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Proving Kepler’s second law will require us to determine the areas swept out by Mercury
during certain times of the year. We will use the following time periods since they represent
the same number of days , . huaryl~~~
__ ep~~ber 20~, 19_68to 0..£!Q_ er 3!_
0~
= 41 days
= 41 days
To determin e the position of Mercury in its orbit you first need to find the Earth on these
particular dates. Follow the line you used to plot the orbit, where it crosses (touches) the
orbit is Mercury’ s position on that date.
Mercury’ s position on Date #2
Earth’s position on Date #2
Area swept out by Mercury
in its orbit during this time.
Mercury’ s position on Date # 1
Earth’s position on Date #1
Area swept out by Mercury
during next time period.
The two time periods overlap slightly and we will use this to our advantage.
Project Requirements for the Orbit of Mercu ry
The primary goal of your poster is to show your application of Keple
r’s law through
Mercury’s observational data.
Your poster cannot be smaller than 22″ by 28″ (average poster size)!
NO FOAM!
Your final poster/project.must contain the following:
• Demonstration/proof of all three of Keple r’s Laws using your model
o 1st Law – Define
• Measure, record, and label – E, c, a
• Show calculations
• Error measurement for E
o 2nd Law – Define
• Show. areas and label triangles
• Show calculations
• Error measurement (% difference in area)
o 3rd Law – Define
• Measure,” record, and label semi-major axis
• Show calculations for “D” and “P”
• Show error measurements for “D” and “P”
• Definitions of the following terms:
o Eccentricity, elongation, aphelion, perihelion
o Label the locations of aphelion and perihelion on your model
• Data table of elongations, scale bar, title
• Name and Period # on BACK of your poster only!!
• Be creative, make your project stand out!
BONUS POINTS 1 point – Look up the most recent greatest elongation for Mercury and
plot it on
your diagram.
1 point – Measure the distance between the Earth and Mercury on Octob
er I,
·196″9 and report it on your poster.
1 point – Find the closest distance that Mercury and Earth can come to
each other
and report it on your poster (show where the planets would be and report
the
distance).
1 point_:_ List at least 5 sources of error. These are things that you may
have done
that resulted in the error percentages you calculated.
The Orbit of Mercury Project
Purpose – In this project you will use a set of
simple observations, which you could have made
yourself, to discover the size and shape of Merc ury’s
orbit.
I
L
Introduction – How do we know what the orbit of a
planet is like? At first glance this appears to be a
difficult question, but in many cases it is surprisingly
easy to derive the orbit from basic unaided eye
observations. You will be repeating the work that
Johannes Kepler did to formulate his laws of plane tary
motion. Kepler made his first discoveries while
studying the planet Mars. Then he extended his
analysis to the six planets then known. We will see
how he studied the orbit of Mercury.
The ancient astronomers of Greece were familiar with
the planet Mercury, but they did not
recog nize it as the same object when it appeared in
the evening and morning sky. It was
know n as Apollo when seen in the morning sky and
as Mercury when seen in the evening
sky. Sixte en hund red years later the motions of the
planets were observed and recorded by
the Dani sh astronomer Tycho Brahe. Brah e’s recor
ds covered over 20 years, and on his
death in 1601 these records were taken by one of his
assistants, Johannes Kepler. From
Brah e’s records Kepl er was able to find the maximum
angular distance from the Sun during
each of its appearances in the morning and evening
sky.
The diagram below reviews the definition of the terms
opposition, conjunction, inferior
conjunction, superior conjunction, greatest eastern
elongation, and greatest western
elongation. You should familiarize yours elf with these
terms –
Opposition
I
I
Superior
Co11jtu.1ction
Greatest Western Elongation
‘f
,
‘
Analysis – Use your plotted data to answer the following questions and problems. Most of what
you do below will go somewhere on your poster.
Does it appear that the orbit you have drawn is a circle? How could you be sure?
Kepler had the same problem that circles did not fit the obsen:ations of the planets. At laS t
he hit upon the idea of using ellipses for the orbits. They fit nicely.
_
1. Draw in the major axis of Mercury’s orbit. It will be the longest diameter possible in the
orbit of Mercury and will go through both foci (one of which is the Sun).
a
2.
Measure the length of the major axis to the nearest 0.5 mm. This is twice as long as “a”.
What is the length of the major axis? – .,:
•
mm
—
3. Draw in the minor axis of Mercury’s orbit. It will be perpendicular (90°) and will bisect
(divide in half) the major axis.
‘
4. Measure the length of “c” to the nearest 0.5 mm. This is the distance from the center of the
ellipse to the Sun.
(__ _
What is the length of “c”? ·-,, ___ mm
5.
All measurements that we make off of our model need to be converted to Astronomical Units
(AU’s) so that we can compare them to the actual values. To determine the scaling factor,
measure the length of the scale bar (to the nearest 0.5 mm) on the bottom of your plot of
Mercury’s orbit.
What is the length of the scale bar? 11 , J,,.
mm
1
How many AU’s are represented by this distance? _]>__,:_,_
Divide the number of AU’s by the ;engt_h of the scale bar. This number is your scaling factor.
Scaling Factor
i9, 0/ I fillould be
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