CHAPTER A. LABORATORY EXPERIMENTS
Name:
A.8
I.
43
Section:
Date:
The Orbit of Mars
Introduction
Have you noticed that NASA launches planetary probes to Mars every two years? This is because about
every two years the Earth and Mars get relatively close to each other and it requires less fuel to send the
probes to Mars. In this activity you are going to determine the orbit of Mars using the method developed
by Kepler.
II.
Reference
• 21st Century Astronomy, Chapter 3, pp. 56 – 58 (Kepler’s 1st law).
III.
Materials Used
• large graph paper
• ruler
• protractor
IV.
Activities
Mars’ orbital period (687 days) is close to twice that of the Earth (365 days × 2 = 730 days). Thus, every
time Mars comes back to the same point in its orbit, the Earth has not completed two orbits yet. So if you
are on the Earth and make an observation of Mars every time Mars is at the same point on its orbit, you will
see the planet in a different direction with respect to the background stars. The two lines of sight intersect
at a point on the orbital path of Mars as shown in Fig. A.18.
The observational data you will use (found in Table A.17) shows Mars’ position on various dates between
1991 and 1998. Each pair of observations (e.g., A and A’) are made when Mars is exactly at the same point
in its orbit. The angle to Mars is measured from the vernal equinox as seen from the Earth. The Earth’s
position is the angle measured from the vernal equinox to the Earth as seen from the Sun.
All angles are measured from the direction of the vernal equinox in the counterclockwise direction.
① Draw a 10-cm radius circle on a large sheet of graph paper to represent the Earth’s orbit and assume
that the Sun is located at the center of the circle.
② Draw a line from the Sun to the right and parallel to the grid lines on the graph paper (see Fig. A.19).
This line represents 0◦ and points toward the vernal equinox. This direction will serve as the reference
for measuring angles on the Earth’s orbit. The Earth crosses the 0◦ line on the autumnal equinox
(around September 23) and the 180◦ line on the vernal equinox (around March 21).
③ Locate the Earth’s position on your plot of the Earth’s orbit for the date of each observation. Label
each position.
④ To determine the angle to Mars on any given date, draw a line from the Earth’s position parallel to
the 0◦ line. This line should be parallel to the grid lines on the graph paper. Use a protractor to
measure the angle to Mars in the counterclockwise direction from the 0◦ line. Two lines for each pair
of observations will intersect at a point on Mars’ orbit.
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CHAPTER A. LABORATORY EXPERIMENTS
★
★
Mars' orbit
Background
stars
★
★
Earth's orbit
★
θ
A
0°
θ'
A'
0°
Sun
Figure A.18: Locating Mar’s position on the orbit.
⑤ When you have finished plotting all ten points, use a compass, and by trial and error, draw the best
circle that fits the plotted points.
V.
Questions
1. What is the length of the semi-major axis of Mars’ orbit in AU’s?
2. What is the eccentricity of Mars’ orbit? The eccentricity e of an orbit is defined as e = c/a where c is
the distance between the Sun and the center of the elliptical orbit and a is the semi-major axis. How
well does your value agree with the accepted value of 0.093 (i.e., find the percent error).
3. What is the closest distance of approach for the Earth and Mars in AU?
CHAPTER A. LABORATORY EXPERIMENTS
Pairs
A
A’
B
B’
C
C’
D
D’
E
E’
F
F’
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Table A.17: Observed positions on Mars from the Earth.
Earth’s
Angle to
Pairs
Date
Earth’s
position
Mars
position
Mar 21, 91
180◦
83◦
G
Feb 27, 92
160◦
◦
◦
Nov 9, 96
45
153
G’
Oct 19, 97
24◦
◦
◦
May 17, 91
234
117
H
Apr 24, 92
213◦
◦
◦
Jan 5, 97
107
182
H’
Dec 15, 97
83◦
◦
◦
Jul 13, 91
292
150
I
Jun 20, 92
270◦
◦
◦
Mar 4, 97
165
183
I’
Feb 10, 98
144◦
◦
◦
Sep 8, 91
347
185
J
Aug 17, 92
327◦
Apr 30, 97
218◦
169◦
J’
Apr 8, 98
198◦
◦
◦
Nov 4, 91
40
221
K
Oct 13, 92
19◦
◦
◦
Jun 26, 97
276
183
K’
Jun 5, 98
253◦
◦
◦
Jan 1, 92
101
265
L
Dec 9, 92
77◦
◦
◦
Aug 22, 97
332
217
L’
Aug 1, 98
312◦
Date
Angle to
Mars
309◦
254◦
353◦
300◦
35◦
345◦
73◦
26◦
104◦
67◦
119◦
109◦
Mars
Oct 13, 92
Earth
180°
Mar 21, 91
104°
19°
Sun
0°
Dir. of
Vernal
Equinox
Figure A.19: Earth’s orbit.
VI.
Credit
To obtain credit for this lab, you need to turn in appropriate tables of data, observations, calculations,
graphs, and a conclusion as well as the answers to the above questions. Do not forget to label axes and give
a title to each graph. Show your work in calculations. A final answer in itself is not sufficient. Don’t leave
out units. In the conclusion part, briefly summarize what you have learned in the lab and possible sources
of error in your measurements and how they could have affected the final result. (No, you cannot just say
human errors – explain what errors you might have made specifically.) You may discuss this with your lab
partners, but your conclusion must be in your own words.