The Motion of the Planets

Review Question Define synchronous rotation.

Review Question What are the conditions that need to be met for a solar eclipse to occur?

If you see the Moon setting and it is full, what did the Moon look like when it was on the eastern horizon 12 hours earlier?

Review Question What does it mean to say a planet is in retrograde motion?

Discussion What is science?

The Scientific Method 1. Observations 2. Formulate a hypothesis – a conjecture that is used as a model for describing observations. 3. Use hypothesis to make predictions – a hypothesis which does not make testable predictions is of no use in science. 4. Test predictions by further observations

Occam’s Razor If two or more models encompass the observations equally well, the simplest model is preferred.

Discussion Science is just a collection of facts that need to be memorized.

Science A collection of explanations (theories) that allow us to make predictions about the future.

Fallacy 1 Scientists seek to uncover the truth. The goals of science are actually more limited: to invent theories that make accurate predictions. Example: Creationism may be true, but it is not science!

Fallacy 2 Scientists have to always keep an open mind. Scientists almost always work with a particular hypothesis in mind. The question to answer is always do the observations confirm their hypothesis.

Fallacy 3 Science has facts which have validity that cannot be questioned. Instead the things we loosely refer to as facts are merely inferences from the observations. Examples: The universe is 13.7 billion years old.

Imagine you are in charge of creating the universe What is the simplest possible universe you could come up with? But, it has to contain all the objects we have already talked about, the Sun, the Moon, the stars and planets.

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

What is wrong with our second simplest universe? How can we fix it? Discussion

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

What is wrong with our third simplest universe? Discussion

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

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?

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.

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 farthest from the planet

Synodic vs. Sidereal Periods of the Planets Sidereal = actual orbital period with respect to the stars Synodic = time to return to same configuration with respect to the Sun

Astronomical unit The average distance from the Sun to the Earth is called the astronomical unit (AU).

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.