Transcript 17Sept_2014

Unit 11, problem 3, 16
Unit 12, problem 5, 8, 10, 11, 12
Unit 14, problem 13, 14
Unit 15 problem 10, 13
Kepler’s First Law
• Planets move in elliptical
orbits with the Sun at one
focus of the ellipse
– Developed a heliocentric
(Sun-centered) model
– Did not agree with the
ancients (or Brahe!)
– The shape of the ellipse
is described by its semimajor and semi-minor
axes.
Kepler’s Second Law
• The orbital speed of a planet
varies so that a line joining the
Sun and the planet will sweep
out equal areas in equal time
intervals
• That is, planets move faster
when near the Sun, and slower
when farther from the Sun
• Explained the non-circular
behavior of the planets!
Kepler’s Third Law
• The amount of time a planet takes
to orbit the Sun (its period) P is
related to its orbit’s size, a, by
P2 = a3
• Kepler’s Laws describe the shape
of a planet’s orbit, its orbital
period, and how far from the Sun
the planet is positioned.
• These were empirical
relationships, found from
observation rather than the logic
of the ancients.
Galileo Galilei (1564-1642)
• Using a Dutch-designed telescope that he built
himself, he made several startling observations that
disproved ancient thinking about the Universe
– Found sunspots, showing that the Sun was not a
perfect sphere
– Found craters on the Moon, showing that the Moon
was not a perfect sphere
– Discovered four moons of Jupiter, showing that not
everything revolved around the Sun
– Observed the rings of Saturn
– Observed that Venus passed through all phases, just
as the Moon does. In a geocentric model, the phases
of Venus were limited to crescents.
• One of the principal founders of the experimental
method for studying scientific problems.
Isaac Newton (1642-1727)
• Isaac Newton described the
fundamental laws covering the
motion of bodies
• Had to invent his own
mathematics (Calculus) to do it!
• His work is used even today in
calculating everything from how
fast a car stops when you apply
the brakes, to how much rocket
fuel to use to get to Saturn!
• And he did most of it before his
24th birthday…
Sun is approximately ...... than Earth
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a. 100x wider and 300 000x as massive as;
b. 10000x wider and 100x as massive as;
c. 10x wider and 300x as massive as;
d. 100000000x wider and 10x as massive as.
When the Northern Hemisphere experiences
summer the Southern Hemisphere
experiences
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a. spring;
b. summer;
c. fall;
d. winter.
The size of the galaxy is about ....... times the size of
the Solar System.
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a. 10
b. 100
c. 1000
d. 100 000 000
If an event were to take place on the Sun, how long
would it take to reach us?
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a. 8 minutes
b. 11 hours
c. 1 second
d. 10 days
If the Sun is located at one focus of Earth’s elliptical
orbit, what is the other focus?
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A. Earth
B. The Moon
C. Nothing
D. This is a trick question. An ellipse has only one
focus
The time it takes a planet to complete one full orbital
revolution is known as its
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A. Period
B. frequency
C. orbital domain
D. Velocity
Kepler’s law can be expressed mathematically as
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A. P=A
B. P=A2
C. P2=A3
D. P3=A2
Suppose a planet has a semimajor axis of 4AU. How
long does it take for this planet to orbit once around
the Sun in terms of Earth years
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A. 2 Earth-years
B. 4 Earth-years
C. 8 Earth-years
D. 16 Earth-years
Sun is approximately ...... than Earth
•
•
•
•
a. 100x wider and 300 000x as massive as;
b. 10000x wider and 100x as massive as;
c. 10x wider and 300x as massive as;
d. 100000000x wider and 10x as massive as.
When the Northern Hemisphere experiences
summer the Southern Hemisphere
experiences
•
•
•
•
a. spring;
b. summer;
c. fall;
d. winter.
The size of the galaxy is about ....... times the size of
the Solar System.
•
•
•
•
a. 10
b. 100
c. 1000
d. 100 000 000
If an event were to take place on the Sun, how long
would it take to reach us?
•
•
•
•
a. 8 minutes
b. 11 hours
c. 1 second
d. 10 days
Mass and Inertia
• Mass is described by the
amount of matter an object
contains.
• This is different from weight –
weight requires gravity or some
other force to exist!
• Ex: while swimming, your
weight may feel less because
the body floats a little. Your
mass, however, stays the same!
• Inertia is simply the tendency
of mass to stay in motion
The Law of Inertia
•
Newton’s First Law is sometimes
called the Law of Inertia:
– A body continues in a state of rest, or
in uniform motion in a straight line at
a constant speed, unless made to
change that state by forces acting on it
– Or, more simply, a body maintains the
same velocity unless forces act on it
•
A ball rolling along a flat, frictionless
surface will keep going in the same
direction at the same speed, unless
something pushes or pulls on it
– Gravity!
Another View of Newton’s First Law
• If an object’s velocity is
changing, there must be
forces present!
– Dropping a ball
– Applying the brakes in a
car
• If an object’s velocity is not
changing, either there are
no forces acting on it, or
the forces are balanced and
cancel each other out
– Hold a ball out in your
hand, and note that it is not
moving
– Force of gravity
(downward) is balanced by
the force your hand applies
(upward)!
Circular Motion
•
Tie a string to a ball and swing it
around your head
– Law of inertia says that the ball
should go in a straight line
– Ball goes in a circle – there
must be forces!
• Where’s the force?
– It’s the tension in the string
that is changing the ball’s
velocity
– If the string breaks, the ball
will move off in a straight
line (while falling to the
ground)
Acceleration
• The term acceleration is used to
describe the change in a body’s
velocity over time
– Stepping on the gas pedal of a
car accelerates the car – it
increases the speed
– Stepping on the brakes
decelerates a car – it decreases
the speed
• A change in an object’s
direction of motion is also
acceleration
– Turning the steering wheel of
a car makes the car go left or
right – this is an acceleration!
– Forces must be present if
acceleration is occurring
Newton’s Second Law
• The force (F) acting on an
object equals the product of its
acceleration (a) and its mass
(m)
• F=ma
• We can rearrange this to be:
• a = F/m
• For an object with a large
mass, the acceleration will be
small for a given force
• If the mass is small, the same
force will result in a larger
acceleration!
•
Though simple, this expression can
be used to calculate everything
from how hard to hit the brakes to
how much fuel is needed to go to
the Moon!
Newton’s Third Law
•
When two bodies interact, they
create equal and opposite forces on
each other
•
If two skateboarders have the same
mass, and one pushes on the other,
they both move away from the
center at the same speed
If one skateboarder has more mass
than the other, the same push will
send the smaller person off at a
higher speed, and the larger one off
in the opposite direction at a smaller
speed
•
– Why?
This works for planets, too!
Orbital Motion and Gravity
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Astronauts in orbit around the Earth are
said to be in free fall, a weightless state.
– Are they falling? Yes!
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Imagine a cannon on top of a mountain
that fires a cannonball parallel to the
ground
The cannonball leaves the cannon and is
pulled toward the ground by gravity
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If the ball leaves the cannon with a slow
velocity, it falls to the ground near the
mountain
If the cannonball has a higher velocity, if
falls farther from the mountain.
What if we gave the cannonball a very
large velocity, so large that it “misses” the
Earth?
The cannonball would be in orbit around
the Earth, and it would be falling!