1. MARS
JOHANNES KEPLER
THE SOLAR SYSTEM
LAWS OF PLANETARY MOTION

2. Danish astronomer Tyco Brahe ( ) had an island observatory and the best measurements of the positions for all known planets (Mercury, Venus, Mars, Jupiter, and Saturn) and the Moon.
Picture of Brahe

3. Austrian mathematician Johannes Kepler ( ), interested in how the planets move around the sun, went to Tyco’s island to get these accurate measurements.

4. 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…

5. HOME
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

6. What is an ellipse? FIRST LAW OF PLANETARY MOTION
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.
2 foci
FIRST LAW OF PLANETARY MOTION

7. HOME
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

8. HOME
Kepler’s SECOND Law
“The line joining the planet to the sun sweeps out equal areas in equal intervals of time”

9. SECOND LAW OF PLANETARY MOTION
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 from the sun to Mars, were equal over the same amount of time.
A B
SECOND LAW OF PLANETARY MOTION

10. HOME
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

11. HOME
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

12. THIRD LAW OF PLANETARY MOTION
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
T R1 3
T 2 = T x T ( ) =
R3 = R x R x R
T R2 3
THIRD LAW OF PLANETARY MOTION

13. Earth’s sidereal year (T) and distance (R) both equal 1
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). T2 R2
Kepler’s Third Law, then, changes to
T R1 3
T R1 3
or T1 2 = R1 3 = or =
T R2 3

14. Orbital Data The orbital data of various planets
HOME
Orbital Data
The orbital data of various planets
We find that T2 and R3 are essentially equal.

15. Astronomical Unit Astronomical unit – AU
HOME
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

16. 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

17. 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.

18. Newton's Laws

19. 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.

20. Balanced Force
Equal forces in opposite
directions produce no motion

21. Unbalanced Forces Unequal opposing forces produce an unbalanced force
causing motion

22. 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.

23. Newton’s First Law (law of inertia)
MASS is the measure of the amount of matter in an object.
It is measured in Kilograms

24. Newton’s First Law (law of inertia)
INERTIA is a property of an object that describes how ______________________ the motion of the object
more _____ means more ____
much it will resist change to
mass
inertia

25. 1st Law
Unless acted upon by an unbalanced force, this golf ball would sit on the tee forever.

26. There are four main types of friction:
What is this unbalanced force that acts on an object in motion?
Friction!
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

27. 1st Law
Once airborne, unless acted on by an unbalanced force (gravity and air – fluid friction) it would never stop!

28. Inertia

29. Terminal Velocity

30. Newton’s Second Law
Force equals mass times acceleration.
F = ma

31. 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?

32. WEIGHT is a measure of the force of ________ on the mass of an object
Newton’s Second Law
WEIGHT is a measure of the force of ________ on the mass of an object
measured in __________
gravity
Newtons

33. 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

34. For every action there is an equal and opposite reaction.
Newton’s Third Law
For every action there is an equal and opposite reaction.

35. Newton’s 3rd Law
For every action there is an equal and opposite reaction.
Book to
earth
Table to
book

36. 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).

37. 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

38. 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!

39. Action and Reaction on Different Masses
Consider you and the earth
Action: earth pulls on you
Reaction: you pull on earth

40. Action: tire pushes on road Reaction: road pushes on tire

41. Reaction: gases push on rocket
Action: rocket pushes on gases

42. Consider hitting a baseball with a bat
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
(b) the force applied to the bat by the ball

43. Newton’s 3rd 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?

44. Newton’s 3rd 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.

45. 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.