Lesson 3 Lab - Solar System Models Worksheet
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Name: Adli M. Cruz Santana
Lesson 3 Lab - Solar System Models
Background Material
Review the Geocentric Model background material. The simulation of
Ptolemy’s model
demonstrates the dominate model when Copernicus presented his heliocentric model.
Thoroughly review the Heliocentric Model background material.
Question 1: (1 point) Look at the Animation of the Copernican Solar System on the
“Heliocentricism” page. What relationship do you notice between how fast a planet
moves in its orbit and its distance from the Sun?
The relationship between how fast a
planet moves in its orbit all depends on distance, the closer to the sun the faster the
planets move in orbit and the further from the sun slower they go with each other.
Question 2: (1 point) The table below concerns various elongation configurations for a
hypothetical superior planet.
Complete any missing elongations, terminology,
or lettered labels
on the drawing
where the Sun and Earth are shown.
NAAP – Solar System Models 1/8
Location
Elongation
Term
A
180°
Opposition
B
90 degress
W
Western Quadrature
C
0 degress
Conjunction
D
East 120°
XXX
C
Sun
Earth
Question 3: (1 point) The table below concerns various elongation configurations for a
hypothetical inferior planet.
Complete any missing elongations, terminology, or lettered labels
on the drawing where the Sun and Earth are shown.
Simulator Exercises
Open up the Planetary Configurations Simulator and
complete the following exercises.
Question 4: (1 point) In this exercise we will measure the synodic period of Mercury. Set the
observer’s planet to Earth and the target planet to Mercury.
The synodic period of a planet is the
time it takes to go from one elongation configuration to the next occurrence of that same
configuration.
However, it makes sense to use an easily recognized configuration like superior
conjunction.
Drag a planet (or the timeline) until Mercury is at superior conjunction.
Now zero
the counter, click start animation, and observe the counter.
A synodic period is that time until
Mercury is once again at superior conjunction.
What is the synodic period of Mercury?
0.332 years
NAAP – Solar System Models 2/8
Location
Elongation
Term
A
0 degrees
Superior Conjunction
B
0 degrees
Inferior Conjunction
C
46.5 E
(venus)
Greastet elongation
D
West 20°
XXX
Question 5: (1 point) In the previous exercise superior conjunction was used as the reference
configuration, but in practice it is not the best elongation configuration to use. Explain why.
What is the best elongation configuration to use? (Hint: when is an inferior planet easiest to
observe in the sky?) Do you get the same result for the synodic period you got in Question 4?
Superior conjunction is not best used to reference configuration because due to the
planets lining along line a straight line joining the Earth and the Sun on the opposite side, which
is the furthereat inferior planet are easier to observe because the sky is closer.
Question 6: (1 point) Use greatest elongation as the reference configuration to calculate the
synodic period of Venus. (Be careful. There are two different occurrences of greatest elongation
for an inferior planet: eastern and western.) Also, record the value of the greatest elongation of
Venus
Synodic period of Venus:
225 day
Greatest elongation of Venus:
584
What general trend do you notice between an inferior planet's distance from the Earth and its
synodic period?
The general trend is when it close to a inferior planet is close to earth its
synodic pattern in slower and faster when further because of how fast orbits its synodic patter
takes less time.
Question 7: (1 point) Now use the simulator to find the value of Mercury's greatest elongation.
Greatest elongation of Mercury:
23 degrees
Compare the values of greatest elongation for Mercury and Venus. What relationship do you
notice between the value of greatest elongation of a planet and its distance from the Sun? Can
you create a hypothetical 3
rd
inferior planet in the simulator to check your reasoning?
The
relationship between mercury and Venus greatest elongation includes how Venus period is twos
NAAP – Solar System Models 3/8
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time than Mercury, the greatest elongation of a planet and its distance from the sun are the same,
concluding both values is the same.
Question 8: (1 point) Now we will measure the synodic period of Mars. As before, set Mars up in
a particular elongation configuration, zero the counter, and then animate the simulator again to
see how long it takes Mars to return to the same configuration.
Synodic period of Mars:
2.144 years
Question 9: (2 point) Just as with superior conjunction in Question 2, conjunction is not the best
configuration to observe a superior planet in the sky. Explain why this is and explain which
configuration is best for observing a superior planet. Conjunction is not the best configuration to
observe superior planets is opposition because the planets position the sun and earth are all
aligned in a straight line.
Measure the synodic periods of Jupiter and Saturn .
Synodic period of Jupiter:
11.9 years
Synodic period of Saturn:
29.5 years
Question 10: (2 point) Look over the synodic periods of the superior planets. Is there a trend?
What value does the synodic period of a superior planet approach as we consider planets farther
and farther away from Earth? Explain this trend.
The superior planets that are farther from
earth are bigger with orbits will have faster synodic periods because the observer’s planet will be
able to go around its orbit faster.
NAAP – Solar System Models 4/8
Question 11: (2 point) Compare your answer above and your answer to the last part of Question
5, and then state a relationship between a planet’s synodic period and its distance from Earth that
is valid for both inferior and superior planets.
A similar relationship between inferior and superior planets is that planets
further from earth will have shorter synodic periods.
Question 12: (2 point) So far we have only considered elongations of planets as viewed from
Earth. Suppose you were standing on Mars, watching the planets go through their motions.
Could you use the same terminology as before to explain the configurations of other planets?
Yes, you could – the only difference would be that there is an additional inferior planet: the
Earth. As an observer on Mars, you would see the Earth go through the same configurations as
any other inferior planet. For example, when the Earth appears on the opposite side of the Sun as
viewed from Mars, it is at superior conjunction. When the Earth appears at superior conjunction
from Mars, at what configuration does Mars have as seen from Earth?
Mars
oppositions
happen about every 26 months. Opposition happens while the red planet is closest to the sun.
Every 15 to 27 years, opposition occurs within a few weeks of Mars perihelion which is the point
in its orbit when it is closest to the sun.
Set up the simulator so that the Earth appears at superior conjunction from Mars and time how
long it takes the Earth to return to this same elongation configuration – that is, the synodic period
of Earth as observed from Mars.
Record the synodic period of Earth as viewed from Mars:
2 years 52 days
How does this answer compare with the synodic period of Mars as found in Question 8? Explain
why they are related.
Earth and Mars have similarities because they are both closest to the sun
which conclude both have longer synodic periods.
NAAP – Solar System Models 5/8
Question 13: (2 point) Copernicus was interested in measuring the synodic periods of the planets
so that he could calculate their sidereal periods. In this exercise we will calculate the sidereal
periods of the planets using the data you have already collected.
You may use a handheld
calculator or make use the “Synodic Period Caclulator” on the Elongations and Configurations
background page.
Recall that the sidereal and synodic periods of a planet are related by
1
S
=
1
P
−
1
E
,
for inferior planets
1
S
=
1
E
−
1
P
,
for superior planets
where P stands for the planet's sidereal period, S stands for the planet's synodic period, and E
stands for the Earth's sidereal period.
We will now work an example to see how these formulas
are used to find a planet’s sidereal period. The synodic period of Jupiter is 1.09 yr. Since E is 1
year, we have
1
1
1
1
1
, so
0.0826
, therefore
12 yr.
1.09yr
1yr
yr
P
P
P
Now calculate the sidereal periods of the rest of the planets to complete the table below. (Be
sure to use the same units of time for each of the variables. If you measured S in days then you
should convert it to years by dividing by 365.25 days/year.)
Planet
Synodic Period
(from exercises above)
Sidereal Period
(calculated)
Mercury
116
88 days
Venus
584
225 days
Earth
Not Applicable
1 yr
Mars
780
1.9years `
Jupiter
1.09 yr
12 yr
Saturn
378
29.5 years
Is there a relationship between the sidereal period of a planet and its distance from the Sun? How
does this relate to your observations in Question 1?
The farther a planet is from the sun, the
NAAP – Solar System Models 6/8
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longer its sideral period becomes. This relates to my point of view in the first question as planets
become closer to the sun, the faster they orbit and the longer a planets sideral period would be
for sun to return to the same position.
Question 14: (2 point) Put yourself on the planet Mars and carefully note the location of the sun
on the Zodiac Strip.
Now zero the counter, animate, and time how long it takes for the apparent
position of the sun relative to the background to return to the same position.
How does this
value for the Sidereal Period of Mars agree with your value in the table from Question 12?
The farther a planet is from the sun, the longer its sideral period becomes. This values
agrees with the in question 12 as it was estimated that the sidereal period of mars would be 1.88
years
______________________________________________________________________________
________________
NAAP – Solar System Models 7/8
(2 point) Make Earth the Observer’s Planet and Mars the target planet. Zero the Counter and note
the location of Mars in the Zodiac Strip. Animate the planets until Mars (the target planet) comes
back to the same place in the Zodiac Strip. How long did it take? It this number related to either
the sidereal or synodic period? Why or why not?
On the Zodiac strip, it takes Mars 2,144
years to go from 18 degrees East, this is the same as the synodic period of Mars.
Question 15: (2 point) Let’s use the simulator to observe the retrograde loops of a superior
planet.
Set up the simulator for being located on the Earth and viewing Mars at conjunction.
Zero the counter and start the animation.
How long after conjunction does retrograde motion
start and how long does it last?
A year after mars has been viewed from Earth at
conjunction. As it approaches opposition, retrograde motion starts. The two planets form a
straight line with the Sun, and retrograde motion lasts for roughly 2 years, until Earth passes
Mars at a point beyond opposition.
NAAP – Solar System Models 8/8