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Astronomy Fall Block 2 Gravity and the Planets
Objectives
 Compare /Contrast Ptolemaic, Copernican, and Brahe observations
 Kepler’s three laws of planetary motion; geometry/observations
 Galileo’s first views of craters on the Moon / moons orbiting Jupiter
 State / identify examples of Newton’s three laws
 State Newton’s law of universal gravitation;
Standard
CCSS
CCR 4. Interpret words and phrases as they are used in a text, including
determining technical, connotative, and figurative meanings, and analyze
how specific word choices shape meaning or tone.

Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are
used in a specific scientific or technical context relevant to grades 11-12 texts and topics.
Vocab
Heliocentric
Retrograde motion
Parallax
Elliptical Opposition
Conjunction
Sidereal
Synodic
Packet Work List
1. Cover, Vocab
2. WCW
3. Nicolaus Copernicus 1473-1543
Tycho Brahe 1546 - 1601
4. Kepler’s Laws 1571-1630
Galileo Galilei 1564 - 1642
5. Christian Huygens 1629-1695
Isaac Newton 1642-1727
6. Newton to Kepler
7.
Focus Questions
1. What is the shape of the Earth’s orbit around the Sun?
2. Do the planets orbit the Sun at constant speed?
3. Do the planets all orbit the sun at the same speed?
4. How much force does it take to keep an object moving in a straight line
at a constant speed?
5. How does an object’s mass differ when measured on the Earth and on
the Moon?
WCW Block 2 Gravity and the Planets
8/28 thu
Warm-up
How is the Waltz, the dance, related to the motion of the
planets orbiting the Sun?
Critical thinking
How is an epicycle different from rotation on the axis?
Wrap-up
The major difference between Geocentric and Heliocentric models of our Solar
system is…
9/3 even wed
Warm-up
How did Copernicus model differ from the Ptolemaic model?
Critical thinking
What did Kepler change in the Copernican model that allowed it to gain
acceptance?
Wrap-up
Describe the three laws of Newton.
9/5 even fri
Warm-up
Critical Thinking
Wrap-up
# 3 Notes
Nicholas Copernicus
Polish astronomer 1473-1543
Before Ptolemaic model of the solar system which
placed Earth at the center of the universe
introduced the heliocentric model, centered around the
sun
all the planets, including Earth, moved in orbits
around the sun, and showed how this new system
could accurately calculate the positions of the planets
Retrograde motion- apparent
backward motion of a planet caused
by its being lapped by another planet,
or vice-versa
Mercury and Venus Vs Mars
Fewer epicycles than Ptolemaic,
observations of
a supernova (literally: nova=
Danish astronomer 1546-1601
"new star") in 1572 (we now
For over twenty years, accurate observations of the
know that a supernova is an
night sky (over 1000objects) especially mars which
exploding star, not a new
plays a key role in Kepler’s laws, all without the aid of star). 18 months
a telescope, (not invented)
observations of a comet in
records were used by Johan Kepler to describe the
1577
orbits of planets around the sun and disprove the
come tis farther from us then
Ptolemaic theory, Mathematically
the moon, Aristotle, who had
held that comets were
atmospheric
Tycho Brahe
Galileo Galilei
Italian astronomer / physicist 1564-1642
Galileo was the first person to use a telescope to look
at the heavens. He discovered sunspots, and craters
and peaks in the moon. Jupiter had moons also, and
other objects seemed to be orbiting the Sun.
Johan Kepler
German astronomer 1571-1630
He introduced three important laws of planetary motion and
helped the Copernican model of the solar system gain general
acceptance.
Kepler inherited Tycho Brahe's observational data on Mars
following Brahe's death and showed, mathematically, that Mars
followed an elliptical orbit. This new revelation contradicted
the age old belief that heavenly bodies all moved in perfect
circles.
also cast horoscopes and wrote science fiction novels.
Christian Huygens
Dutch physicist and astronomer 1629-1695
He found new methods for grinding and polishing lenses,
making telescopes more powerful. Using a telescope he had
made, Huygens first identified Saturn's rings and one of
Saturn's moons.
Huygens also invented the pendulum clock, increasing the accuracy
of timekeeping, and proposed the wave theory
Isaac Newton
English scientist and mathematician 1642-1727
Newton’s idea that gravity, the force which keeps us bound to
the Earth, also controls the motion of planets and stars.
Newton's contributions to science include the universal law of
gravitation, the development of a whole new field in
mathematics called calculus, and his famous three laws of
motion.
Opposition-Earth has a shorter orbital period than Mars, we pass in between Mars and the Sun on
a fairly regular basis (approx. every 780 days, or 2 years and 50 days). When we do so, we see
Mars in the opposite direction from the Sun, at opposition
Outer planets
Inner planets
Sidereal period-1 complete orbit around the sun
Synodic period- planet moving from a chosen position and back

Tycho Brahe disn’ ancient ideas
November 1572, for 18 months light from an exploding star (supernova) was seen
Parallax- is an apparent displacement (difference in the position) of an object viewed along two
different lines of sight, and is measured by the angle or semi-angle of inclination between those
two lines (fyi-angle is displacement also)

Kepler’s laws-orbital shapes, changing speeds, planetary years
1st law elliptical orbit
Orbital eccentricity- e- (0 circular, 1 near line)
Perihelion-closest to sun
Aphelion-farthest from sun
2nd law a line joining a planet and the sun sweeps out equal areas in equal time
3rd law- orbital period squared = semi major axis cubed
http://qhstearth.blogspot.com/2009/10/homework-geocentric-vs-heliocentric.html
http://www.youtube.com/watch?v=QR2vxfwiHAU khan academy
Notes
 Galileo’s heliocentric
Early 1600’s proves kepler and Copernicus –
telescope invention
Two lenses can bring objects closer
30X magnification used to view sky
Phases of venus, moon’s craters, saturns rings,
satellites orbiting Jupiter,
all bodies fall at the same speed in a vacuum
 Newton
1600’s mid
Motion of objects, kepler’s data of planetary motion,

Laws http://www.phys.ufl.edu/demo/1_Mechanics/

1st law
Objects remain at
constant acceleration
unless acted upon by an
outside force
2nd law
Objects experience a force
equivalent to mass times
acceleration
3rd law
Objects that apply a force
experience a force applied on
them equal in magnitude and
opposite in direction

 Newton’s gravity vs. Kepler’s laws
"inverse square law"
"universal" force of gravitation F
F = G mM/r2
M mass of Earth,
R radius
m mass of object
F = m GM/R2 = m g
g = GM / R2
G universal gravitation
Earth, sphere of radius 1 RE = 6,317,000 m
If a satellite is in a stable circular orbit and its velocity is V,
then F
mg = F = mV2/RE
Dividing both sides by m shows that the mass of the satellite does not matter,
V2/RE = g

Frontiers unknown
Galileo Galilei Astronomer, Physicist 1564 - 1642
1. What prompted Galileo's thinking about pendulums? __________________________
___________________________________________________________________________
___________________________________________________________________________
2. What is Galileo's Theory of Falling Objects and how did he test it?
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
3. What is the Ptolemaic Theory? ______________________________________________
___________________________________________________________________________
4. What is the Copernican Theory? _____________________________________________
___________________________________________________________________________
5. How did Aristotle and Galileo differ in their view of the universe?
___________________________________________________________________________
___________________________________________________________________________
6. Define "heliocentrism". ____________________________________________________
___________________________________________________________________________
7. What is "heresy" and why was Galileo condemned for it?
___________________________________________________________________________
___________________________________________________________________________
Newton's Laws: Inertia and Mass
1. Inertia is
2. The amount of inertia possessed by an object is dependent solely upon its __________.
3. Two bricks are resting on edge of the lab table. Shirley She-short stands on her toes and spots the
two bricks. She acquires an intense desire to know which of the two bricks are most massive. Since
Shirley is vertically challenged, she is unable to reach high enough and lift the bricks; she can
however reach high enough to give the bricks a push. Discuss how the process of pushing the bricks
will allow Shirley to determine which of the two bricks is most massive. What differences will
Shirley observe and how can this observation lead to the necessary conclusion?
4. Would Shirley She-short be able to conduct this same study if she was on a spaceship in a location
in space far from the influence of significant gravitational forces? _______ Explain your answer.
5. If a moose were chasing you through the woods, its enormous mass would be very threatening.
But if you zigzagged, then its great mass would be to your advantage. Explain why.
6. Inertia can best be described as _____.
a. the force that keeps moving objects moving and stationary objects at rest.
b. the willingness of an object to eventually lose its motion
c. the force that causes all objects to stop
d. the tendency of any object to resist change and keep doing whatever it's doing
7. Mass and velocity values for a variety of objects are listed below. Rank the objects from smallest to
greatest inertia.
_______ < _______ < _______ < _______
Newton's Second Law of Motion
1. The acceleration of an object is __________ related to the net force exerted upon it
and____________ related to the mass of the object. In equation form: a = Fnet / m.
a. directly, inversely
b. inversely, directly
c. directly, directly
d. inversely, inversely
2. Use Newton's second law to predict the effect of an alteration in mass or net force upon the
acceleration of an object.
a. An object is accelerating at a rate of 8 m/s2 when it suddenly has the net force exerted upon
increased by a factor of 2. The new acceleration will be _________ m/s2.
b. An object is accelerating at a rate of 8 m/s2 when it suddenly has the net force exerted upon
increased by a factor of 4. The new acceleration will be _________ m/s2.
c. An object is accelerating at a rate of 8 m/s2 when it suddenly has the net force exerted upon
decreased by a factor of 2. The new acceleration will be _________ m/s 2.
d. An object is accelerating at a rate of 8 m/s2 when it suddenly has its mass increased by a factor
of 2. The new acceleration will be _________ m/s2.
e. An object is accelerating at a rate of 8 m/s2 when it suddenly has its mass decreased by a factor
of 4. The new acceleration will be _________ m/s2.
f. An object is accelerating at a rate of 8 m/s2 when it suddenly has the net force exerted upon
increased by a factor of 2 and its mass decreased by a factor of 4. The new acceleration will be
________ m/s2.
g. An object is accelerating at a rate of 8 m/s2 when it suddenly has the net force exerted upon
increased by a factor of 4 and its mass increased by a factor of 2. The new acceleration will
be________ m/s2.
h. An object is accelerating at a rate of 8 m/s2 when it suddenly has the net force exerted upon
increased by a factor of 3 and its mass decreased by a factor of 4. The new acceleration will be
_________ m/s2.
3. These force diagrams depict the magnitudes and directions of the forces acting upon four objects.
In each case, the down force is the force of gravity. Rank these objects in order of their acceleration,
from largest to smallest:
_______ > _______ > _______ > _______
Object A
B
C
D
50N
50N
50N
50N
20N
50N
50N
10N
40N
15N
30N
50N
50N
50N
50N
Newton's Third Law
A force is a push or pull resulting from an interaction between two objects.Whenever there is a force,
there are two objects involved - with both objects pushing (or pulling) on each other in opposite
directions. While the direction of the pushes (or pulls) are opposite, the strength or magnitudes are
equal. This is sometimes stated as Newton's Third Law of motion: for every action, there is an equal
and opposite reaction. A force is a push or a pull and it always results from an interaction between
two objects. These forces always come in pairs.
1. For each stated action force, identify the reaction force.
Bat hits ball
Man pushes car
Helmet hits bug
2. Identify by words the action-reaction force pairs in each of the following diagrams.
3. TRUE or FALSE:
As you sit in your seat in the physics classroom, the Earth pulls down upon your body with a
gravitational force; the reaction force is the chair pushing upwards on your body with an equal
magnitude. If False, correct the answer.
4. Shirley Bored sits in her seat in the English classroom. The Earth pulls down on Shirley's body with
a gravitational force of 600 N.
Describe the reaction force of the force of gravity acting upon Shirley.
5. Use Newton's third law (law of action-reaction) and Newton's second law
(law of acceleration: a = Fnet/m) to complete the following statements by filling in the blanks.
a. A bullet is loaded in a rifle and the trigger is pulled. The force experienced by the bullet is
____________ (less than, equal to, greater than) the force experienced by the rifle. The resulting
acceleration of the bullet is ____________ (less than, equal to, greater than) the resulting
acceleration of the rifle.
b. A bug crashes into a high speed bus. The force experienced by the bug is ____________ (less
than, equal to, greater than) the force experienced by the bus. The resulting acceleration of the bug is
____________ (less than, equal to, greater than) the resulting acceleration of the bus.
c. A massive linebacker collides with a smaller halfback at midfield. The force experienced by the
linebacker is ____________ (less than, equal to, greater than) the force experienced by the
halfback. The resulting acceleration of the linebacker is ____________ (less than, equal to,
greater than) the resulting acceleration of the halfback.
d. The 10-ball collides with the 14-ball on the billiards table (assume equal mass balls). The force
experienced by the 10-ball is ____________ (less than, equal to, greater than) the force
experienced by the 14-ball. The resulting acceleration of the 10-ball is ____________ (less than,
equal to, greater than) the resulting acceleration of the 14-ball.
UNIVERSAL GRAVITY AND KEPLER'S LAWS WORKSHEET
G = 6.67259 x 10-11 (N•m2)/kg2
Earth
Sun
Mass................................................ 5.98 X 1024 kg
Mass.................. 1.99 X 1030 kg
Radius..............................................6.38 X 106 m
Radius................6.96 X 108 m
Mean distance from the Sun..........1.50 X 1011 m
Moon
Mass................................................ 7.35 X 1022 kg
Radius..............................................1.74 X 106 m
Mean distance from the Earth........ 3.85 X 108 m
1 What is the force of attraction between a 60.0 kg student in the senior parking lot and the school?
The distance between the two is 100.000 m and the mass of the school 65,000,000 kg.
2 You’re on a date with “the significant other.” You are getting close. Your center of masses are 0.50
meters apart. If you have a mass’s of 50.00 kg and 70.00 kg then what is the actual scientific force of
attraction between the two of you?
3 Two asteroids, (m1 = 1.00 X 1012 kg and m2 = 5 X 1012 kg), are floating in space. The force of
attraction between them is 10.000 N. How far apart are their centers of mass?
4 In a car race, the force of attraction between the 1st and 2nd place cars is 3.0349 X 10 -7N. If the
1st place car has a mass of 700 kg and the 2nd place car has a mass of 650 kg, then what is the
distance between the two cars?
5 While on the surface of the the Earth a student has a weight of 450 N. If she is moved twice as far
from the center of the Earth, then how does hew new weight compare to her old?
6 How many Earth Radii distances could fit between the center of the Earth and the Center of the
moon
when it is in orbit around the Earth? If the same 50 kg student in problem #5 is moved out from the
surface of the Earth to this distance away from the center of the Earth, then how does her new weight
compare to her old?
7 An alien space craft is out in space leaving an unknown planet. It detects the pull of gravity due to
this unknown planet to be 100 N. Later the alien rechecks the pull on their space craft and detects it
to be 33 N. By what factor has their distance changed as they left the unknown planet?
8 The space shuttle travels at 17,000 mph, 7,589.288 m/s while in orbit. How far away from
the SURFACE OF THE EARTH is the shuttle?
9 How fast is the moon traveling as it orbits the Earth?
10A geosynchronous orbit is one where a satellite orbits the Earth with the SAME period of
motion as the Earth on it own axis. How far from the center of the Earth is the Satellites orbit?
11 Using Kepler’s 3rd Law of Planetary motion, determine the distance between the center of the
Earth and the center of the Moon.
12 Using Kepler’s 3rd Law of Planetary motion, determine the distance between the center of the
Earth and the center of the Sun.
UNIVERSAL GRAVITY AND KEPLER'S LAWS WORKSHEET
13A planet is in orbit as shown below. Where are the two possible locations for a Sun?
14 The moon Io revolves around Jupiter in 0.0048 sidereal years. Io has an mean orbital radius of
0.0028 Au’s. If the Jupiter moon has a period of rotation of 0.0097 sidereal years, then how far away
is Europa from the center of Jupiter?
15 The planet Mercury takes 0.24 sidereal years to go around the sun. What is the distance from the
center of Mercury to the center of the sun?
16 The moon takes 27.32 days to revolve around the Earth once. The moon is 25,201 mi from the
center of the Earth. The International Space Station orbits in the same orbit as the space shuttle. The
International Space Station makes an orbit around the Earth in 90 minutes, then how high up is the
International Space Station from the center of the Earth and the surface of the Earth? (The
diameter of the Earth is 3950 miles.) Why is this answer different from question #8?
17 The Planet Jupiter’s mean orbital radius is 5.2025 Au’s. What is the period of Jupiter in sidereal
years?
18 The planet Pluto is 39.5 Au’s from the Sun. How long does is take to go around the Sun once?
19 Their is belt of asteroids between Mars and Jupiter. This belt circles the “inside” of our solar
system and is called the Asteroid belt. This belt has a mean radius from the Sun of 2.6 Au’s. how long
does it take for 1 asteroid to in the belt to travel around the Sun once?
ORBITAL VELOCITY
20 A satellite is placed in an orbit 16,090,000 meters above the Earth’s Surface. How fast is the
satellite traveling to remain in orbit?
21 A space ship is to orbit a planet wtih a mass of 8 X 10 20 kg. How far, from the plant’s center,
must the ship travel if it is to travel with a velocity 10,000 m/s?
22 A space craft is to orbit an asteroid of mass 5.00 X 1015 kg at a distance of 55,555 m from the
asteroid’s center. What is the space craft’s period of motion and orbital velocity?
23 The Hubble Telescope orbits the Earth 596,000 m ABOVE THE SURFACE of the earth. What is
the Telescope’s Period and tangential velocity?
UNIVERSAL GRAVITY AND KEPLER'S LAWS WORKSHEET
Answers
1. 2.6023 X 10-5N 7. 9 times farther away 15. 5.76 X 1010m
2. 9.3416 X 10-7 N 8. 54,7771.53 m (340 mi) 16. 437.65 miles
3. 5,774,945.887 m 9. 1018.05 m/s 17. 11.87 Au’s
4. 10.0 m 10. 42255942.3 m 18. 248 sidereal years
5. 1/4 the weight, therefore 112.5 N 11., 12., 13., 19. 4.192 sidereal years
6. 60; New =(1/602)OLD 14. 0.00447 Au’s 20. 4979.89 m/s
21 5, 338,072 m
22 2.451 m/s; 142,440 s
23 7563 m/s; 5795.511 s
UNIVERSAL GRAVITY AND KEPLER'S LAWS WORKSHEET