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AST 101 Lab 9
Retrograde Motion of Mars
Lab 9
Retrograde Motion of Mars
PURPOSE
This laboratory exercise will allow the student to relate the apparent motion of planets in
the sky to the real motion of the planets through the solar system.
REFERENCES
●
Retrograde Motion
(http://www.astro.uiuc.edu/projects/data/Retrograde/)
●
Retrograde Motion in the Copernican System
(http://honolulu.hawaii.edu/distance/sci122/Programs/p9/retromovie.gif)
●
Epicycle Animation
(http://honolulu.hawaii.edu/distance/sci122/Programs/p8/epicycmov.gif)
BACKGROUND
The rising and setting of objects through the course of a night and the slow
changes observed throughout the course of a year involve the apparent motions of the sky
as a whole.
In these phenomena the stars do not move relative to each other.
On the
other hand, since prehistoric times it has been known that the Sun, the Moon and the
planets do move among the stars.
The positions of these bodies on the celestial sphere
constantly change and their motions are complex.
The planets generally move eastward across the sky relative to the background of
stars, but occasionally they reverse directions and briefly move westward, then reverse
directions again and continue to move eastward.
This behavior is called
retrograde
, or
backward, motion.
Ancient astronomers such as Aristotle and Ptolemy believed that the Earth was at
the center of the solar system.
To account for the retrograde motion, they devised an
intricate series of circles upon circles with names such as “deferents” and “epicycles”.
The idea that the Sun is at the center of the solar system was first espoused by
Aristarchus, later revived by Copernicus, and not fully developed until Kepler derived his
three laws of planetary motion.
It is important to remind ourselves of the three basic laws of planetary motion
known as Kepler’s Laws:
1.
The planets move in elliptical orbits with the Sun at one focus of the ellipse.
AST 101 Lab 9
Retrograde Motion of Mars
2.
The orbital speed of the planet varies so that a line joining the Sun and the
planet will sweep out equal areas in equal time intervals.
3.
The amount of time a planet takes to orbit the Sun is related to its orbit size.
The second and third laws have a profound effect on the observed motions of the
planets.
Although the planets continuously orbit the Sun to the east, from the Earth’s
perspective a planet occasionally appears to stop and move to the west for a short period
of time.
The phenomenon is known as
retrograde motion
.
Retrograde motion arises
from the simple fact that the Earth occasionally overtakes a planet (Mars, for example) as
they both orbit the Sun.
The planet never actually moves backwards.
Instead, this
backward motion is an
apparent
effect due to comparing the position of the planet to the
stellar background.
This lab will look at both the apparent and the real motion of the planet Mars.
First, we will plot the position of Mars in Right Ascension (RA) and Declination (Dec) to
show its retrograde motion across the sky.
Then we will plot the relative positions of
Mars and Earth as seen from above the solar system in order to appreciate the physical
reasons for the apparent backward motion of the planet Mars.
EQUIPMENT
●
Graph paper
●
Compass
●
Protractor
●
ruler
PROCEDURE
Exercise 1: The Retrograde Motion of Mars
1)
Table 9-1 lists position data for the planet Mars in terms of RA and Dec.
Plot this
data on a sheet of graph paper, making RA the horizontal axis and Dec the vertical
axis.
Label each point with its
date
.
Important!
RA increases going to the
left
, not the right, on the horizontal
axis.
2)
When the data has been plotted, draw a smooth curve through the data, going
in
order of time
.
Table 9-1: The Position of Mars on the Sky
Date
R.A.(hours)
Dec.(degrees)
Nov. 11 1996
10.60
10.75
Nov. 21
10.93
8.93
Dec.
1
11.23
7.20
AST 101 Lab 9
Retrograde Motion of Mars
Dec. 11
11.52
5.55
Dec. 21
11.78
4.08
Jan.
1
1997
12.03
2.68
Jan. 11
12.22
1.70
************continued on next page**************
Table 9-1: The Position of Mars on the Sky (continued)
Date
R.A.(hours)
Dec.(degrees)
Jan. 21
12.37
1.05
Feb.
1
12.45
0.77
Feb. 11
12.45
0.98
Feb. 21
12.37
1.65
Mar.
1
12.25
2.50
Mar. 11
12.05
3.82
Mar. 21
11.80
5.22
Apr.
1
11.55
6.48
Apr. 11
11.37
7.18
Apr. 21
11.27
7.35
May
1
11.25
7.03
May 11
11.30
6.28
May 21
11.42
5.15
Jun.
1
11.60
3.57
Jun. 11
11.82
1.88
Jun. 21
12.07
0.00
Exercise #2: The Physical Motions of Earth and Mars
Table 9-2 lists heliocentric position data for both the Earth and Mars over several
months.
We will use Figure 9-1 to locate the Earth and Mars at various times in order to
show retrograde motion.
Both of the orbits are represented as circular (which is
approximately true).
The orbit of the Earth is about one inch in radius and the orbit of
Mars is about 1 ½
inches in radius, which reflects the true semi-major axes of 1 A.U. and
1.5 A.U., respectively.
The 0° line is the reference for the heliocentric longitude angle.
All angles will be measured in a counter-clockwise fashion.
1)
Plot the positions of the Earth on the Earth circle for each date and label them 1
through 14.
2)
Plot the positions of Mars on the Mars circle for each date and label them 1
through 14.
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AST 101 Lab 9
Retrograde Motion of Mars
3)
Starting with the number #1 on the Earth circle, draw a line through the #1
position on the Mars circle and extend the line lightly until it runs off the page.
Repeat for each set of numbers.
The lines will eventually cross each other.
4)
Three horizontal dotted lines are drawn across the page below the Earth and Mars
circles.
Starting with #1, plot and label where the line from Earth to Mars hits the
first horizontal line across the page.
Continue until the lines from Earth to Mars
begin to cross.
5)
Then plot and label where the Earth-Mars line hits the second horizontal line
across the page.
Continue until the Earth-Mars lines cross again.
6)
Then plot and label where the Earth-Mars line hits the third horizontal line.
7)
Draw a smooth curve between the points to indicate the motion of Mars.
Table 9-2: The Heliocentric Longitude of Earth and Mars
#
Date
Earth (degrees)
Mars (degrees)
1
Nov. 21, 1996
59.3
125.7
2
Dec. 11
80.6
134.6
3
Jan. 1, 1997
100.9
143.9
4
Jan. 21
121.3
152.6
5
Feb. 1
132.5
157.4
6
Feb. 11
142.6
161.8
7
Mar. 1
160.7
169.7
8
Mar. 21
180.7
178.5
9
Apr. 11
201.4
187.9
10
Apr. 21
211.2
192.4
11
May
1
221.0
197.0
12
May 11
230.6
201.6
13
June
1
250.8
211.3
14
June 21
269.9
221.1
AST 101 Lab 9
Retrograde Motion of Mars
LAB 9
Retrograde Motion of Mars
Data and Results
Name: ______________________
Date: ______10/10
______
Lab Section: _____
Lab Partners:
(1) ____________________
Table Number:
__________________
(2)____________________________________
(3) ____________________________________
Exercise 1: The Retrograde Motion of Mars
1)
Does Mars always appear to move through the sky at the same rate?
No, Mars’ speed changes in relation to Earth’s distance to Mars.
2)
Approximately how long did it take Mars to complete the loop?
From Nov 21, 1996 to June 21, 1997. or 162 Days.
3)
During the loop, approximately how much time was spent in retrograde motion?
41 days. March 21 - May 1st.
4)
Approximately where did Mars begin and end the retrograde portion of the loop?
Began - March 21st
Ended - May 1st
Exercise #2: The Physical Motions of Earth and Mars
1)
At what points does the retrograde motion begin and end as seen from the Earth?
March
21st
-
retrograde
begins
May 1st - retrograde ends
AST 101 Lab 9
Retrograde Motion of Mars
2)
At what point is the distance between Mars and Earth the least?
Point 8, March 21st
3)
What is the relationship between the Sun, Earth, and Mars at the time of
maximum (fastest) retrograde motion?
Points 8 and 9 - when the planets are aligned.
0
Orbit of Mars
Orbit of Earth
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AST 101 Lab 9
Retrograde Motion of Mars
Figure 9-1:
Retrograde Motion from the Relative Motions of Earth and Mars