Download Laboratory : Retrograde Motion

Grade 9 Academic Science – Space
Retrograde Motion
Objectives
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Demonstrate understanding of the celestial sphere and the celestial grid.
Draw a graph of planetary motion given its celestial coordinates at various times.
Demonstrate ability to read a graph and its coordinates.
Demonstrate understanding of retrograde motion of a planet against the fixed star background.
Demonstrate understanding of the geocentric and heliocentric explanations for retrograde motion.
Demonstrate ability to make conclusions about planetary motion from analysis of pictorial and
graphical information.
Discuss the difficulties in determining the correctness of either the geocentric or the heliocentric
explanations using observational data alone.
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 nears the ecliptic (apparent
path of the Sun across the night sky). Occasionally each planet turns around and moves to the east ('backwards') for
awhile, then turns around to head westward again. This movement makes an apparent loop or zigzag when viewed
against the background of stars.
 The last statement is very important. Why?
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 centre 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. It is easy to see why our ancestors thought the
Earth was the centre of the Universe when we watch the movement of the heavens. It is much easier to imagine that
we are motionless at the centre 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 moon. It was the erratic movement 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 insists all heavenly motion must be circular.
Mars repeats its retrograde motion every 26 months, but each retrograde episode traces a slightly 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 zigzag. In this exercise you to plot and graphically observe the retrograde motion of Mars during the
period from October 1970 to May 1971. The graphed motion will allow you to see how it can be explained by both
a geocentric and a heliocentric model. NOTE: Drawing the graph is NOT your primary objective. More importantly
is reading and interpreting graph (e.g., the actual motion of Mars through the sky during one particular retrograde
episode; your explanation of the motion).
A. Graphing a Retrograde Loop
Table 1 gives the actual location in the night sky of Mars at ten day interval 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.
Plot ALL of the points from Table 1. Indicate on the graph, the points which represent the dates shown in bold with
an asterisk (*). This will help you to connect the points in the correct chronological order. Connect the points with
a smooth curve by date.
Table 1. Positions of Mars * Indicate these dates on the graph
Date
Right Ascension
Declination
Hour
Minute
Degrees
Minutes
11 Oct
8
5
21
49
21 Oct
8
26
20
54
31 Oct*
8
46
19
58
10 Nov
9
3
19
2
20 Nov
9
19
18
12
30 Nov
9
31
17
31
10 Dec
9
41
17
4
20 Dec*
9
47
16
56
30 Dec
9
48
17
11
9 Jan
9
45
17
50
19 Jan
9
37
18
51
29 Jan*
9
23
20
3
8 Feb
9
8
21
13
18 Feb
8
52
22
5
28 Feb
8
39
22
33
10 Mar*
8
32
22
35
20 Mar
8
31
22
17
30 Mar
8
34
21
42
9 Apr*
8
41
20
52
19 Apr
8
52
19
59
29 Apr*
9
5
18
34
9 May
9
21
17
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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?
Figure 1
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.
B. Geocentric Explanation for Retrograde Motion
In the geocentric system, Earth is at the centre 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. Now try to visualize how the dot would appear to move if viewed from the centre of the circle looking
outward.
1. Sketch a diagram which illustrates how epicycles could produce retrograde motion on the circle
surrounding Earth below.
2. Indicate on the diagram where Mars would be in retrograde motion.
3. See second diagram for a hint.
Figure 2. The epicycles for Part B
HINT: For a visual explanation of Geocentric Retrograde see the webpage at
 http://alpha.lasalle.edu/~smithsc/Astronomy/retrograd.html
C. Heliocentric Explanation for Retrograde Motion
Figure 3 shows the actual orbits of Earth and Mars around the Sun. Each number represents the position of the two
planets at consecutive one-month intervals (NOTE: 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.
4. Answer the questions after you complete the diagram.
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? That is, when are the planets
close together?
4. What is the relationship between Sun, Earth and Mars at the time of maximum (fastest) retrograde motion?
5. How could you decide which of these two models really explains retrograde motion as we see it?
Figure 3. Draw the lines for Part C
BONUS
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Why does this picture not represent the true orbit of planets around the Sun?