# Laboratory

## Objectives

1. Demonstrate undersanding of the celestial sphere and the celestial grid.
2. Draw a graph of planetary motion given its celestial coordinates at various times.
3. Demonstrate ability to read a graph and its coordinates.
4. Demonstrate undersanding of retrograde motion of a planet against the fixed star background
5. Demonstrate undersanding of the geocentric and heliocentric explanations for retrograde motion
6. Demonstrate ability to make conclusions about planetary motion from analysis of pictorial and graphical information.
7. Discuss the difficulties in determining the correctness of either the geocentric or the heliocentric explanations using observational data alone.

## References

Discussion of heliocentric and geocentric models is in Booth & Bloom, pp. 11-12, Spielberg & Anderson, pp.30 - 37.

Also see the relevant sections of program 4 [the celestial sphere][the planets],program 7 [Plato's Question], program 8 [Ptolemaic System], program 9.[Uniform Circular Motion], [Schoastic Cosmology], [Copernicus]

## Introduction

Retrograde motion refers to the change of direction of the planets as they wander through the fixed background of the stars.

Most of the time the nightly course is east to west in fairly predictable paths near the ecliptic. Occasionally each planet turns around and moves to the east ('backwards') for awhile, then turns around to head westward again, making a loop or zig-zag against the star background.

There are two good explanations or models to explain retrograde motion. One involves a geocentric view, where the sun and planets go around the Earth which is stationary. The other is a heliocentric view, where the earth and planets go around a stationary sun.

For twenty five centuries or more people thought that the earth was the center of the universe. They believed that the geocentric model explained the movements of the stars and planets, thinking that they revolved around the earth the way the celestial sphere appears to from our vantage point on earth.Today we have much evidence that the earth is just one of the many planets, and that it revolves around the sun once per year as it rotates on its own axis once per day.

It is easy to see why our ancestors thought the earth was the center of the universe when we watch the movement of the heavens. It is much easier to imagine that we are motionless at the center of a universe which revolves around us than to imagine the result of the combined daily rotation and annual revolution of earth. This is especially true when it comes to the motion of the other planets in relation to the earth's own moions..

It was the erratic motions of the planets that gave early astronomers problems. The motions of the stars, sun, and moon can easily be explained geocentrically. The retrograde motion of the planets is much more difficult to explain, especially if one is locked into a paradigm that insistst that all heavenly motiion must be circular.

Program 3 helped us to understand how paradigms affect thinking and perception, while programs 6, 7, 8, and 9 studied how the circular paradigm became so deeply entrenched..

Here is an animation of Mars in retrograde in 2004 (320 KB). It is speeded up one million times faster than the actual speed. The actual time spanned by the video is eight months. The video is in mp4 format and will require that you have Quicktime installed. You can download for free the latest version of Quicktime movie player from http://www.apple.com/quicktime/ in either PC or Mac versions.

Mars repeats its retrograde motion every 26 months, but each retrograde episode traces a slighty different path, so there is no way to predict in advance how your graph will look. It might be a loop to the left, a loop to the right, or merely a zig-zag.

Here is an mp4 animation of 4 consecutive retrograde episodes of Mars. Remember when watching that the retrograde phases occur every 26 months, so this is speeded up eight and one half million times.

In this exercise you to plot and graphically observe the retrograde motion of Mars during the period from October 1970 to May 1971, and it will allow you to see how it can be explained by both a geogentric and a heliocentric model. Although drawing the graph is an important part of the exercise it is not the promary objective. While working on this exercise you should think about what the graph represents (the actual motion of Mars through the sky during one particular retrograde episode), and also how you might explain this motion.

Try your best to keep your prejudices (e.g.your paradigm) from 'deciding' for you which explanation makes more sense. You will probably find it difficult to do so!

## A. Graphing a retrograde loop.

Table 1 gives the actual location in the night sky of Mars for at ten day intervals in 1970 - 71 when retrograde motion occurred.The numbers in table 1 are the coordinates on the small section of the celestial grid in which the motion occurred.

Right ascension and declination are coordinates on the celestial sphere. Right ascension is measured in hours and minutes west of the vernal equinox, declination is measured in degrees and minutes from the celestial equator. Click for more information about graphing.

1. Plot ALL of the points from table 1 on the graph of figure 1.
2. Indicate on the graph the points which represent the dates shown in red with an asterisk (*). This will help you to connect the points in the correct chronological order.
3. Connect the points with a smooth curve by date.

Click here for the coordinates in decimal form for plotting in Excel or other graphing software.

or

Download an Excel spreadsheet with the decimal coordinates and here for instructions on how to draw the graph using Excel (also included on the Excel spreadsheet)

8 5 21 49

8 26 20 54

8 46 19 58

9 3 19 2

9 19 18 12

9 31 17 31

9 41 17 4

9 47 16 56

9 48 17 11

9 45 17 50

9 37 18 51

9 23 20 3

9 8 21 13

8 52 22 5

8 39 22 33

8 32 22 35

8 31 22 17

8 34 21 42

8 41 20 52

8 52 19 59

9 5 18 34

9 21 17 6

## B. Geocentric Explanation for Retrograde Motion

In the geocentric system, Earth is at the center of a series of circles. The simplest model to illustrate the motion contains epicycles. Imagine a ball rolling around a big wheel. Suppose the ball is transparent and has a black dot painted on it. Then try to visualize how the dot would appear to move if viewed from the center of the circle looking outward..

1. Sketch a diagram which illustrates how epicycles could produce retrograde motion on the circle surrounding Earth on the figure below.
2. Indicate on the diagram where Mars would be in retrograde motion.

## C. Heliocentric Explanation for Retrograde Motion

Figure 3 shows the actual orbits of Earth and Mars around the sun. Each number represent the position of the two planets at consecutive one-month intervals (but not the same as in table 1).

1. Connect the corresponding points in the orbits of Earth and Mars with straight line. Extend the lines to intersect the vertical line at the right.
2. Number these intersection points on the vertical line following the example.
3. Indicate on the figure where Mars would appear to be in retrograde?

## Figure 1. Plot the graph from A.

Remember that there are sixty minutes of time in one hour and sixty minutes of arc in one degree. You can round to the nearest five minutes when plotting. Click here if you need help in plotting the graph.

## Questions for part A.

1. Does Mars always move through the sky at the same rate?
2. About how long did it take for Mars to complete the loop?
3. During the loop, how much of the time was spent in retrograde motion?
4. Approximately when did Mars begin and end the retrograde portion of the loop?

## Fig. 2 Draw the epicycles for part B here.

See the illustration on page 12 in Booth & Bloom and page 32 in Speilberg & Anderson to see what the epicycles look like, or watch these two small animations. The sketch does not need to be complicated or to represent the actual motion of Mars. It only need to show how retrograde motion can happen using epicycles, as in the animation at theleft below.

The animation on the right illustrates how the addition of an additional epicycle can cause complex motion.

Another excellent animation can be viewed from here as well.:(The animated gif was obtained from Astronomy 161 web site at The University of Tennesee, Knoxville.)

## Figure 3. Draw the lines for part C here.

You can see an animation of this motion here. (The animated gif was obtained from Astronomy 161 web site at The University of Tennesee, Knoxville.)

Here is another animated retrograde that shows the relative motions of earth and Mars side-by-side with the planet's path through the background stars. (from the astronomy department at the University of Illinois, Urbana-Champaign)

## Questions for part C.

1. What do the numbered lines represent?
2. At what points does the retrograde motion begin and end as seen from earth?
3. At approximately what point is the distance between Mars and Earth least (when are they at their closest distance)?
4. What is the relationship between Sun, Earth, and Mars at the time of maximum (fastest) retrograde motion?

## Questions For Thought

Here is an animation that shows the retrograde motion of Mars with heliocentric and geocentric motion to scale side-by-side. At the top is shown the motion of Mars as seen from either perspective. This animation is from the University of Toronto.

1. Without additional knowledge or information (using only the path of Mars through the sky as represented on the graph in Figure 1) how could you decide which of these two models really explains retrograde motion as we see it; could you know which is the better explanation?
2. What additional information might convince you of the correctness of one or the other models?
3. Which model do you think represents the actual motion of Mars?