Grade Level/Subject
11th/12th Grade
Astronomy
Unit
Models of the Universe
Enduring
Understanding
The physical and orbital properties of the Earth
and all of the objects that orbit the Sun are
regulated by their mass and proximity to the
Sun.
SOL Objectives
N/A
Title
Heliocentric Model Lab
Lesson Objective
Visualization of different orbits from the earth’s
perspective. The reason why Venus and Mercury
always appear close to the Sun, while others
maybe possibly be visible at any time during the
night.
Inquiry Level
Level 2 – Questions and methods given,
solution open
Materials Required
Computer with Internet access
Name ____________________________________ Date _________________ Pd ____________
Heliocentric Model
Lab
Use the following website:
http://astro.unl.edu/naap/ssm/
 Go to the page titled Elongation.
1. What is elongation? Explain in
words and make a diagram.
Copernicanum
The Harmonia Macrocosmica of Andreas Cellarius
From
http://www.staff.science.uu.nl/~gent0113/cellarius/c
ellarius_plates.htm
2. Which planets have “greatest elongations?” Inferior or Superior
3. How can planets have a ‘greatest’ elongation? Explain with a diagram that includes
earth (where we are), Venus, and the sun. Show the angle that is made by using the
Greek letter θ (pronounced ‘theta’).
4. What are superior and inferior conjunctions? Draw diagrams to help explain your
answer.
Name ____________________________________ Date _________________ Pd ____________
 Now check out the page titled “Elongations and Configurations”
5. Which planets can be in quadrature? Inferior or Superior
6. Place the planet at locations A-D according to the information in the boxes, or fill the
boxes accordingly. Be sure to draw elongation angles in the diagram.
Location Elongation
A
Term
180°
B
Earth
Western Quadrature
Sun
C
D
East 120°
No term for this
configuration
C
7. Complete the table below, place the planet at
the indicated positions, and draw elongation
angles.
Location Elongation
A
Term
Earth
Superior Conjunction
Sun
B
Inferior Conjunction
C
C
D
West 20°
No term for this
configuration
Name ____________________________________ Date _________________ Pd ____________
8. What is a synodic period?
 Open the Planetary Configurations Simulator. Select the “Show Elongation Angle” option.
9. Find the synodic period for the Earth and Mercury. Use a configuration, such as
superior conjunction as your reference point to tell whether a whole period has
passed. You can drag the planets around and be sure to reset your counter for the
new configuration.
Synodic period of Earth/Mercury: ______________________
10. Why is superior conjunction not the best reference for measuring synodic period?
Hint: look at the zodiac view. Compare this to other configurations. Which would
be the best configuration for measuring synodic periods?
11. Use greatest elongation as the reference configuration to calculate the synodic
period of Venus. Be sure to stick with either East or West.
Synodic period of Earth/Venus: _____________________
Greatest elongation of Venus: __________________
12. What trend do you notice between an interior planet’s distance from the Earth and
its synodic period?
Name ____________________________________ Date _________________ Pd ____________
13. Now use the simulator to find the value of Mercury’s greatest elongation.
Greatest elongation: ______________________
What relationship do you notice between the value of greatest elongation of a planet and its
distance from the Sun?
14. Measure the synodic period of Mars. Set up a preferred configuration between the
two planets, reset the counter, and animate. How long does it take to for Mars and
the Earth to return to the same configuration?
Synodic Period of Mars __________________________________
15. Just as with superior conjunction in Problem #10, why is conjunction not the best
configuration to observe a superior planet in the sky? What would be a better
configuration?
16. Measure the synodic periods of Jupiter and Saturn.
Synodic Period of Jupiter _________________________________
Synodic Period of Saturn _________________________________
Name ____________________________________ Date _________________ Pd ____________
17. 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 the trend.
18. Fill in the table below based on the data from your past runs.
Planet
Synodic
Period (Yr)
Distance from
Earth (AU)
Looking at your data table, what’s a
relationship between a planet’s
synodic period and its distance
from the Earth?
Name ____________________________________ Date _________________ Pd ____________
Supplementary Lab
The following lab is a supplementary lab if more time is given on the Ptolemaic Model (geocentric).
Name ____________________________________ Date _________________ Pd ____________
Ptolemaic Model Lab
Use the following website for this lab: http://astro.unl.edu/naap/ssm/animations/ptolemaic.html
1. Draw a basic Ptolemaic System. Include the earth, an equant, deferent (with center),
a planet with an epicycle, the sun, and background stars/constellations/zodiac.
2. When the sun goes around once in the animation, how long of a period of time is it?
3. Choose Venus and “start animation.” Epicycles were invented to account for
apparent retrograde motion. Describe in complete sentences how epicycles account
for this motion as seen from the earth. Note the planet’s perceived movement
relative to the zodiac.
4. Describe what each of the settings do:
a. Epicycle size:
b. Eccentricity:
c. Motion rate:
d. Apogee angle:
Name ____________________________________ Date _________________ Pd ____________
5. Epicycles were invented to account for apparent retrograde motion. What do you
think equants were invented for?
6. What do the inferior/superior options refer to?
7. Using the planet presents, what happens to the epicycle size as you get to outer
planets?
8. What happens to “motion rate” as you go from inner to outer planets? What do you
think this corresponds to in our modern model of our solar system?
9. Rank the planets in terms of how quickly they go through the background
stars/zodiac.
10. An “inferior planet” is one in which the planet at apogee (closest approach to earth)
is collinear with the earth and the moon. Draw a sketch of what you see at apogee.
Which planet did you choose?
11. Venus has been called both the “morning star” and the “evening star.” Why do you
think that is? Use the simulation to support your assertion.
Name ____________________________________ Date _________________ Pd ____________
12. Make a data table of the number of orbits the sun completes for each complete orbit
of the planets.
Planet
Number of orbits
of the sun (years)
What trend do you notice?
13. What does “apparent retrograde motion” look like according to the fixed zodiac?
14. If Mercury were on this simulation, what would you expect its orbit to be like?
Go to the following page: http://astro.unl.edu/naap/ssm/ssm.html
Use the pages under Geocentric Model to answer the following questions
and prompts.
15. Describe elongation, opposition, superior and inferior conjunction, and quadrature.
Draw a diagram for each.
Name ____________________________________ Date _________________ Pd ____________
16. Generally, which direction to the planets move with respect to the stars?
17. Draw a diagram of what apparent retrograde motion looks like. Include arrows,
directions (east, west, etc.).