PHYS 1403 Lab 4 Solar System Models
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Apr 3, 2024
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Name: Solar System Models – Student Guide
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. https://astro.unl.edu/naap/ssm/ssm.html
Question 1: 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 closer the planet is to the sun, the faster it moves.
Question 2: 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 1/7
Location
Elongation
Term
A
180°
Opposition
B
90
Western Quadrature
C
0
Conjunction
D
East 120°
XXX
C
Sun
Earth
Question 3: 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: 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
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? The best elongation
configuration for observing inner planets like Mercury and Venus is greatest elongation, when
they are at their maximum angular distance from the Sun as viewed from Earth
NAAP – Solar System Models 2/7
Location
Elongation
Term
A
0
Superior Conjunction
B
0
Inferior Conjunction
C
46 East
Greatest elongation
D
West 20°
XXX
Question 5: 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
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 synodic pattern slows when it is close to an inferior planet and speeds up
when further away.
Question 6: 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? Mercury
typically achieves a greatest elongation of approximately 18-28 degrees from the Sun, while
Venus, farther from the Sun, reaches a greater greatest elongation of about 45-47 degrees,
indicating a positive relationship between a planet's distance from the Sun and its greatest
elongation value.
Question 7: 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: 2.14
Question 8: 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 optimal configuration
for observing superior planets because only inferior planets can be in inferior conjunction. The
best configuration for observing superior planets is opposition because it occurs when the planet,
the Sun, and Earth are all aligned in a straight line, providing an ideal viewing opportunity.
Measure the synodic periods of Jupiter and Saturn .
Synodic period of Jupiter: 11.9 yrs
Synodic period of Saturn: 29.5 yrs
NAAP – Solar System Models 3/7
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Question 9: 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 synodic periods of superior planets, which are farther
from Earth and possess larger orbits, are typically shorter because the observer's planet can
complete its orbit more rapidly.
Question 10: 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 comparable relationship between inferior and superior planets is that those farther from
Earth will exhibit shorter synodic periods.
Question 11: 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 occur
approximately every 26 months, coinciding with the red planet's closest approach to the Sun.
Every 15 to 17 years, an opposition coincides closely with Mars' perihelion, its nearest point to
the Sun in its orbit
Question 12: .
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 and 52 days
How does this answer compare with the synodic period of Mars as found in Question 8? Explain
why they are related. Both Earth and Mars share similarities in being closest to the Sun, which
leads to longer synodic periods for both planets.
Question 13: 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
NAAP – Solar System Models 4/7
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 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
0.241 yr
Venus
584
0.616 yr
Earth
Not Applicable
1 yr
Mars
780
1.9 yr
Jupiter
1.09 yr
12 yr
Saturn
378
29.5 yrs
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? There is a relationship between the sidereal
period of a planet and its distance from the Sun. Planets that are farther from the Sun have longer
sidereal periods, while those closer to the Sun have shorter sidereal periods.
Question 14: 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? NAAP – Solar System Models 5/7
NAAP – Solar System Models 6/7
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Question 15: 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, Mars takes 2.144
years to complete a journey from 18 degrees East to 18 degrees East, mirroring its synodic
period.
Question 16: 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? One year after Mars is observed from Earth during conjunction, as it nears
opposition, it begins its retrograde motion. During this phase, both planets align in a straight line
with the Sun, and Mars continues its retrograde movement for approximately two years.
NAAP – Solar System Models 7/7