Download Developing the Science of Astronomy

Developing the Science of Astronomy
(Chapter 4)
Student Learning Objectives
• Examine the contributions of ancient and modern
astronomy to the understanding of gravity and
planetary motion.
 Identify contributions from the first Astronomers
 Recall and apply Kepler’s Laws to our solar system
 Apply Newtonian physics to our solar system
 Describe gravity and its effects
 Analyze orbital motion
How did early Greek philosophers describe motions in the sky?
 The Greeks had 3 basic
theories for the sky
1.
2.
3.
All heavenly bodies spheres
that move in circles
Heavens unchangeable
Earth stationary at center of
universe
 Most Greeks in B.C. times
believed in the geocentric
model.
 Aristotle (300 B. C.)
Placed Earth at the center of
the universe by logic
(persisted for 2000 years)
 Ptolemy (150 A. D.)
Developed the epicycle model
to explain Mars backwards
motion
retrograde motion
Ptolemy’s Epicycle Model
 Copernicus (mid-1500’s)
Used mathematics to
determine the Sun was at the
center of the solar system.
Heliocentric Model
The Early Models
Aristotle
Stationary Earth
Earth at Center
Circular Motion
Orbital speeds
same for all
Based on
Observation of
Apparent Motion
Ptolemy
Stationary Earth
Earth at Center
Circular motion
Orbital speeds
same for all
Based on
Observation of
Apparent Motion
Copernicus
Rotating Earth
Sun at Center
Circular motion
Orbital speeds
depend on distance
Based on
Mathematics
Practice
Write a compare and contrast sentence
which relates these models.
The Transition
 Tycho Brahe (late-1500’s)
Designed and utilized new instruments for measuring precise
angles in the sky.
Although Tycho Brahe
believed in a geocentric
system, his measurements
were later used to provide
proof for the heliocentric
system. lol
What are Kepler’s Laws?
 Kepler (1600’s)
Used Tycho Brahe’s
observations and
measurements of planetary
positions to develop three
laws of planetary motion.
Kepler’s 1st Law
Planets move in elliptical
orbits with the Sun at one
focus. (Ellipses)
 Kepler’s 2nd Law
Planets sweep out equal areas of space in equal
time intervals. (Equal Areas)
 Kepler’s 3rd Law
The orbital period of a planet is related to the semi-major
axis of it’s orbit.
P2 = a3
Orbital Period Squared = Semi-major Axis Cubed
Practice
1) Which planet has the longer orbital period?
Saturn: a = 9.54 AU
Jupiter: a = 5.2 AU
2) How do we measure birthdays?
http://www.exploratorium.edu/ronh/age/index.html
 The planets in our solar system follow orbits that
are nearly circular.
Circles vs Ellipses
 Eccentricity indicates the elongation of the ellipse.
(e = 0 to 1)
Galileo Galilei
 Galileo (1600’s)
Used observations to provide visual proof of Copernicus’s Sun
centered system.
First to use telescope to view sky
Planet positions confirmed
Moon & Sun not perfect spheres
Objects orbiting Jupiter (not Sun or Earth)
How are the motions of objects described?
 Average speed is the
amount of distance
traveled in some amount
of time. (65 mph)
s=d
t
 Velocity is speed in a
particular direction.
(65 mph South)
Acceleration
 Acceleration is the
change of velocity in
some amount of time.
 Change in speed or
direction
 All objects on Earth have
the same acceleration,
downward.
9.81 m/s2
Practice
1) How fast would an object dropped from the tower of
Pisa be traveling after 2 seconds, in the absence of air?
2) If the Moon is orbiting at a speed of 1,023 m/s, does the
moon experience acceleration?
3) Is the acceleration due to gravity greater on a book or a
feather?
What are Newton’s Laws of Motion?
 Newton’s 1st Law
An object will remain at rest or maintain a constant
velocity unless an unbalanced force causes the object’s
motion to change. (Inertia)
 Inertia is the tendency of an object to maintain its motion.
Newton’s 2nd Law of Motion
An unbalanced force acting on a mass gives the mass an
acceleration in the same direction as the unbalanced
force. (F = ma)
 More push = more acceleration
http://www.physicsclassroom.com/mmedia/kinema/stl.cfm
Mass vs Weight
 Mass is a fundamental quantity.
 Mass is the amount of material contained in an object.
Average Man
73 kg
Sun
1.989 x 1030 kg
Earth
5.972 x 1024 kg
more mass
 more inertia
 harder to change motion
 Weight is the gravitational force acting on a mass.
W = mg
Earth
1kg = 2.2 lbs = 9.8 N
http://www.exploratorium.edu/ronh/weight/index.html
Practice
1) Mass is often defined in elementary school as “the
amount of space an object takes up”. Why is this not
correct?
2) Would your mass be different if you were on the moon
right now?
3) What would a 75 kg person weigh on Earth? What would
this person weigh on Mars where the acceleration due to
gravity is 3.72 m/s2?
 Newton’s 3rd Law of Motion
When two objects interact, they create equal and opposite
forces on each other. (Action-Reaction)
Same Pull
Opposite Directions
Space X
Practice
1) Apply each of Newton's laws to our solar system.
2) If a person weighs 135 pounds, how much force does the
floor apply to the person? How much force does the
floor apply to a person who weighs 175 pounds, if they
stand on the same spot?
What is Gravity?
Gravity is a property of mass
Newton’s Universal Law of Gravitation
Every object with mass attracts every other object with
mass with a force.
Fg = GMm
d2
Mutual Force of Attraction
Both masses pull the same on each other!
Inverse Square Law
Force decreases with the square of the distance.
Practice
1) Is the gravitational force zero in space?
2) If Earth had twice as much mass, would this change
your weight? Would it change your mass?
3) If the distance changes between two objects, does the
acceleration due to gravity change?
What is Einstein’s description of Gravity?
According to Einstein
 Einstein’s Theory of gravity
Every object with mass creates a curvature of space-time.
 Mass does not create a force
 Mass changes space
 Space alters path of objects and light
More Mass = More Curvature
Image Credit: oneminuteastronomer.com
Question to Consider
1) What does gravity effect or cause? Name as many
phenomena as you can.
2) How do Newton’s and Einstein’s descriptions of gravity
compare and contrast?
Effects of Gravity
Orbits
Orbital Perturbations
Atmospheres
Synchronous Motion
Galaxies
Weight
Star Formation
Tides
Shapes of Objects
Motion
Ocean Tides
Changing Systems
 Our Earth-Moon system is changing.
 Earth’s rotation is slowing (0.0015 seconds/century)
 Our Moon is drifting away (3.8 cm/year)
 The synchronous orbit of the Moon (same face)
Weightlessness
 The feeling of weightlessness occurs when an object and
its reference frame accelerate at the same rate.
 Objects fall together.
Image Credit
wired.com
Practice
1) The Sun's tidal affects are weak compared to the Moon.
Why?
2) The astronauts on the space station have no weight.
(true or false)
3) Does the moon have weight?
What is the physics of orbital motion?
 Objects move in a straight
line, unless an unbalanced
force changes the motion.
 In circular motion, a
centripetal force is causing
a change in motion.
 Objects in orbit around the Earth, are falling around Earth.
Earth’s escape velocity = 11.2 km/s
Earth’s circular velocity = 8 km/s
Practice
1) If the force keeping an object in a circular orbit is
removed, what will be the path of the orbiting
object?
2) What is a geosynchronous orbit?
3) What would be the path of an open orbit?
Center of Mass
Astronomical objects actually orbit about the center
of mass of the system. (Elliptical Orbits)
Common
Center
Of Gravity
Conservation Of Energy
 Elliptical orbits are maintained by conservation of
mechanical energy.
GPEMax
KEMax