object may be determined by measuring the amount of parallax.

The apparent change in the location of an object due to the difference in location of the observer is called parallax.

Because the parallax of the “star” was too small to measure, Tycho knew that it had to be among the other stars, thus disproving the ancient belief that the “heavens” were fixed and unchangeable.

The phenomenon of parallax is A) the change in the apparent position of a nearby object compared to

background objects as a result of the motion of the object. B) the change in direction of motion of a planet from retrograde to direct

motion. C) the apparent change in angular size of an object as it moves toward or

away from an observer. D) the change in apparent position of a nearby object compared to

background objects as a result of the motion of the observer.

After Tycho Brahe’s death, After Tycho Brahe’s death, Johannes Kepler (pictured Johannes Kepler (pictured here with Tycho in the here with Tycho in the background) used Tycho’s background) used Tycho’s observations to deduce the observations to deduce the three laws of planetary three laws of planetary motion.motion.

1571-1630

KEPLER’S THREE LAWS OF PLANETARY MOTIONKEPLER’S THREE LAWS OF PLANETARY MOTION

LAW #1. The orbit of a planet around the Sun is an ellipse LAW #1. The orbit of a planet around the Sun is an ellipse with the Sun at one focus.with the Sun at one focus.

Kepler's first law states that a planet moves around the Sun A) in a circle, with the Sun at the center. B) in an elliptical orbit, with the Sun at one focus. C) in an elliptical orbit, with the Sun on the minor axis of the ellipse. D) in an elliptical orbit, with the Sun at the center of the ellipse.

The semimajor axis of an ellipse is A) the distance from the center of the ellipse to one end, along the largest

diameter of the ellipse. B) the distance from the center to one side of the ellipse, along the shortest

diameter of the ellipse. C) the distance from one focus to any point on the circumference of the

ellipse. D) half the distance between the foci of the ellipse.

The amount of elongation in a planet’s orbit is defined as The amount of elongation in a planet’s orbit is defined as its its orbital eccentricity.orbital eccentricity. An orbital eccentricity of 0 is a An orbital eccentricity of 0 is a perfect circle while an eccentricity close to 1.0 is nearly a perfect circle while an eccentricity close to 1.0 is nearly a straight line. straight line.

In an elliptical orbit, the distance from a planet to the In an elliptical orbit, the distance from a planet to the Sun varies. The point in a planet’s orbit closest to the Sun varies. The point in a planet’s orbit closest to the Sun is called Sun is called perihelion, perihelion, and the point farthest from the and the point farthest from the Sun is called Sun is called aphelion.aphelion.

KEPLER’S THREE LAWS OF PLANETARY MOTIONKEPLER’S THREE LAWS OF PLANETARY MOTION

LAW #2: A line joining the planet and the Sun sweeps out LAW #2: A line joining the planet and the Sun sweeps out equal areas in equal intervals of time.equal areas in equal intervals of time.

Planet moves Planet moves faster in its orbit faster in its orbit when closer to the when closer to the Sun.Sun.

Planet moves Planet moves slower in its orbit slower in its orbit when farther away when farther away from the Sun.from the Sun.

Kepler's second law states: A) A line joining a planet to the Sun moves equal distances along the

planet's orbit in equal times. B) A line joining a planet to the Sun sweeps through equal angles in equal

times. C) A line joining a planet to the Sun points in the same direction at all

times. D) A line joining a planet to the Sun sweeps out equal areas in equal times.

Kepler's second law states that a planet moves fastest when it A) passes through the minor axis. B) is closest to the Sun. C) is farthest from the Sun. D) is at conjunction.

KEPLER’S THREE LAWS OF PLANETARY MOTIONKEPLER’S THREE LAWS OF PLANETARY MOTION

LAW #3: The square of a planet’s sidereal period around the Sun LAW #3: The square of a planet’s sidereal period around the Sun is directly proportional to the cube of its semi-major axis.is directly proportional to the cube of its semi-major axis.

This law relates the amount of time for the planet to complete one orbit around the Sun to the planet’s average distance from the Sun.

If we measure the orbital periods (P) in years and distances (a) in astronomical units, then the law mathematically can be written as P2 = a3.

Kepler's third law tells us that A) the period of a planet in years is the same number as its semimajor axis

in AU. B) the square of a planet's period in years is the same number as the cube

of its semimajor axis in AU. C) the square of a planet's period in years is the same number as the fourth

power of its semimajor axis in AU. D) the cube of a planet's period in years is the same number as the square

of its semimajor axis in AU.

Kepler's third law can be described in which of the following ways? A) The time to complete one revolution of its orbit is dependent upon the

size or radius of the planet. B) The smaller the radius of a planet, the more rapidly it rotates on its axis. C) The smaller the orbit, the longer it takes for the planet to complete one

revolution. D) The larger the orbit, the longer it takes for the planet to complete one

revolution.

Galileo was the first to use a telescope to Galileo was the first to use a telescope to examine celestial objects. His examine celestial objects. His discoveries supported a heliocentric discoveries supported a heliocentric model of the solar system.model of the solar system.

Galileo discovered that Venus, like the Moon, undergoes a series of phases as seen from Earth. In the Ptolemaic (geocentric) model, Venus would be seen in only new or crescent phases. However, as Galileo observed, Venus is seen in all phases, which agrees with the Copernican model as shown.

1564-1642

Galileo also discovered moons in orbit around the planet Jupiter. This was further evidence that the Earth was not the center of the universe.

Galileo's early observations of the sky with his newly made telescope included

A) the discovery of Pluto. B) the discovery of the phases of Venus. C) the discovery of of Jupiter's magnetosphere. D) the discovery of retrograde motion in planets.

Which of the following statements CORRECTLY states the significance of Galileo's observation that Jupiter has satellites (moons)?

A) It showed that Jupiter must be four times the size of the Earth (because Jupiter has four moons and the Earth has one).

B) It showed that bodies can orbit an object other than the Earth. C) It was interesting but had no other particular significance. D) It showed that Jupiter must orbit the Sun, not the Earth.

Isaac Newton formulated three laws to Isaac Newton formulated three laws to describe the fundamental properties of describe the fundamental properties of physical reality.physical reality.

NEWTON’S THREE LAWS OF MOTIONNEWTON’S THREE LAWS OF MOTION

LAW #1: A body remains at rest or moves LAW #1: A body remains at rest or moves in a straight line at constant speed unless in a straight line at constant speed unless acted upon by a net outside force.acted upon by a net outside force.

LAW #2: The acceleration of an object is LAW #2: The acceleration of an object is proportional to the force acting on it.proportional to the force acting on it.

LAW #3: Whenever one body exerts a LAW #3: Whenever one body exerts a force on a second body, the second body force on a second body, the second body exerts an equal and opposite force on the exerts an equal and opposite force on the first body.first body.

1642-1727

According to Newton's first law, A) if no net force is acting upon an object, then both the object's speed and

direction of travel will be constant. B) the larger the rate of change of speed of an object, the larger the force

acting upon the object. C) an applied force always causes a change in the speed of an object. D) an applied force always causes a change in the direction of travel of an

object.

The acceleration of an object is defined as A) the rate of changes of its speed. B) the rate of change of its velocity. C) the rate of change of its direction of travel. D) the rate of change of its position.

Which of the following four objects or persons is NOT accelerating? A) A bicyclist gradually slowing down on a straight road while coasting

toward a stop sign B) A motorcyclist traveling around a circular racetrack at a constant speed C) An apple falling to the ground from an apple tree D) An Olympic swimmer exerting considerable force to maintain a

constant speed in a straight line through the water

Two spaceships that have different masses but rocket engines of identical force are at rest in space. If they fire their rockets at the same time, which ship will speed up faster?

A) The one with the lower mass B) The one with the higher mass C) They will increase speed at the same rate because they have identical

rocket engines. D) They will not speed up at all, but move at a constant speed because they

are in space and the rocket has nothing against which to push.

An unbalanced force acting on an object will ALWAYS cause it to A) change its direction of travel. B) change its speed or its direction of travel or both. C) change its acceleration. D) change its speed.

Which of the following statements is a CORRECT version of Newton's third law?

A) Whenever some object A exerts a force on some other object B, B must exert a force of equal magnitude on A in the same direction.

B) Whenever some object A exerts a force on some other object B, B must exert a force of equal magnitude on A in the opposite direction.

C) Whenever two forces act, they must be equal in magnitude and opposite in direction.

D) Whenever any object feels some force, it must also feel another force of equal magnitude in the opposite direction from some other source.

Newton also discovered that gravity, the force that Newton also discovered that gravity, the force that causes objects to fall to the ground on Earth, is the causes objects to fall to the ground on Earth, is the same force that keeps the Moon in its orbit around same force that keeps the Moon in its orbit around the Earth. the Earth.

NEWTON’S LAW OF UNIVERSAL GRAVITATIONNEWTON’S LAW OF UNIVERSAL GRAVITATION

Two objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

With his laws, Newton was able to derive Kepler’s three laws, as well as predict other possible orbits.

The force of gravity between two objects is proportional to A) the sum of their masses. B) the difference of their masses. C) the ratio of their masses. D) the product of their masses.

Newton’s laws were applied to other objects in our Newton’s laws were applied to other objects in our solar system.solar system.

Using Newton’s methods, Edmund Halley worked out the details of a comet’s orbit and predicted its return.

Deviations from Newton’s Laws in the orbit of the planet Uranus led to the discovery of the eighth planet, Neptune.

How was the planet Neptune discovered? A) It was discovered by mathematical prediction using Newton's laws. B) It happened to pass close to Jupiter in the sky and was discovered by an

astronomer studying Jupiter. C) It was discovered accidentally during a telescopic survey of the sky. D) No one knows—it has been known since ancient times.

accelerationangular momentumaphelionastronomical unitconfiguration (of a planet)conjunctionconservation of angular

momentumcosmologyellipseelongationfocus (of an ellipse)forceGalilean moons (satellites)gravityheliocentric cosmology

hyperbolainferior conjunctionKepler’s lawskinetic energylaw of equal areaslaw of inertialight-yearmassmodelmomentumNewton’s laws of motionOccam’s razoroppositionparabolaparallaxparsec

perihelionphysicspotential energyretrograde motionscientific methodscientific theorysemimajor axis (of an ellipse)sidereal periodsuperior conjunctionsynodic perioduniversal constant of gravitationuniversal law of gravitationvelocityweightwork

Key TermsKey Terms