Motions of the Planets

As we said in the previous lecture, all of the planets orbit the Sun in the same plane, along with the Earth. When we look from our vantage point on the Earth, the Earth's orbital motion makes the Sun appear to move along the ecliptic, taking 1 year to make a complete trip. That means the stars gain 4 minutes on the Sun every day. The length of a "star" day, then, is 23h 56m, and this is called a SIDEREAL day. The normal kind of 24h day is the SOLAR day. So, the stars gain 4 minutes per day, which after a month is (4 minutes/day)*(30 days/month) = 2 hours per month. If you want to see that same stars next month that you can see at 9 pm tonight, you will have to go out at 7 pm next month! Of course, 2 hours per month adds up to 24 hours over 1 year.

Lecture Question #1

The Sun appears to move along the ecliptic due to the Earth's orbit. Because the other planets are in the same plane, they also appear to move along the ecliptic. Even the Moon is nearly in this same plane (only 5 degrees off), so it too is always found near the ecliptic. So the ecliptic was a very important line in the sky to ancient peoples trying to understand the universe. One thing that puzzled the ancients was that some planets, like the Sun and Moon, moved smoothly along the ecliptic, but others, like Mars, seem to move in an erratic fashion. They move smoothly along for most of their orbits, but sometimes they actually slow down, back up, and then move forward again. This motion is called RETROGRADE motion.

The history of astronomy is based on written accounts, but of course we have only a fraction of what had been written, much of which is now lost.  We know that "Western" civilization became well established by 3000 B.C. in the Middle East, Egypt, and Mesopotamia.  The great pyramids were constructed in Egypt between 2700-2100 B.C., and were aligned using astronomical observations of the "north star" of the time, Thuban.  The Egyptians believed that the Sun was a god of fire, Ra, which was born anew each morning, traveled across the sky, and was destroyed each night.

Modern ideas of astronomy were first developed by the ancient Greeks starting around 500 B.C.  The partial works of many Greek writers, or mention of their writings by later writers, allow us to know some of these ideas.  Alexander the Great led an expansion of the Greek empire to a wide region around the Mediterranean and the Middle East.  He had a great interest in scholarship and learning, and he founded a city of learning, Alexandria, on the Nile delta of Egypt.  He died at age 35, but his dream was accomplished by the creation of the great library of Alexandria, which became the center of research for 700 years, well into Roman times.  By the end of this period, it contained about 1/2 million "books" in the form of papyrus and vellum (skin parchment) scrolls.

The Greek astronomers used geometry to understand the heavens and the Earth.  Eratosthenes, around 200 B.C., measured the circumference of the Earth to within 1%, suggested that India could be reached by sailing west from Spain, and determined that the length of the year was 365.25 days, even suggesting adding a leap day every four years.  Aristarchus postulated a heliocentric "universe" with the Sun at the center.  Unfortunately, most of these ideas and accomplishments were lost (or disbelieved), and what survived of the Greek studies, mostly the view taught by Aristotle (384 - 322 B.C.), was set down much later in a famous surviving work by Claudius Ptolemy (100 - 170 A.D.) called the Almagest.  This was the model of the Earth-Centered Universe that was taken into religious teachings of the time and became entrenched with Christian dogma during the Middle Ages (sometimes called the "Dark Ages").

What do we mean by a scientific model?  It is a framework, or conceptual model that can be used to explain currently known facts and make predictions that can be tested.  The starting point for the Ptolemaic model is the common sense idea that the Earth is flat and immobile, and that all of the celestial bodies (the Sun, Moon, planets, stars) move around the Earth.  The Ptolemaic model was also based on the idea that the heavens should be built on geometrical ideals.

Earlier we discussed the convenience of considering the stars to be on a ficticious celestial sphere.  Ptolemy considered the celestial sphere as an actual, very real, crystalline sphere.  The stars were thought to be fixed onto this outer perfect sphere.  Inside this sphere were other perfect spheres on which were attached the 7 "planets" in the following order (outer to inner)--Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon.  Each of these perfect spheres turned at their own rate, and anything attached to them would have motions that are perfect circles.  However, Ptolemy (and each of the earlier Greek scholars) was quite aware of the retrograde motion problem--the planets appear at times to move backwards in the sky.  Since all motions had to be on perfect circles, Ptolemy (and earlier scholars) embellished the model by adding epicycles, little circles on circles.  He also offset the circles so that they were not centered on Earth.   With these enhancements, the model could predict the future positions of the planets to within a degree or so, which was pretty good at the time.

The book by Ptolemy that described this model would have been kept at the library in Alexandria.  However, in 415 A.D., around the time of the fall of the Roman Empire, the library was destroyed (burned) by anti-intellectual mobs, and many many irreplaceable manuscripts were lost.   Much more would have been lost, but a new center of scholarship arose about the same time in Baghdad (present-day Iraq).  There, the book by Ptolemy received its name, the Almagest.  Many of the star names we use today date from this time, and have Arabic names (e.g. Betelgeuse--armpit of the giant; Algol--the Ghoul--actually representing the eye of Medusa).

Again, the Ptolemaic model became Church dogma, and was taught throughout Europe during the Middle Ages.  It became blasphemous to challenge these ideas, and led to severe problems for early modern scientists like Kepler and especially Galileo.

The Ptolemaic system lasted for almost 1300 years before Nicholas Copernicus (1473-1543), a Polish canon of the Church, set down in a small, handwritten work around 1514 the following axioms:

• There is no one centre in the universe.
• The Earth's centre is not the centre of the universe.
• The centre of the universe is near the sun.
• The distance from the Earth to the sun is imperceptible compared with the distance to the stars.
• The rotation of the Earth accounts for the apparent daily rotation of the stars.
• The apparent annual cycle of movements of the sun is caused by the Earth revolving round it.
• The apparent retrograde motion of the planets is caused by the motion of the Earth from which one observes.

He later wrote these into his great work, De Revolutionibus, published just after his death, that indeed caused a revolution. His version of the model did not look so different from Ptolemy's, but there was one major difference--the Earth was no longer an immovable object at the center of the Universe. His ideas were not immediately accepted, and indeed there was considerable controversy due mostly to the apparent conflict with Church dogma. He recognized that this might happen, which is one reason that he had it published only after his death.

The heliocentric model accounts for retrograde motion as due to the simultaneous motions of the Earth and an outer planet such as Mars. The Earth moves faster in its orbit, and in essence catches up with the slower-moving Mars, as shown in this demonstration.

 Lecture Question #2

Last Days Before the Telescope

We have just discussed the two world systems: the Earth-centered model of antiquity, also called the Ptolemaic model, and the Sun-centered (heliocentric) model of Copernicus, published around 1543. In the decades after Copernicus, but before the invention of the telescope, one of the most interesting characters in astronomy, Tycho Brahe (1546-1601), did his famous work. Tycho was a danish nobleman, who did not believe in the Copernicus model but had his own ideas about how the planets worked. In particular, he believed that the Sun and Moon (and stars) orbited Earth, but that all of the other planets orbited the Sun. (See the map of the Tychonic model). He was fascinated by the planet Mars, and set out to prove his theory by making the most careful observations of Mars. This set Tycho firmly among scientists, since he understood that observations were the way to confirm a theory.

To make his observations, without a telescope, he set about making the world's most precise instruments for measuring angles of objects in the sky. He built a home/observatory, Uraniborg, and could make observations from within. While previous astronomers measured positions to only about 1/2 degree precision, his measurements were good down to as little as 1/100th of a degree. His measurements failed to prove his theory, but they paved the way for his follower, Johannes Kepler, to solve the riddle of planetary orbits.

Galileo's Historic Observations

The next milestone in the history of astronomy was the invention of the telescope. It was Galileo Galilei (1564-1642), an Italian mathematician and philosopher, who heard about the telescope and, without actually having seen one, set about making his own. In 1609, his telescope was ready and he turned it toward the sky. He is credited as the first human to see a long list of wonders:

• The mountains, valleys, and craters of the Moon
• Dark spots on the Sun, and the rotation of the Sun (drawings from 1612)
• Four moons of Jupiter (translation), which he called the Medicean stars (after his patron), but which are now called the Galilean moons. Use the Solar System Simulator to see today's view.
• The phases of Venus. Here are Prof. Gary's photos of the phases of Venus in 2004.

Lecture Question #3

Each of these discoveries offered important support for the Copernican (Sun-centered) theory. The mountains on the Moon showed that the Moon is a body similar to Earth, and if it is round and moves through the heavens, why not Earth also. The spots on the Sun showed that the heavens are not "perfect." The moons of Jupiter showed that objects orbit other large bodies. And the phases of Venus showed that Venus is indeed orbiting the Sun and not the Earth (although even the Ptolemaic system assumed that).