Unit 11, problem 3, 16 Unit 12, problem 5, 8, 10, 11, 12 Unit 14, problem 13, 14 Unit 15 problem 10, 13

Kepler’s First Law Planets move in elliptical orbits with the Sun at one focus of the ellipse –Developed a heliocentric (Sun-centered) model –Did not agree with the ancients (or Brahe!) –The shape of the ellipse is described by its semi- major and semi-minor axes.

Kepler’s Second Law The orbital speed of a planet varies so that a line joining the Sun and the planet will sweep out equal areas in equal time intervals That is, planets move faster when near the Sun, and slower when farther from the Sun Explained the non-circular behavior of the planets!

Kepler’s Third Law The amount of time a planet takes to orbit the Sun (its period) P is related to its orbit’s size, a, by P 2 = a 3 Kepler’s Laws describe the shape of a planet’s orbit, its orbital period, and how far from the Sun the planet is positioned. These were empirical relationships, found from observation rather than the logic of the ancients.

Galileo Galilei ( ) Using a Dutch-designed telescope that he built himself, he made several startling observations that disproved ancient thinking about the Universe –Found sunspots, showing that the Sun was not a perfect sphere –Found craters on the Moon, showing that the Moon was not a perfect sphere –Discovered four moons of Jupiter, showing that not everything revolved around the Sun –Observed the rings of Saturn –Observed that Venus passed through all phases, just as the Moon does. In a geocentric model, the phases of Venus were limited to crescents. One of the principal founders of the experimental method for studying scientific problems.

Isaac Newton ( ) Isaac Newton described the fundamental laws covering the motion of bodies Had to invent his own mathematics (Calculus) to do it! His work is used even today in calculating everything from how fast a car stops when you apply the brakes, to how much rocket fuel to use to get to Saturn! And he did most of it before his 24 th birthday…

Sun is approximately than Earth a. 100x wider and x as massive as; b x wider and 100x as massive as; c. 10x wider and 300x as massive as; d x wider and 10x as massive as.

When the Northern Hemisphere experiences summer the Southern Hemisphere experiences a. spring; b. summer; c. fall; d. winter.

The size of the galaxy is about times the size of the Solar System. a. 10 b. 100 c d

If an event were to take place on the Sun, how long would it take to reach us? a. 8 minutes b. 11 hours c. 1 second d. 10 days

If the Sun is located at one focus of Earth’s elliptical orbit, what is the other focus? A. Earth B. The Moon C. Nothing D. This is a trick question. An ellipse has only one focus

The time it takes a planet to complete one full orbital revolution is known as its A. Period B. frequency C. orbital domain D. Velocity

Kepler’s law can be expressed mathematically as A. P=A B. P=A 2 C. P 2 =A 3 D. P 3 =A 2

Suppose a planet has a semimajor axis of 4AU. How long does it take for this planet to orbit once around the Sun in terms of Earth years A. 2 Earth-years B. 4 Earth-years C. 8 Earth-years D. 16 Earth-years

Sun is approximately than Earth a. 100x wider and x as massive as; b x wider and 100x as massive as; c. 10x wider and 300x as massive as; d x wider and 10x as massive as.

When the Northern Hemisphere experiences summer the Southern Hemisphere experiences a. spring; b. summer; c. fall; d. winter.

The size of the galaxy is about times the size of the Solar System. a. 10 b. 100 c d

If an event were to take place on the Sun, how long would it take to reach us? a. 8 minutes b. 11 hours c. 1 second d. 10 days

Mass and Inertia Mass is described by the amount of matter an object contains. This is different from weight – weight requires gravity or some other force to exist! Ex: while swimming, your weight may feel less because the body floats a little. Your mass, however, stays the same! Inertia is simply the tendency of mass to stay in motion

The Law of Inertia Newton’s First Law is sometimes called the Law of Inertia: –A body continues in a state of rest, or in uniform motion in a straight line at a constant speed, unless made to change that state by forces acting on it –Or, more simply, a body maintains the same velocity unless forces act on it A ball rolling along a flat, frictionless surface will keep going in the same direction at the same speed, unless something pushes or pulls on it –Gravity!

Another View of Newton’s First Law If an object’s velocity is changing, there must be forces present! –Dropping a ball –Applying the brakes in a car If an object’s velocity is not changing, either there are no forces acting on it, or the forces are balanced and cancel each other out –Hold a ball out in your hand, and note that it is not moving –Force of gravity (downward) is balanced by the force your hand applies (upward)!

Circular Motion Tie a string to a ball and swing it around your head –Law of inertia says that the ball should go in a straight line –Ball goes in a circle – there must be forces! Where’s the force? –It’s the tension in the string that is changing the ball’s velocity –If the string breaks, the ball will move off in a straight line (while falling to the ground)

Acceleration The term acceleration is used to describe the change in a body’s velocity over time –Stepping on the gas pedal of a car accelerates the car – it increases the speed –Stepping on the brakes decelerates a car – it decreases the speed A change in an object’s direction of motion is also acceleration –Turning the steering wheel of a car makes the car go left or right – this is an acceleration! –Forces must be present if acceleration is occurring

Newton’s Second Law The force (F) acting on an object equals the product of its acceleration (a) and its mass (m) F = m  a We can rearrange this to be: a = F/m For an object with a large mass, the acceleration will be small for a given force If the mass is small, the same force will result in a larger acceleration! Though simple, this expression can be used to calculate everything from how hard to hit the brakes to how much fuel is needed to go to the Moon!

Newton’s Third Law When two bodies interact, they create equal and opposite forces on each other If two skateboarders have the same mass, and one pushes on the other, they both move away from the center at the same speed If one skateboarder has more mass than the other, the same push will send the smaller person off at a higher speed, and the larger one off in the opposite direction at a smaller speed –Why? This works for planets, too!

Orbital Motion and Gravity Astronauts in orbit around the Earth are said to be in free fall, a weightless state. –Are they falling? Yes! Imagine a cannon on top of a mountain that fires a cannonball parallel to the ground The cannonball leaves the cannon and is pulled toward the ground by gravity If the ball leaves the cannon with a slow velocity, it falls to the ground near the mountain If the cannonball has a higher velocity, if falls farther from the mountain. What if we gave the cannonball a very large velocity, so large that it “misses” the Earth? The cannonball would be in orbit around the Earth, and it would be falling!