## Sample Lesson

#### From the book: Astronomy

Retrograde motion is here described by the movement of the planet Venus observed at the same time of the evening over a six-month period. Notice how over the six month period that little by little, the planet is observed to move backward through the pathway of the ecliptic [the annual path of the sun] with each successive month. [We say backwards because the motion is opposite to the direction of the setting sun] At some point, it will be observed to quit this backward motion and begin to stand still until it starts to move forward following the direction of the setting sun. This is designated in the illustration above as occurring in April. Finally it will return to its backward course moving nearer eastward with each successive week until another retrograde.

These retrograde motions are called epicycloids in the work of Copernicus. He inherited the system of movements explained by Ptolemy's earth-centered universe. It was a brilliant insight hit upon by Copernicus after thousands of calculations of how this retrograde motion could be explained in a sun-centered universe. The illustration on the following page describes his insight. Here one can see the sun in the center and the earth and a planet circling around it. The earth will make a complete circuit around the sun in a single year, but the planet, say Jupiter for instance, will take 12 years to make a complete orbit. In the illustration, you see 6 positions of the earth's orbit in a complete revolution, but the planet completes only about 1/12 of its orbit in its corresponding 6 positions. Look at what happens from the point of view of the moving earth when one connects lines of sight with each corresponding position ( I with 1; II with 2, etc.) The planet appears to heading in the same direction as the earth, but then after position six, when the earth begins its second orbit, the planet has moved ahead to position 7, but seen from the earth it looks like it has reversed its direction. Then the earth moves to position II and the planet now in position 8 has reversed itself again and moves on its original course. The appearance in the sky is that of an epicycloid or a loop---retrograde motion. Copernicus was able to show how the appearance of these movements were caused by the changing perspective from earth as both planets circled the sun.

However, one need not consider this phenomenon as a mere illusion caused by the shifting view from two moving bodies. There is genius at work in the appearing of these retrograde movements. Consider the illustrations on the following page. Here one can see how the looped retrograde path of Mars, metamorphoses its shape through the years. Now hold this picture in mind while considering the next diagram. This is a view of the planet Venus seen from the earth projected at an altitude high above the North Pole. Notice the beautiful near perfect symmetry and also the five-fold quality created by the planet's retrograde motions that is suggestive of the inherent geometry in a plants such as the rose. Given the perfect archetype seen from above (our second illustration) and the variations on a theme given by metamorphosis of the loops (the first picture we considered), form-giving patterns of the plant kingdom are suggested. If one explores this further, one will find different plant geometrical forms created by the other planets. We are not in the position to offer conclusive evidence of the influence of the planets upon the plant forms of the earth: we only offer this as something suggestive and worthy of our awe at the intelligence found in every fiber of nature both macrocosmic and microcosmic.

Lesson Activity

The student should draw the illustration on planetary retrograde motion given by Copernicus into his main lesson book using a sharp pencil and compass. Have him write several sentences of description in his own words demonstrating his understanding of the phenomenon.