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MARS
JOHANNES KEPLER
THE SOLAR SYSTEM
LAWS OF PLANETARY MOTION
Picture of Brahe
Danish astronomer
Tyco Brahe (1546-1601)
had an island
observatory and the
best measurements of
the positions for all
known planets
(Mercury, Venus, Mars,
Jupiter, and Saturn)
and the Moon.
Austrian
mathematician
Johannes Kepler
(1571-1630),
interested in how
the planets move
around the sun,
went to Tyco’s
island to get these
accurate
measurements.
At that time, many astronomers
believed that planets orbited around
the sun in perfect circles, but Tyco’s
accurate measurements for Mars
didn’t fit a circle.
Instead, the mathematician Johannes
Kepler found that the orbit of Mars fit
an ellipse the best…
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Kepler’s FIRST Law
• “The orbit of each planet is an
ellipse and the Sun is at one focus”
• Kepler proved Copernicus wrong –
planets didn’t move in circles
What is an ellipse?
2 foci
An ellipse is a
geometric shape with
2 foci instead of 1
central focus, as in a
circle. The sun is at
one focus with
nothing at the other
focus.
FIRST LAW OF PLANETARY MOTION
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Aphelion & Perihelion
• Aphelion is the point on the orbit
farthest from the sun
• Perihelion is the point on the orbit
closest to the sun
KEPLER’S
FIRST
LAW
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Kepler’s SECOND Law
• “The line joining the planet to
the sun sweeps out equal areas
in equal intervals of time”
Kepler also found that Mars changed
speed as it orbited around the sun:
faster when closer to the sun, slower
when farther from the sun…
But, areas A and B,
swept out by a line
A
B
from the sun to
Mars, were equal
over the same
amount of time.
SECOND LAW OF PLANETARY
MOTION
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In Another Words…
• The area from one time to another
time is equal to another area with
the same time interval
• All of the areas (in yellow and peach)
have equal intervals
of time
KEPLER’S
SECOND
LAW
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Kepler’s THIRD Law
• “The square of the period of any
planet is proportional to the cube
of the semi-major of its axis”
• Also referred to as the Harmonic Law
Kepler found a
relationship between the
time it took a planet to
go completely around
the sun (T, sidereal
year), and the average
distance from the sun
(R, semi-major axis)…
T1
R1
T2
R2
T1 2
T2 2
=
R1 3
R2 3
T2=TxT
( R3 = R x R x R )
THIRD LAW OF PLANETARY MOTION
R2
T2 Earth’s sidereal year (T)
and distance (R) both
equal 1. The average
distance from the Earth
to the sun (R) is called 1
astronomical unit (AU).
Kepler’s Third Law, then, changes to
T1 2
R1 3
T1 2
R1 3
2 = R 3
or
T
or
=
=
1
1
2
3
T2
R2
1
1
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Orbital Data
• The orbital data of various planets
Planet
eccentricity
(e)
T (yr)
a (AU)
T2
a3
Mercury
0.206
0.24
0.39
0.06
0.06
Venus
0.007
0.62
0.72
0.39
0.37
Earth
0.017
1
1
1
1
Mars
0.093
1.88
1.52
3.53
3.51
Jupiter
0.048
11.9
5.2
142
141
Saturn
0.056
29.5
9.54
870
868
We find that T2 and R3 are essentially equal.
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Astronomical Unit
• Astronomical unit – AU
• AU is the mean distance between
Earth and the Sun
• 1 AU ≈ 1.5 x 108 km ≈ 9.3 x 107 miles
KEPLER’S
THIRD
LAW
Kepler’s Laws apply to any celestial
body orbiting any other celestial body.
•
•
•
•
•
Any planet around a sun
The moon around the Earth
Any satellite around the Earth
The international space station
Any rings around any planet
Later, Isaac Newton built upon Kepler’s Laws
to confirm his own Law of Gravitation.
If it wasn’t for Mars and its complicated
travels across the night sky, Johannes Kepler
may not have derived his Laws of Planetary
Motion. Isaac Newton might not have had a
foundation for his Law of Gravitation...
THE RED PLANET MARS IS FOREVER
LINKED TO OUR UNDERSTANDING OF
THE SOLAR SYSTEM AND ONE OF THE
4 BASIC FORCES OF NATURE.
Newton’s First Law
(law of inertia)
An object at rest tends to stay at rest
and an object in motion tends to stay
in motion unless acted upon by an
unbalanced force.
Balanced Force
Equal forces in opposite
directions produce no motion
Unbalanced Forces
Unequal opposing forces
produce an unbalanced force
causing motion
If objects in motion tend to stay in motion,
why don’t moving objects keep moving
forever?
Things don’t keep moving forever because
there’s almost always an unbalanced force
acting upon them.
A book sliding across a table slows
down and stops because of the force
of friction.
If you throw a ball upwards it will
eventually slow down and fall
because of the force of gravity.
Newton’s First Law
(law of inertia)
• MASS is the measure of the
amount of matter in an object.
• It is measured in Kilograms
Newton’s First Law
(law of inertia)
• INERTIA is a property of an object
that describes how
______________________
much
it will resist change to the
motion of the object
mass means more ____
inertia
• more _____
1st Law
• Unless acted
upon by an
unbalanced
force, this golf
ball would sit on
the tee forever.
What is this unbalanced force that acts on an object
in motion?
• There are four main types of friction:
–
–
–
–
Sliding friction: ice skating
Rolling friction: bowling
Fluid friction (air or liquid): air or water resistance
Static friction: initial friction when moving an
object
1st Law
• Once airborne,
unless acted on
by an
unbalanced force
(gravity and air
– fluid friction)
it would never
stop!
Inertia
Terminal Velocity
Newton’s Second Law
Force equals mass
times acceleration.
F = ma
Newton’s Second Law
• Force = Mass x Acceleration
• Force is measured in Newtons
ACCELERATION of GRAVITY(Earth) = 9.8 m/s2
• Weight (force) = mass x gravity (Earth)
Moon’s gravity is 1/6 of the Earth’s
If you weigh 420 Newtons on earth, what will you
weigh on the Moon?
70 Newtons
If your mass is 41.5Kg on Earth what is your
mass on the Moon?
Newton’s Second Law
• WEIGHT is a measure of the
gravity on the mass
force of ________
of an object
Newtons
• measured in __________
Newton’s Second Law
One rock weighs 5 Newtons.
The other rock weighs 0.5
Newtons. How much more
force will be required to
accelerate the first rock
at the same rate as the
second rock?
Ten times as much
Newton’s Third Law
For every action there is an equal and
opposite reaction.
Newton’s
rd
3
Law
• For every action there is an equal and opposite
reaction.
Book to
earth
Table to
book
Think about it . . .
What happens if you are standing on a
skateboard or a slippery floor and push against
a wall? You slide in the opposite direction
(away from the wall), because you pushed on
the wall but the wall pushed back on you with
equal and opposite force.
Why does it hurt so much when you stub
your toe? When your toe exerts a force on a
rock, the rock exerts an equal force back on
your toe. The harder you hit your toe against
it, the more force the rock exerts back on your
toe (and the more your toe hurts).
Newton’s Third Law
• A bug with a mass of 5
grams flies into the
windshield of a moving
1000kg bus.
• Which will have the
most force?
• The bug on the bus
• The bus on the bug
Newton’s Third Law
• The force would be the
same.
• Force (bug)= m x A
• Force (bus)= M x a
Think I look bad?
You should see
the other guy!
Action and Reaction on Different Masses
Consider you and the earth
Action: earth pulls on you
Reaction: you pull on earth
Reaction: road pushes on tire
Action: tire pushes on road
Reaction: gases push on rocket
Action: rocket pushes on gases
Consider hitting a baseball with a bat. If we
call the force applied to the ball by the bat the
action force, identify the reaction force.
(a) the force applied to the bat by the hands
(b) the force applied to the bat by the ball
(c) the force the ball carries with it in flight
(d) the centrifugal force in the swing
Newton’s
rd
3
Law
• Suppose you are taking a space
walk near the space shuttle, and
your safety line breaks. How
would you get back to the shuttle?
Newton’s
rd
3
Law
• The thing to do would be to take one of the tools
from your tool belt and throw it is hard as you can
directly away from the shuttle. Then, with the help
of Newton's second and third laws, you will
accelerate back towards the shuttle. As you throw
the tool, you push against it, causing it to
accelerate. At the same time, by Newton's third
law, the tool is pushing back against you in the
opposite direction, which causes you to accelerate
back towards the shuttle, as desired.
Review
Newton’s First Law:
Objects in motion tend to stay in motion
and objects at rest tend to stay at rest
unless acted upon by an unbalanced force.
Newton’s Second Law:
Force equals mass times acceleration
(F = ma).
Newton’s Third Law:
For every action there is an equal and
opposite reaction.