Day 3 Chapter 2 Gravitation and the Motion of the Planets

Science is the key to understanding Science: a body of knowledge and a process of learning about nature (called the scientific method). Knowledge is acquired by observations and experiments. Scientific method is a process for gaining more knowledge, that can be tested and accepted by everyone. Scientific theory is an explanation of observations or experimental results that can be described quantitatively and tested. The theory must make testable predictions that can be verified by new observations or experiments, and can possibly be refuted. Theories can be modified and should be the simplest version that explains the observations (Occam’s razor). Observe, hypothesize, predict, test, modify, economize.

The Copernican Revolution The development of the current model of the solar system began with careful measurement of the movement of the Sun, the Moon, and the planets. Let’s review the motion and the phases of the Moon, as we currently understand them. When we watch the Moon, it’s shape changes from one night to the next:

From the astronomy picture of the day web site ( link )link

Lunar Phases

Explaining the Motion of the Planets was a major challenge to the ancient astronomers. The motion of the Moon and Sun seemed fairly simple, almost like they were moving in circles around the Earth. The Moon moves from west to east on the celestial sphere in a very orderly way. Five other objects did NOT move in this simple way. They are the planets, the wanderers in the Heavens. The planets usually move from west to east on the celestial sphere, but …not always. The most perplexing aspect of the planets’ motion is motion in the opposite direction, from east to west, called retrograde motion, which occurs on a regular basis.

Planetary Motions include Retrograde motion

Retrograde motion occurs over several weeks, and involves motion to the west, as compared to prograde (direct) motion, which is to the east (relative to the stars of the ”celestial sphere”).

Geocentric Model of planetary motion (Greek philosophy)

The Geocentric Model does explain retrograde motion, using concepts like deferent and epicycle. These could be illustrated by swinging a ball on a cord as we revolve a center of an epicycle around the Earth. (class demonstration here)

Ptolemy’s Model of planetary motion used deferents (big circles) and epicycles (little circles centered on a point that moves on the deferent). This involved up to 80 circles to describe 7 objects!

Nicholas Copernicus and his Heliocentric model of the Solar System explained this in a simpler way with the Sun at the center.

The Heliocentric Model also explains the Retrograde Motion of the planets.

More illustrations of retrograde motion, using Earth and Mars as the example.

Retrograde Motion of Mars as seen from Earth

Galileo Galilei and the Birth of Modern Astronomy Galileo built a telescope in 1609 and looked at the sky. Four objects: The Moon The Sun Jupiter Venus (and much more)

Galileo looked at the Moon and saw mountains, craters, valleys, and topography like you might find on the Earth. The Moon was perhaps an object like the Earth! By projecting an image of the Sun, he could see imperfections on the Sun. Sunspots could be seen to move from east to west on the Sun and he deduced that the Sun rotated about once a month.

Galilean Moons of Jupiter Small point of light could be seen near Jupiter. By observation during several weeks he deduced that these were moons and that they revolved around Jupiter. Perhaps this planet was like the Earth, with several moons of its own. It also seemed like a miniature model of the heliocentric solar system.

Venus Phases in the Heliocentric model These are consistent with the observations in a telescope.

Venus Phases in the Geocentric model are obviously wrong as soon as you observe with a telescope

Johannes Kepler and the Laws of Planetary Motion

Tycho Brahe obtained data over a period of 21 years that were later used by his assistant Johannes Kepler

Kepler’s three laws of planetary motion Orbital paths of the planets are ellipses. An imaginary line connecting the planet with the Sun sweeps out equal areas of the ellipse in equal intervals of time. The square of a planet’s orbital period is proportional to the cube of its semi-major axis. Kepler published this in 1609, the same year that Galileo built his first telescope.

An Ellipse can be drawn with string and TWO foci

For an ellipse, r 1 + r 2 = 2a The eccentricity is defined as: e = c/a A circle results when e = 0 GeoGebra demonstration:

Some Properties of Planetary Orbits

Kepler’s Second Law: equal areas in equal time This also means higher speed at closer distances.

Another graphic on Kepler’s Second Law:

The Astronomical Unit is about 150,000,000 km

Kepler’s Third Law: P 2 (in years) = a 3 (in a.u.) Basically, it means that large orbits have long periods.

Real orbits have the center of mass as one focus For the Sun and planets, this is not a large effect. For binary stars, the center of mass may be near the middle of the line connecting them.

Let’s review Kepler’s Laws. Review: see if you can tell what these are simulating: s_sim.html im.html s_sim.html im.html

The first exam is on Thursday, Sept. 10 (next week!) We will have about 30 minutes of class before the exam. Then you will take the exam (which uses a Scantron). The exam is multiple choice and true/false questions. Coverage is Chapters 1 and 2 in your textbook. To review, look at the chapter summaries, my day notes, and a study guide that I will post this weekend.