Path of Mars

Discussion Suppose Mars is moving in retrograde motion and will rise at midnight. Since Mars is moving with retrograde motion, that means that during the night it will be moving west-to-east rather than east-to-west. So at midnight it will rise in the west and move across the sky and then set in the east Do you agree or disagree?

Two types of planets Superior planets – Mars, Jupiter, and Saturn Superior planets can appear in the sky at any time of the night. Inferior planets – Mercury and Venus Inferior planets always stay close to the Sun.

Discussion If we consider the Moon to be a planet, what type of planet would it be?

The simplest universe Nothing ever changes! The Sun and Moon do not move in the sky There are no seasons The stars do not move in the sky The planets do not move in the sky

Second simplest universe Stars unchanging and fixed to the celestial sphere Celestial sphere rotates about Earth moving east to west once a day carrying the Sun, Moon and planets with it. The Earth is at the center of the universe and does not move, geocentric model

Third Simplest Universe Sun, Moon, and planets are carried east to west along with rotation of celestial sphere Sun, Moon and planets move more slowly west to east against celestial sphere

Ptolemy’s explanation for retrograde motion Each planet moves on a small circle called and epicycle. The center of each epicycle moves along a larger circle centered near the Earth called a deferent.

Ptolemaic system Very successful at predicting positions of the planets but was not perfect Offered no explanation of why the planets moved on deferents and epicycles There was no relationship between period of revolution and epicycle size

Alternatives to Ptolemy’s model Aristarchus proposed a heliocentric model of the Solar System in the 3 rd century B.C.E. Reintroduced in the 16 th century by Copernicus

Heliocentric model Sun at the center Diurnal motion explained by rotation of the Earth All the planets including Earth revolve about the Sun in circular orbits with different speeds

Disadvantages of the heliocentric model Still required epicycles Was no better at predicting planetary positions No stellar parallax observed

Advantages of heliocentric model Provides natural explanation of retrograde motion. Provides natural explanation for the motion of mercury and Venus as inferior planets, i.e. their orbits are interior to that of the Earth. Provides a relationship between distance from Sun and orbital period. Planets farther from the Sun took longer to complete an orbit.

Retrograde motion

Inferior planets

How could you explain the the motion of the inferior planets Mercury and Venus with deferents and epicycles in the geocentric model? Discussion

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.

Tycho’s model of the solar system

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

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? Discussion

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

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 = a 3 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.

Galileo’s Physics Inertia: A moving object will stay in motion unless acted upon by a force. Rate of falling: Gravity accelerates all objects, regardless of weight, by the same amount

Speed Example: a car moving at 60 miles/hour

Velocity Velocity refers to not only how fast an object is moving but its direction as well. Example: a car moving 60 miles/hour due west.

Acceleration Acceleration refers to any 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

Example A car accelerates from a stop light at 10 m/sec 2 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/sec 2 at what speed is the car moving?

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? 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?

In the absence of air resistance, all objects fall with the same constant acceleration regardless of the objects mass. Law of falling objects

Newton

Newton’s first law of motion The Law of inertia A body remains at rest or moves in a straight line at a constant speed unless acted on by a net external force. Inertia is the tendency of an object to resist a change in velocity.

Discussion Using Newton’s first law of motion why is it a good idea to be wearing a seatbelt in case of an car accident?

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 2 nd law of motion, explain why you can throw a baseball farther than a shot- put.

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 Earth pushes your foot with an equal and opposite force. While the forces are equal and opposite the response to that force is not, because the masses are very different.

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 Your on a space walk outside the space station using Nasa’s jetpack to move around when it breaks down leaving you stranded 500 feet from safety. All you have is a bag of tools. How do you get back to the space station.