Download The Motions of Celestial Bodies, and Newton`s Laws of Motion

The Motions of Celestial
Bodies, and Newton’s Laws of
Motion
Announcements
•  The results of Quiz 1 are posted in OWL
•  Looking ahead:
–  Homework 1 is on-going, and is due on Thu, Sept.
29th;
–  Homework 2 will be available through SPARK/
OWL starting on Thu. Sept 29th; it is due on
Thu, Oct. 6th
–  The second in-class quiz will take place on Tue,
Oct 4th
–  The First in-class Exam will take place on Thu,
Oct 6th
Assigned Reading
•  Units 13 and 14.
Section 2:
Tools of Astronomy
Section 2: Tools of Astronomy
They include:
Ø  Understanding the Motions of Astronomical Bodies
(gravity, inertia, mass, force, velocity, acceleration,
etc.)
Ø  Understanding matter, light, and their interactions
Ø  Understanding the structure of the smallest of
particles: atoms, and how they determine the
appearance of some of the biggest of objects (stars,
galaxies, etc.)
Today’s goals
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Review the Laws of Planetary Motion
Understand the concept of Inertia
Introduce the concept of momentum
Newton’s First Law of Motion
Kepler’s Laws of Planetary Motion
1 
2 
3 
The orbits of the planets are ellipses, with the Sun at
one focus of the ellipse.
Planets move proportionally faster in their orbits
when they are nearer the Sun (cover equal areas in
equal time.
More distant planets take proportionally longer to
orbit the Sun
Kepler’s Second Law of Orbits
2. As a planet moves around it’s orbit, it sweeps
out equal areas in equal times.
1 month
Calculations Using Kepler's Third Law
The ratio of the squares of the revolutionary periods
for two planets is equal to the ratio of the cubes of
their semimajor axes.
R3=P2
(R in AU; P in years)
As an example, the "radius" of the orbit of Mars
(the length of the semimajor axis of the orbit) is:
R=P2/3=(1.88)2/3=1.52 AU
Survey Question
A planet that is farther away from the Sun than the
Earth, takes:
an equal amount of time to orbit the Sun
a smaller amount of time to orbit the Sun
a larger amount of time to orbit the Sun
Survey Question
A planet that is farther away from the Sun than the
Earth, takes:
an equal amount of time to orbit the Sun
a smaller amount of time to orbit the Sun
a larger amount of time to orbit the Sun
P2 = R3
The Motions of
Astronomical Bodies
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Speed, velocity, acceleration, force
Mass, momentum and inertia
Newton’s three laws of motion
The Force of Gravity
Survey Question
•  `Common sense’:
If the Earth spins on an axis, why don’t
objects fly off the spinning Earth?
If the Earth revolves around the Sun, why
aren’t birds `left behind’?
1. Because of `superglue’
2. Because of the pressure of the atmosphere
3. Because of gravity
4. Because we are at the center of the Universe
Survey Question
•  `Common sense’:
If the Earth spins on an axis, why don’t
objects fly off the spinning Earth?
If the Earth revolves around the Sun, why
aren’t birds `left behind’?
1. Because of `superglue’
2. Because of the pressure of the atmosphere
3. Because of gravity
4. Because we are at the center of the Universe
Describing Motion
•  Motion is when the position of an object
changes in time
•  If position does not change, the object is
at rest
•  To describe motions we need to monitor
position and time
•  The rate at which an objects covers a
given amount of space in a given amount of
time is called speed
Ø  v = s/t
Inertia
•  Inertia is the tendency of any
physical objects to resist change
in its state of motion (including
rest)
Galileo and the Concept of Inertia
Aristotle held that objects at rest remained
at rest unless a force acted on them, but
that objects in motion did not remain in
motion unless a force acted constantly on
them: F = v (Incorrect).
Galileo concluded that an
object in a state of motion
possesses an ``inertia'' that
causes it to remain in that
state of motion unless an
external force acts on it
(Correct).
Inertia and Friction:
think of Teflon
•  Teflon (polytetrafluoroethylene) : the
most `slippery’ solid substance currently
known
•  What would happen if our planet were
suddenly to change to teflon?
Inertia and Mass
•  We measure Inertia by an object’s Mass,
which is the amount of material in the
object.
•  Weight is the force exerted on the object
by the gravity of another object, e.g. The
force exerted by the planet Earth on you.
•  Thus, for an object, weight depends on the
location of the object.
•  Your mass is the same on the moon, but
your weight on the surface of the moon is
smaller
Survey Question
The mass of an astronaut on the Moon is:
smaller than his/her mass on the Earth
the same as his/her mass on the Earth
larger than his/her mass on the Earth
Survey Question
The mass of an astronaut on the Moon is:
smaller than his/her mass on the Earth
the same as his/her mass on the Earth
larger than his/her mass on the Earth
Survey Question
The weight of an astronaut on the Moon is
smaller than his/her weight on the Earth.
True
False
Survey Question
The weight of an astronaut on the Moon is
smaller than his/her weight on the Earth.
True
False
The mass of the Moon is 100 times smaller than that of the
Earth, thus its gravitational pull is smaller (smaller weights)
Sir Isaac Newton and the
Unification of Physics & Astronomy
•  Newton was by many standards the
most important figure in the
development of modern science.
•  He demonstrated that the laws
that govern the heavens are the
same laws that govern the motion
on the surface of the Earth.
•  Newton's Three Laws of Motion.
•  Theory of Universal Gravitation
(1642-1727)
Vectors,
or things with a direction
•  There are physical quantities in nature for
which only one number, their intensity,
tells the whole story: e.g. mass,
temperature, luminosity, color
•  Other quantities need both an intensity
and a direction to be fully described: e.g.
velocity (speed with a direction), force,
acceleration.
•  These quantities with a “direction” are
called VECTORS
Law of Inertia
(Newton’s First Law)
•  In the absence of a net force, an object moves with
constant velocity, or it conserves its momentum
(quantity of motion).
•  (paraphrased) If nothing acts on an object, the
object will keep moving in a straight line and at a
constant speed. If it was at rest (zero velocity), it
will try to remain at rest.
•  Objects `resist’ change. Only a force can change
the “quantity of motion” (momentum) of an
object, either by changing its speed, or by
changing its direction of motion, or both
Momentum
•  Momentum is a quantitative way to
describe an object’s tendency to continue
to do whatever it was previously doing.
•  An object’s momentum is simply its
mass times its velocity.
P = m·v
Don’t forget that velocity is a vector, so
momentum is a vector: the direction
of motion is very important!
Survey Question
You are driving your car and suddenly you
brake. What happens to the grocery bag on
the passenger’s seat?
It stays where it is
It tends to continue moving forward
It tends to fall backward
Survey Question
You are driving your car and suddenly you
brake. What happens to the grocery bag on
the passenger’s seat?
It stays where it is
It tends to continue moving forward
It tends to fall backward
The grocery bag tends to keep its momentum constant.
Momentum is Conserved
P = m·v
P1 = m1·v1
P2 = m2·v2
If two objects collide and stick together, the
final momentum must be the same as the
initial momentum.
Pfinal = P1 + P2
Linebacks and Fullbacks
P = m v;
m in kg; and v in m/s
Momentum Conservation