MARS JOHANNES KEPLER THE SOLAR SYSTEM LAWS OF PLANETARY MOTION

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. Picture of Brahe

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…

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

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

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

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

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

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

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

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 T1 2 R1 3 T 2 = T x T ( ) = R3 = R x R x R T2 2 R2 3 THIRD LAW OF PLANETARY MOTION

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 T1 2 R1 3 T1 2 R1 3 or T1 2 = R1 3 = or = T2 2 R2 3 1 1

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.

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

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 Laws

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 ______________________ the motion of the object more _____ means more ____ much it will resist change to mass inertia

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

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

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?

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

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

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

Newton’s 3rd 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

Action: tire pushes on road Reaction: road pushes on tire

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

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

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?

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.

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.