Download Chapter 2 - AstroStop

Reminders
Answering cell phones during class
shaves a little off your grade each time.
 You will be dropped after six hours of
absence.
 The attendance requirement applies not
only to students who can attend class, but
also to students who cannot attend class.

CHAPTER 2:
Gravitation
and the
Waltz of the
Planets
For the Quiz




Know the basics of the
Geocentric and
Heliocentric theories, and
be able to explain
planetary motion in terms
of each.
Be able to state Kepler’s
laws and understand their
meaning.
Be able to define
“aphelion” and
“perihelion.”
Be able to state Newton’s
laws of motion, and
understand their
meaning.



Be able to state Newton’s
law of gravitation and
understand its meaning.
Define synodic and
siderial period of a planet.
Know the important
observations Galileo
made with his telescope,
and why those
observations were
important.
WHAT DO YOU THINK?






What makes a theory scientific?
What is the shape of the Earth’s orbit around the
Sun?
Do the planets orbit the Sun at constant speeds?
Do all the planets orbit the Sun at the same
speed?
How much force does it take to keep an object
moving in a straight line at a constant speed?
How does an object’s mass differ when
measured on the Earth and on the Moon?
The scientific method is used to develop new scientific
theories. Scientific theories are accepted when they
make testable predictions that can be verified using
new observations and experiments.
Early models of the universe attempted to explain the
motion of the five visible planets against the
background of “fixed” stars. The main problem was
that the planets do not move uniformly against the
background of stars, but instead appear to stop, move
backward, then move forward again. This backward
motion is referred to as retrograde motion.
Ptolemy explained this motion using a geocentric (Earthcentered) model of the solar system in which the planets
orbited the Earth indirectly, by moving on epicycles
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
first heliocentric (sun-centered) model
of the solar system. In this model, the
retrograde motion of Mars is seen
when the Earth passes Mars in its orbit
around the Sun.
1473-1543
We define special positions of the planets in their orbits depending
where they appear in our sky. For example, while at a conjunction, a
planet will appear in the same part of the sky as the Sun, while at
opposition, a planet will appear opposite the Sun in our sky.
However, the cycle of these positions (a synodic
period) is different from the actual orbital period of the
planet around the Sun (a sidereal period) because 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,
Johannes Kepler (pictured
here with Tycho in the
background) used Tycho’s
observations to deduce the
three laws of planetary
motion.
1571-1630
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #1. The orbit of a planet around the Sun is an ellipse
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
its orbital eccentricity. An orbital eccentricity of 0 is a
perfect circle while an eccentricity close to 1.0 is nearly a
straight line.
In an elliptical orbit, the distance from a planet to the
Sun varies. The point in a planet’s orbit closest to the
Sun is called perihelion, and the point farthest from the
Sun is called aphelion.
KEPLER’S THREE LAWS OF PLANETARY MOTION
LAW #2: A line joining the planet and the Sun sweeps out
equal areas in equal intervals of time.
Planet moves
slower in its orbit
when farther away
from the Sun.
Planet moves
faster in its orbit
when closer to 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 MOTION
LAW #3: The square of a planet’s sidereal period around the Sun
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
examine celestial objects. His
discoveries supported a heliocentric
model of the solar system.
1564-1642
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.
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
describe the fundamental properties of
physical reality.
NEWTON’S THREE LAWS OF MOTION
LAW #1: A body remains at rest or moves
in a straight line at constant speed unless
acted upon by a net outside force.
LAW #2: The acceleration of an object is
proportional to the force acting on it.
LAW #3: Whenever one body exerts a
force on a second body, the second body
exerts an equal and opposite force on the
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
causes objects to fall to the ground on Earth, is the
same force that keeps the Moon in its orbit around
the Earth.
NEWTON’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
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.
Key Terms
acceleration
angular momentum
aphelion
astronomical unit
configuration (of a planet)
conjunction
conservation of angular
momentum
cosmology
ellipse
elongation
focus (of an ellipse)
force
Galilean moons
(satellites)
gravity
heliocentric cosmology
hyperbola
inferior conjunction
Kepler’s laws
kinetic energy
law of equal areas
law of inertia
light-year
mass
model
momentum
Newton’s laws of
motion
Occam’s razor
opposition
parabola
parallax
parsec
perihelion
physics
potential energy
retrograde motion
scientific method
scientific theory
semimajor axis (of an
ellipse)
sidereal period
superior conjunction
synodic period
universal constant of
gravitation
universal law of
gravitation
velocity
weight
work