Monday January 31 2011

********* The Planets ***************

From prehistoric times, humans had noticed 5 objects that looked much like stars, but that moved against the pattern of the "fixed" stars. These 5 objects became known as "planets", derived from the word for "wanderer". These 5 objects are now known as: Mercury, Venus, Mars, Jupiter and Saturn.

Naked eye observations over years showed some obvious aspects of the motion of the planets: (1) they moved along the path of the Sun in the sky (the ecliptic) (2) Mercury and Venus were always found relatively close to the Sun (in angular distance), while Mars, Jupiter and Saturn could be at any angle from the Sun and (3) Mars in particular (but also Jupiter and Saturn) sometimes changed direction of its motion against the background stars. This motion is called a "retrograde loop" (pictures below).

Mars retrograde loops- The diagram

Mar's retrograde loops - The Movie.

Mar's retrograde loop - The Photo. If you carefully noted the position of Mars relative to background stars over a period of a few months, you would find that Mars mostly moves eastward relative to the stars, but sometimes it "backs up" , moves to the west for a while, then turns around again and heads to the east.. This motion is called a "retrograde loop".

The first slide shows diagrams of what 3 of these loops look like against the background stars. The second link shows an animation of a loop. Note the date counter in the lower corner. The third slide is a photo montage of a loop along with the background stars and constellations. The numbers next to the images of Mars are the dates. Mars starts on the western (right hand) edge of the frame on 8/18 (August 18), then moves steadily eastward (to the left) until about 11/10 (November 11). At this point Mars "turns around" and heads towards the west until 1/31 (January 31 of next year), at which time it again "turns around" and starts heading east again until it reaches the left hand edge of the frame in May. The top part of Orion is shown, alongs with a few other constellations. Left of Betelgeuse is Canis Minor (the Little Dog). Canis Major (the Big Dog) is off the picture, below Canis Minor.

Geocentric model. The ancient Greeks (Aristotle and partcularly Ptolemy) thought the planets moved around the *Earth* (geocentric model) on circular paths at constant speed. Obviously, its impossible for a planet to do a "retrograde loop" in this model. To account for retrograde loops, Ptolemy said the planets went around little circles whose centers went around the Earth on big circles. This shows some aspects of geocentric models. The top panel shows an "epicycle" which is a small circle that a planet follows. The center of the epicycle follows a larger circle (the "deferent") around the Earth. Some models put the Earth not quite in the center of the circle.

The bottom panel shows Ptolemaic (geocentric) system. Note that Mercury and Venus orbit points on a line between Earth and Sun. This is how the geocentric model sought to explain the fact that we only see Mercury and Venus within a limited angular distance from the Sun. The other planets (Mars, Jupiter and Saturn) orbit on epicycles around deferents that are centered at (or near) the Earth.

Retrograde loops in geocentric system This is how Ptolemy explained the retrograde loops of Mars- with a "wheel on a wheel" - an epicycle.

Geocentric model. Another diagram of the Ptolemaic system. Again note the different configurations of Mercury and Venus as opposed to Mars, Jupiter and Saturn.

Heliocentric (Copernican) model For almost 1500 years, scholars accepted the geocentric model of the planetary motions. To better account for the observed motions, some astronomers put in extra epicycles: "wheels on wheels on wheels". Finally, Copernicus came along and proposed that the planets (including Earth) orbited the Sun - the heliocentric system. Copernicus's model did not at first do a much better job than the Ptolemaic model, as Copernicus did not give up the idea of circular orbits. However, the heliocentric model naturally explains both retrograde motion of Mars (and Jupiter and Saturn) and the fact that Mercury and Venus can only appear near the sun. Mercury and Venus differ from Mars, Jupiter and Saturn in that they are closer to the Sun than is the Earth, while the other three bodies are farther from the Sun than is the Earth. In the heliocentric system, the Earth becomes the "third rock from the Sun"- a body orbiting the Sun, just like the other planets, rather than the center of the solar system.

In this old drawing of the Copernican system we see the Sun (Sol) in the center, with circles (going outward) for Mercury, then Venus, then Earth (Terra) with the Moon orbiting the Earth, then Mars, Jupiter and Saturn. The outermost circle is for the stars. The spacing is all wrong, and the orbits are not really pure circles, but the basic idea- the Earth is the 3rd rock from the Sun, with Mercury and Venus closer to Sun than us, and the other planets farther, is right on.

Retrograde loops in heliocentric model- The Diagram

Retrograde loops in heliocentric model- The Movie Retrograde loops of Mars, Jupiter and Saturn are easily explainable in heliocentric model, occuring when we pass the outer planet as both Earth and the outer planet orbit Sun. Planets closer to the Sun orbit the Sun in a shorter time than planets farther from Sun.