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The
Motion of
the Planets
Tyco Brahe
Tycho Brahe’s Epilepsy Medicine:
The basic substance is the head of a person who
has been hanged or otherwise executed. The
head should be dried and crushed together with
peony seeds to a powder. This medicine should
not be taken at the full moon.
Tycho Brahe showed that the
celestial sphere could change
• Tycho’s supernova of 1572 – showed that
this new star had no parallax and thus was
more distant than the Moon
• Comet of 1577 – showed that it too was
beyond the distance of the Moon
Sextant
Tycho Brahe
Carefully tracked the position of the
planets for 20 years to unprecedented
accuracy in an attempt to disprove the
ideas of Copernicus.
Galileo
Galileo
Did not invent the telescope, but was
the first to publish astronomical
observations made with a telescope
Galileo’s Observations
• The Sun had spots which were considered
imperfections
• The Moon had mountains and valleys
• The Milky Way resolved into countless stars
• Jupiter had four moons that clearly orbited
it and not the Earth
• Venus had phases
Discussion
Explain why the observations of the phases
of Venus prove that Venus must orbit the
Sun. Why is this different than the Moon,
which also has phases but orbits the Earth?
Discussion
Why did Galileo's observations of the orbits
of the moons of Jupiter convince him that
the Copernican model of the solar dydtem
had to be correct?
Jupiter acted like a smaller
version of the Solar System
• Jupiter is bigger than its four moons and
the moons orbit it
• Jupiter’s moons orbit with periods that are
longer for those moons that are furthest
from the planet
Galileo is arrested
Galileo claimed that his observations proved
the Earth must revolve about the Sun which
was at odds with the teaching of the Church.
In reality, his observations merely proved
that Mercury and Venus orbited the Sun and
not the Earth.
Galileo’s Physics
• The Earth’s gravity accelerates all objects,
regardless of weight, by the same amount
• A moving object will stay in motion in a
straight line at a constant speed unless
acted upon by a force
Discussion
If I had two identical inclined planes placed
so that they faced each other and I rolled a
ball down one of the planes. How high up
the second inclined plane will the ball get
before it stops rolling with no friction?
Explain.
Discussion
What if the second inclined plane is
replaced by one which is half as steep as the
first inclined plane. How high will the ball
reach on this plane?
Kepler’s first law of planetary
motion
The orbit of a planet about Sun is an ellipses
with the Sun at one focus.
Semimajor axis
½ the long axis of an ellipse
The distance between the Sun and the
planet averaged over the entire orbit
Kepler’s Second law of planetary
motion
A line drawn from the planet to the Sun
sweeps out equal areas in equal intervals of
time.
Kepler’s third law of planetary
motion
The square of the sidereal period is equal to
the cube of the semimajor axis of the orbit.
Example
p 2 = a3
An asteroid has a period of 8 years.
8  8 = 64 = 4  4  4
So the semimajor axis of this asteroid’s
orbit is 4 AU.
Kepler’s Laws
Planets orbit Sun in elliptical orbits
Line drawn from planet to Sun sweeps out
equal areas in equal times
The cube of the semimajor axis is equal to
the square of the sidereal period
Kepler’s Laws can correctly predict
the future positions of the planets
Everyone used Kepler’s laws to predict the
positions of the planets, even those that
continued to believe the Sun orbited the
Earth.
Kepler offered no explanation as to why the
planets followed these laws.
Newton
Speed
distance traveled
Speed 
time
Example: a car moving at 60 miles/hour
Velocity
Velocity is speed and direction
Example: a car moving 60 miles/hour due west.
Speed vs. Velocity
A race car may move at a constant speed
around a race track but its velocity is
changing because the direction of motion is
changing.
Newton’s first law of motion
The Law of inertia
An object at rest or in motion will stay at rest
or in motion with a constant velocity unless
acted on by an outside force.
Discussion
Using Newton’s first law of motion why is
it a good idea to be wearing a seatbelt in
case of a car accident?
Acceleration
Acceleration is the rate of change in the
velocity of an object.
An acceleration can mean a speeding up, a
slowing down, or simply a change in the
direction of motion with no change in
speed.
Units of acceleration
velocity distance
Accelerati on 

2
time
time
Example
A car accelerates from a stop light at 10 m/sec2
following a straight path. So, at time t = 0 the
car’s speed is 0 m/sec.
After one second of acceleration, the car’s
speed is 10 m/sec (velocity 10 m/sec south).
After two seconds, the car’s speed is 20 m/sec.
Discussion
After one minute of accelerating at 10 m/sec2
at what speed is the car moving?
Newton’s second law of motion
Force = mass  acceleration
If the same force is applied to an object with
half the mass, the acceleration of that object
will be twice as much.
Discussion
Using Newton’s 2nd law of motion, explain why
you can throw a baseball farther than a shotput.
Discussion
If I pull on either side of the a pen as hard as I
can, what is the net force I exert on the pen?
Discussion
Which will do more damage to your car.
Hitting a brick wall at 60 miles per hour which
does little damage to the brick wall.
A head on collision with another car traveling at
60 miles per hour in the opposite direction with
the same mass such that both cars immediately
come to rest.
Newton’s third law of motion
For any force there is always an equal and
opposite reaction force
Example: Walking
In order to walk, you have to push, with your
foot, back on the ground. The ground pushes
back on your foot with an equal and opposite
force.
Discussion
If I put my car in neutral and try to push it
with a force F, according to Newton’s third law
my car pushes back with the same force.
Therefore, the car should never move. Is
Newton wrong? Why or why not?
Discussion
You’re an astronaut working on the Hubble
Space Telescope (HST) with a number of
tools. You lose your grip and start floating
away from the space shuttle. How do you
get back to safety?
Rocket Power
A rocket engine works by accelerating rocket
fuel out the back of the rocket. A force is
required to accelerate the exhaust, which
applies an equal force in the opposite direction
on the rocket.
Discussion
Consider an object in uniform circular motion.
That is, an object traveling in a circle with a
constant speed. Is there a force acting on this
object? Why or why not?
Discussion
Consider an object in uniform circular motion:
that is, an object traveling in a circle with a
constant speed.
How is the velocity of the object changing and
how must the force on the object be directed to
change its velocity in this way?