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LESSON TEMPLATE
Lesson Code:
E 0 9
C 0 3
Date: For October 7th, 2003 submission
Lesson Title: Solar System Stability
Author: Brian Wilson
Ohio Standards Connection:
Standard(s): Earth & Space Sciences- Grade Nine The Universe
Benchmark(s): C: Explain the 4.5 billion-year history of Earth and the 4 billionyear history of life on Earth based on observable scientific evidence in the
geologic record.
Indicator(s): 3: Explain that gravitational forces govern the characteristics and
movement patterns of the planets, comets and asteroids in the solar system.
Indicator Tie to Benchmark: “The long-term stability of the solar system is an element of
uniformitarianism. In this outlook, geological and biological processes on earth have
progressed at very slow rates. Necessary to this view are solar system stability, absence
of significant impacts of comets, asteroids, etc., and the stability of the sun. Thus solar
system instability is incompatible with uniformitarianism.” Corliss, William, The Sun
and Solar System Debris (Sourcebook Project, Glenn Arm, Maryland 21057, 1986) p. 23.
Associated Standards: Ideas in this lesson are also related to concepts found in Grade 8
Earth & Space Benchmark A, Indicators 1,2,3,4.
Lesson Summary:
Most students will likely know some information about gravitation, solar system,
standard long age Earth history model, and uniformitarianism. In this lesson, students
will build on this knowledge as they inquire and research various views on: the long term
stability of the sun and solar system and the absence or presence of significant extraterrestrial impacts on the earth and solar system. Students will investigate further the
observable scientific evidence in the geologic record pertaining to gravitational forces
that govern the characteristics and movement patterns of solar system objects.
The lesson begins with showing portions of a video about an impact of an extra-terrestrial
object with Earth and the resulting after effects. Discussion immediately follows relating
the movie to the lesson items.
The students will then research and present their findings on the lesson subject matter by
use of a poster board visual display. A follow-up gallery walk of the poster boards will
next occur with the students writing in their journal key points of each poster board.
Estimated Duration:
3 to 5 classroom periods
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Pre-Assessment:
Instructions to the Teacher:
To start Part 1A, Gravitational Forces & Solar System Stability- a vocabulary sheet will be handed
out and briefly discussed in class. Fig 1 will then be handed out which the students are requested to
read.
Fig 1
Initial Introductory Reading by the Student
It is the Sun’s gravitational field that dominates the motion of planets and that to a good
first approximation each has an elliptical orbit around the sun. The planets also influence
each other’s motion however all according to the inverse square law. Minor unmodeled
perturbations, such as the gravitational tug of asteroids or of passing stars, could also alter
planetary longitudes substantially, although they are unlikely to change the character of the
motion.
The Solar system does not exist in the ideally empty space. Planets are constantly
bombarded by meteorites. It is possible that in the history of the solar system that the
planets were hit by asteroids. Every such collision must change the planet’s orbits.
The climatic history of the Earth is affected by changes in its orbit by impacts of asteroids
and comets, and possibly also by the accumulation of interplanetary dust particles that are
generated by asteroids and comets. Thus the long term orbital dynamics of the planets and
small bodies in the solar system is pertinent to the habitability of our planet the Earth. The
question can thus be posed- What are the characteristics of a stable planetary system or one
that harbors a habitable planet ?
END OF FIG 1
In Part 1B, Earth Impact- teacher selected portions of an appropriate rental video relating to
castrophic asteroid or comet impact on the Earth will be briefly shown. During the movie students
are to list those vocabulary words that pertain to the movie. In addition they are to write in their
journal notebook events from the video that tie into gravitational forces and solar system stability.
Afterwards a teacher guided classroom discussion follows pertaining to the vocabulary and
gravitational force events shown in the movie snippets.
Transition into Part 1C, Properties of the Sun, Planets, Moon, Comets, Asteroids, Meteors [2] [8]
[22]- Fig 2 will be handed out which contains questions about general properties of the Solar
System. Each student is requested to circle the correct answer to the following questions:
Fig 2
Initial Comprehension Questions [44]
Properties of the solar system:
1. [All/ some/ few/ none] planets orbit in the same direction
2. [All/ some/ few/ none] planets (except Pluto) orbit in nearly the same plane
3. [All/ some/ few/ none] planets have nearly circular orbits
4. [Inner (terrestrial) / outer(Jovian)] planets are rocky,
5. [Inner (terrestrial) / outer(Jovian)] planets are gaseous
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6. [Inner (terrestrial) / outer(Jovian)] planets have basically no satellites;
7. [Inner (terrestrial) / outer(Jovian)] planets have whole families of them
8. Most of the mass of the solar system (98%) is in the [Sun/ planets]
9. Most of the angular momentum of the solar system (over 90%) is in the [Sun/ planets].
END OF FIG 2
The teacher collects the student’s answers, and after the class is over evaluates each students
answers individually to gauge the student’s prior knowledge of the subject matter.
Answers to Fig 2
1) All, 2) All, 3) All, 4) Inner, 5) Outer, 6) Inner, 7) Outer, 8) Sun, 9) Planets
Fig 3 will then be handed out which the students are requested to read. This additional information
should clarify most if not all of the questions previously covered in Fig 2.
Fig 3
After Question Readings by the Student [45]
Basic understanding of the current physical aspects of the solar system. Our Solar System is
made of the Sun, nine major planets, at least sixty planetary satellite, thousands of asteroids
and comets that all span an immense distance. Each planet has its own individual
characteristics and seven of which have one or more satellites. There are thousands of
asteroids, mainly congested in the area between Mars and Jupiter, as well as countless
comets that all travel in a spherical orbit around our Sun. The Sun contains approximately
99 percent of the mass in the Solar System, but only 2 % of the systems angular momentum.
It lies in the center of our system while all planets, asteroids and alike rotate in elliptical
orbits around it in the same plane. The smaller inner planets have solid surfaces, lack ring
systems and have far fewer satellites then the outer planets. Atmospheres of most of the
inner planets consist of large quantities of oxidized compounds such as carbon dioxide.
While on the other hand, the outer planets are far more massive then the inner terrestrial
planets, and have gigantic atmospheres composed mainly of hydrogen and helium.
Asteroids and comets make up the smallest portion of the Solar System entities.
END OF FIG 3
The teacher leads a guided classroom discussion pertaining to the reading of Fig 3 and any
additional questions that the student may still have regarding the questions in Fig 2.
Scoring Guideline:
This is an informal evaluation of the students understanding and knowledge. Teachers should make
informal notations and record anecdotal comments about the level of understanding of the students.
Post-Assessment:
Instructions to the Teacher:
Transition into Part 2 Post-assessment topics shown in the table below.
An evaluation is undertaken for the topic/concept subject matter in each individually numbered row.
Have students break into groups of two. Ask for volunteers for each pair of Application &
Anomaly Items listed in Table 1. It should be noted that the students will demonstrate their ability
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to perform critical thinking skills by incorporating known scientific anomalies into the research
activity. Each pair will research two Items and then create a visual presentation such as a poster
board for each Item. See Attachment 1- General Student Research and Reporting Guidelines for
specifics. Note that Attachment 2 is a completed example of what type of format the students
should model their individual research report on. This example is for Line #6 in Table 1 below.
The teacher may elect to hand out Attachment 2 and present to the students as a teacher led
demonstration activity before they start their individual research. A gallery walk will then occur
with students writing in their journal notebook key concepts of each poster. The teacher will take a
picture of each poster board and distribute copies to each student for their journal notebook.
Table 1
Gravity, Movement & Stability Subjects Outline
#
1
CONCEPT
Newtonian Law
APPLICATION
Ocean Tides
Orbital Mechanics
4
TOPIC
Gravitational
Forces
Movement
Patterns
Movement
Patterns
Solar system
5
Planets
6
Solar System
Stability
Observed Effect w/o
Theoretical
Underpinning [26],[38]
Uniformitarianism
[26],[38]
Keplers’s 3 Laws
[29], [30]
Multi Body Problem
Solution [7] [27]
Expected ratio
Sun/Planets [26],[38]
Titus Bode Law
[26],[38]
7
Solar System
In-Stability
Castrophism
[35]
2
3
Newton’s Mechanics
Angular Momentum
Resonance
(Commensurability)
[4], [26],[31], [38]
Historical Climate
Dynamic Simulation
[33]
ANOMALY [26]
Distance Earth to Moon
Increasing [40]
Perihelion Mercury
[26],[38]
Planetary Perturbations
[9]
Actual ratio
Sun/ Planets [26],[38]
Neptune, Pluto do not
Follow Law
[26],[38]
Faint Young Sun
Problem
[33]
Long Age of Solar
System is Inconsistent.
[26],[38]
END OF TABLE 1
Scoring Guideline:
Table 2
Rubric for Grading the Displays
CATEGORY
Depth of
Understanding
Evidence of
Inquiry
Level 4
Scientific information
and ideas are
accurate, thoughtfully
explained and
accurately linked to
the Item.
Evidence and
explanations have a
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Level 3
Scientific
information and
ideas are
accurate and
linked to the
Item.
Evidence and
explanations
Level 2
Scientific
information has
occasional
inaccuracies or
is simplified.
Evidence and
explanations
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Level 1
Scientific
information
has major
inaccuracies
or is overly
simplified.
Evidence and
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clear and logical
relationship.
Communication Scientific information
is communicated
clearly and precisely
but may also include
inventive/ expressive
dimensions.
Background
Relevance to
information provides
Society
clear context for
interpretation.
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have a logical
relationship.
Scientific
information is
communicated
clearly.
have an implied
relationship.
Scientific
information has
some clarity.
have no
relationship
Scientific
information is
unclear.
Background
information
provides
context for
interpretation.
Background
information
provides some
context for
interpretation.
Background
information
provides
minimal
context for
interpretation.
Instructional Procedures:
Engagement
Instructions to the Teacher:
Part 1A- Gravitational Forces and Solar System Stability
1. If the teacher or their students want to do some preliminary research on the topic before the
lesson go to a standard Earth & Space Science textbook and/or the following internet sites: [11]
[12] [19]
2. A vocabulary sheet will be handed out and briefly discussed in class.
3. Fig 1- Initial Introductory Reading will be handed out for the students to read.
Part 1B- Earth Impact
4. Teacher selected portions of an appropriate rental video relating to castrophic asteroid or comet
impact on the Earth will be shown.
5. During the movie students are to list those vocabulary words that pertain to the movie. In
addition they are to write events from the video that tie into gravitational forces and solar system
stability.
6. Afterwards a teacher guided classroom discussion follows pertaining to the vocabulary and
events in the movie showing gravitational forces and/or solar system stability.
Part1C- Properties of the Sun, Planets, Moon, Comets, Asteroids, Meteors
7. Fig 2- Initial Comprehension Questions is handed out to the students. Each student is requested
to circle the correct answer to the questions.
8. The teacher collects the student’s answers and after the class is over evaluates each student
answers individually to gauge the student’s prior knowledge of the subject matter.
9. Fig 3- After Question Readings will be handed out for the students to read. This information
should clarify most if not all of the questions previously covered in Fig 2.
10. The teacher leads a guided classroom discussion pertaining to the reading of Fig 3 and any
additional questions that the student may still have regarding the questions in Fig 2.
Allow total of one whole class period for Parts 1A,B,C
Instructions to the Student for Parts 1A,B,C,:
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Write down your questions and comments while you read the two handout readings and watch the
video snippets.
What would you want to know or hope to learn about the solar system?
Be prepared to share your questions and comments with the class
Development
Instructions to the Teacher:
Part 2 Gravity, Movement & Stability
11. Hand out Table 1. State that research will be done by groups for each individually numbered
topic/concept subject matter.
12. Have students break into groups of two. Ask for volunteers to research each pair of
Application & Anomaly Items listed in Table 1. It should be noted that the students will
demonstrate their ability to perform critical thinking skills by incorporating known scientific
anomalies into the research activity.
13. The teacher hands out Attachment 2 as a completed example of what type of format the students
should model their individual research report on. This example is for Line #6 in Table 1. The
teacher may optionally decide to present Attachment 2 as a teacher led demonstration activity
before they start their individual research.
14. Each student pair will do joint research on two topic/concepts. For information resources,
students are to use standard Earth & Space Science textbooks, Library Research and/or internet web
sites to perform the research. The specifics listed in Attachment 1- General Student Research and
Reporting Guidelines should be followed by the students.
15. The group should provide copies of all background information that was used, when they hand
in their poster boards. One half class period should be allowed for the initial start of the research
phase of both topics. It is understood that some additional out of classroom time will be needed by
the student for them to finish and complete their research.
16. Each pair will then create a separate visual presentation such as a poster board, for each of the
two topics that they have. One half class period should be allowed for the initial start of the
presentation phase of both topics. It is understood that some additional out of classroom time will
be needed by the student for them to finish and complete their presentation.
17. A gallery walk will then occur with students writing in their journal notebook key concepts of
each poster. One class period should be allowed for the gallery walk.
18. The teacher will take a picture of each poster board and distribute copies to each student for
their journal notebook.
19. Up to one half a period is taken by the class as a whole to answer any questions that the
students may have regarding the poster board displays
20. The teacher collects the student’s poster boards and after the class is over evaluates each group’s
poster board to gauge the student’s knowledge per the Rubric.
Instructions to the Student:
Your teacher can help guide you on potential reference sources to use or suggest key words/phrases
to try when using internet web search engines.
Follow Attachment 1 guidelines on research and reporting.
If you have any questions regarding what format to use in your presentation, ask your teacher to
help you when following Attachment 2 as a model.
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If there are still any questions after the poster board gallery walk presentation do not hesitate to ask
for further help.
Differentiated Instructional Support: Instruction is differentiated according to learner needs, to
help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met,
to advance beyond the specified indicator(s).
For students who struggle with the material covered in this lesson plan, partner them with others
that possess understanding. Use material from a textbook, internet site, or other lesson plan that
contains similar subject material. Encourage the struggling student to work on the material,
preferable with the helper partner whenever possible, outside of instructional time. This can take
place prior to or after the daily lesson, during shared study hall periods, before or after school, etc..
Possible use of supplemental multi-media software.
Extension:
Part 3 Extended Learning
Instructions to the Teacher:
For extended learning each student has an option on researching a related topic that was not covered
in this lesson cycle and write a report on the topic. Possible topics include the following:
Fig 4
List of potential Extension questions : [11], [13], [16], [17], [20], [26]
Note suggested possible answers are given in [bracketed italics]
1) What is the physical explanation behind the Titus Bode law which fairly accurately
predicts the distances of most planets from the sun? [26],[38] [Observational only no
physical explanation] Why does Neptune and Pluto not follow this ‘law’ at the present
time? [26],[38] [Anomaly to the ‘law’] Might there have been other planets e.g. Mars that
previously did not follow this law but through a close planetary encounter straighten out its
orbit to align itself with this law.[32] [Several writers including Velikovsky have
hypothesized this ] What geologic effects on the Earth would a close planetary encounter
create? [Crustal deformation, spin axis shift, catastrophic event]
2) Was there a Planet X [14] [15] between Mars and Jupiter as predicted by the Titus Bode
law [Possible, this would fit law]. The Asteroid belts now inhabit this region of the Solar
System. What effects might Asteroid collision with Earth cause to the Earth’s Poles? [If
large enough and at proper impact angle might cause pole shift]
3) On billion-year time scales, the classic question for climatologists is the so-called “faint
young Sun problem”: How did Earth’s climate remain warm despite a solar luminosity
decrease of 20-30 percent compared to today? [33] [Hypothesize greater green house effect
was previously in existence] Increases in volcanogenic CO2 and biogenic CH4 can
contribute to long term climate stability due to the greenhouse effect. Several times in
Earth’s history this stability appeared to have broken down leading to periods of global or
near-global glaciation. The question of how Earth’s biota managed to survive these climate
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catastrophes is thus posed? [33] [Several episodes of mass extinctions, anomaly why life
would survive all of these catastrophes]
4) Explain why NASA’s Near-Earth Object Program Office at the Jet Propulsion
Laboratory thinks that Near-Earth Objects are so important to life on Earth.[1] [Potential for
future catastrophic occurrence of an extra-terrestrial object striking the Earth]
5) Are any ancient writings reliable in regards to their reporting castrophic events in Earth
history caused by extra-terrestrial impacts? [35] [Open ended question, depends on ones
viewpoint thus no right or wrong answers]
6) Coral which makes the reefs, only lives within a couple hundred feet of sea level; yet
remains of coral are to be found deep in the ocean. According to Darwin’s uniformitarian
theory, oceans have risen at a slow rate for millions of years thus allowing the coral reefs to
gradually grow higher as the oceans filled. What does coral growth patterns show? [47],[48]
END OF FIG 4
Copies of all references used by the student shall be presented along with the written report. After
the reports are turned in the student shall prepare a brief presentation on their findings. The teacher
will then conduct a teacher directed discussion on the topic. Allow 1 week for the students to
prepare the report as homework, and minimum 2 minutes, maximum 3 minutes for each student
presentation, with a maximum 2 minute class discussion immediately following each presentation.
Allow one half a period. [11], [13], [17], [20], [26]
Instructions to the Student:
Your teacher can help guide you on potential reference sources to use or suggest key words/phrases
to try when using internet web search engines.
Follow Attachment 1 guidelines on research and reporting.
If you have any questions regarding what format to use in your presentation, ask your teacher to
help you when following Attachment 2 as a model.
Homework Options and Home Connections:
Instructions to the Teacher:
Research the following types of near Earth objects. Write a brief one page paragraph on one or
more of the following examples as shown in the table below. Assume one half period to discuss
any questions relating to the homework.
Table 3
Examples of Near Earth Objects Impact/ Near Miss
Object
Wayward
Planets
Evidence of Mars ?
event in Past Venus ?
(Velikovsky
[32]/other)
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Comets
Asteroids
Meteroids
Manmade
ShoemakerLevy 9
crash into
Jupiter
Sudbury
Basin in
Ontario
[36], [37]
Meteor
Crater in
Arizona
[36], [37]
Satellites/
Space junk
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Prediction of event in Future
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Near-Earth Object Program
http://neo.jpl.nasa.gov/ [1]
Instructions to the Student:
Your teacher can help guide you on potential reference sources to use or suggest key words/phrases
to try when using internet web search engines.
Follow Attachment 1 guidelines on research and reporting.
Interdisciplinary Connections: Grade 9
Social Studies (Social Studies Skills and Methods- Thinking and Organizing Indicators 1,2,3)
English Language Arts (Reading Applications: Informational, Technical and Persuasive Text
Indicators 2,4; Research Indicators 2,3,4)
Materials and Resources:
Science notebooks, Poster sized paper, Colored pencils or magic markers, Masking tape,
Textbook, Library and internet access by the Teacher and/or Student
Note for classrooms with only one computerAn overhead, LCD or television screen can be used to project images from the computer onto a
classroom screen. The lesson can be bookmarked or previously downloaded onto the computer or
CD. This will facilitate a more organized and predictable large group presentation and minimize
glitches.
Note for Classrooms that do not have computer accessFor teachers with school library or home computers with internet access selected parts of the lesson
may be printed out on paper or transparencies.
If there are one or more computers located outside the classroom inside at the school or nearby at a
local library, students may experience their research lesson individually or in small groups as a
learning station.
For those students with home computer internet access, their research lesson may be done as
homework or as an extension lesson.
Rental video of extra-terrestrial object impact on earth. Teacher is to preview movie and select
those scenes that highlight scientific content and fit within one classroom setting.
Vocabulary:
Uniformitarianism, catastrophism, stability, extra-terrestrial, Titus Bode law, asteroids, meteor,
gravitational field, Keplers law, perihelion, multi body problem, planetary perturbations, angular
momentum, resonance, chaos, orbital period, retrograde motion, orbital mechanics.
Technology Connections:
Internet web sites, multi-media computer downloads, VHS videos, analog photo copies or scanned
digital images
Research Connections:
Inquiry strategies, theory on multiple intelligence, Marzano cooperative group learning,
Identifying similarities and differences, direct vocabulary instruction, writing answers more
memory retention than oral answers
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General Tips:
The indicator does not mandate any teaching requirement as to assigning any age to the Solar
System (whether absolute, relative, apparent, order of magnitude, etc.). Thus it is at the teacher’s
discretion to omit or include any information (whether for or against) regarding the age of the Solar
System.
Attachments:
Attachment 1 General Student Research and Reporting Guidelines
Attachment 2 (Teacher Provided Example Answer for Table 1, Line 6- Solar System Stability
Topic/ Uniformitarianism Concept/ Resonance Application/ Faint Young Sun Anomaly)
References:
The recommended references listed below are the minimum required for the basic core lesson to be
used by all students. Each reference is keyed to one or more appropriate lesson topics by the use of
a bracket containing a bold 2 digit number in italics. For example [14] is Reference 14.
RECOMMENDED REFERENCES for Core Basic Lesson
[2] http://ssd.jpl.nasa.gov/ NASA Solar System Dynamics
[14] www.metaresearch.org/solar%20system/eph/eph2000.asp Exploded Planet
[22] http://astrogeology.usgs.gov/ Solar System and Astrogeology Research
[26] www.science-frontiers.com Online Reference for Scientific Anomalies
[46] www.fortunecity.com/emachines/e11/86/solarsys.html Solar System Stability
Footnotes:
The optional suggested footnotes listed below are for the PreAssessment and PostAssessment
assignments. Each footnote is keyed to one or more appropriate lesson topics by the use of a
bracket containing a bold 2 digit number in italics. For example [14] is Footnote 14.
FOOTNOTES for PreAssessment and PostAssessment Activities
[2] http://ssd.jpl.nasa.gov/ NASA Solar System Dynamics
[4] www.n-t.org/tpe/ng/uss.htm Stability of a solar system
[7] www.ebicom.net/~rsfl/low-tec.htm TRIBODY n-body solution shareware
[8] www.dkrz.de/mirror/tnp/nineplanets.html Multimedia Tour of the Solar System
[9] www.stjarnhimlen.se/comp/tutorial.html Perturbations from other planets
[11] http://webhead.com/wwwvl/astronomy/ Astronomy & Astrophysics Virtual Library
[12] http://teachspacescience.stsci.edu/cgi-bin/topics.plex Space Education Resource
[19] www.fourmilab.ch/solar/ Interactive Orrery of the Solar System
[22] http://astrogeology.usgs.gov/ Solar System and Astrogeology Research
[26] www.science-frontiers.com Online reference for Scientific Anomalies
[27] http://angels.sewanee.edu/Angels/D/doneveu0/html/doneveu0.html 3 body problem
[29] www.liceoalberti.it/Galileo/Keplero/kepler.laws.html Applet software Kepler Laws
[30] www.cuug.ab.ca/~kmcclary/ Orbital Mechanics links
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[31] www.pubmedcentral.nih.gov/articlerender.fcgi?artid=60054 Chaos & Stability
[33] www.ima.umn.edu/geoscience/abstracts/10-29abs.html Dynamic Solar System & Climate
stability/instability
[38] Corliss, William, The Sun and Solar System Debris (Sourcebook Project, Glenn Arm,
Maryland 21057, 1986) p.23
[40] “Moon Slipping Away from Earth”. Geo, Vol.3 (July 1981), p.137
The optional suggested footnotes listed below are suggested for use in the Extended Learning
assignment. Each footnote is keyed to one or more appropriate lesson topics by the use of a bracket
containing a bold 2 digit number in italics. For example [14] is Footnote 14.
ADDITIONAL FOOTNOTES for Extended Learning Figure 4
[1] http://neo.jpl.nasa.gov/ NASA Near-Earth Object Program
[9] www.stjarnhimlen.se/comp/tutorial.html Perturbations from other planets
[13] http://adsabs.harvard.edu/ads_abstracts.html Astrophysics Journal & Paper Abstracts
[14] www.metaresearch.org/solar%20system/eph/eph2000.asp Exploded Planet
[15] www.metaresearch.org/solar%20system/eph/ephrevised/ephrevised.asp Revised [14]
[16] http://sciastro.astronomy.net/ FAQ for sci.astro newsgroup
[17] www.Astroprobe.com Astronomy based search engine
[20] http://sciastro.astronomy.net/sci.astro.1.html Astronomy info links
[32] www.ebi.com.net/~rsf1/vel/velik.htm Velikovsky
[35] www.knowledge.co.uk/sis/ Society for Interdisciplinary Studies, Global cosmic catastrophes
[47] www.agu.org AGU On Line Book Catalog “Earth’s Climate and Orbital Eccentricity: The
Marine Isotope Stage 11 Question”, ISBN# 0-87590-996-5, 2003
[48] www.maik.rssi.ru The Continuous-Discontinuous Development and Growth Rate of Reefs, by
A.A. Baikov, Rostov State University, September 24, 2001
The optional additional footnotes listed below are suggested for use in the optional Homework
assignment. Each footnote is keyed to one or more appropriate lesson topics by the use of a bracket
containing a bold 2 digit number in italics. For example [14] is Footnote 14.
ADDITIONAL FOOTNOTES for Homework Table 3
[36] www.solarviews.com/eng/tercrate.htm Terrestrial impact craters photo gallery
[37] www.unb.ca/passc/ImpactDatabase/ Earth impact database
General Note for all Footnotes:
Where more classroom time is available, or for advanced students as part of extended learning, all
the References and Footnotes may be made available for use by the teacher and student.
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ATTACHMENT 1
General Student Research and Reporting Guidelines:
1. Teacher is to provide topic and question.
2. Suggested reference source(s) and key word(s)/phrase(s) for web search engine will be
provided by teacher.
3. Student is to evaluate the usefulness, and whenever possible the credibility, validity and
possible bias/slant of data, information and sources (primary and secondary). Teacher is to
act in a review capacity during this process.
4. The credentials and past reliability track record of both the author and publisher should be
taken into consideration in evaluating the reference source. One should note though that
some important paradigm shifts in the past were first discovered by investigators working
outside of their specialty field of formal education, e.g. Charles Darwin was a divinity
school graduate. Also, from 1903 until 1908 the two bicycle mechanics Wilbur and Orville
Wright were rejected by Scientific American for their 1903 claim to have successfully built
and flown a heavier than air flying machine.
5. Critical thinking skills should include a check by the student for potential errors in logical
reasoning and/or extrapolation used in the reference source.
6. Where appropriate and available, contrary/anomalous information should also be evaluated
in order to provide an intellectually honest and balanced perspective.
7. An attempt should be made to include some non-American references that provide written
information available in the English language.
8. Student should utilize investigative inquiry methods appropriate to the type of question
being researched.
9. Research should be linked to relevant scientific theory/knowledge, and be germane to the
topic so as to stay on target with the indicator and benchmark.
10. The student should use and describe a logical, coherent and explicit line of reasoning.
11. Information from various resources should be organized, and the sources selected should be
appropriate to support the central ideas, concepts and themes.
12. Students should produce reports that give proper credit for sources.
13. The findings communicated on the substance and processes should include using the proper
modes and media appropriate to the nature and/or type of information.
Modified from Reference: “Scientific Research in Education”, Committee on Scientific Principles
for Education Research, Richard J. Shavelson and Lisa Towne, Editors, National Research Council
ISBN 0-309-08291-9
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(Teacher Provided Example Answer for Table 1, Line 6- Solar System Stability Topic/
Uniformitarianism Concept/ Resonance Application/ Faint Young Sun Anomaly)
Questions concerning the stability of our Solar System have been studied for over 300 years.
Today, the conventional thinking is that the dynamics of our solar system includes both chaotic and
stable motions.
In its scientific usage chaos is not a synonym for disorder; rather it describes the irregular behavior
that can occur in deterministic dynamical systems. Chaotic systems have two defining
characteristics: they show order interspersed with randomness, and their development is extremely
sensitive to initial conditions.
Chaotic dynamics is pervasive in the Solar System. The orbits of small members of the Solar
System- asteroids, comets, and interplanetary dust- are chaotic and undergo large changes on
geologic time scales. The answer to the question as to whether the major planet’s orbits are also
chaotic, is not straightforward. The study of chaos has revealed that even completely deterministic
systems, such as those involving gravitational interactions can be chaotic.
The large planets exhibit remarkable stability of their orbital parameters while also possessing all
the formal characteristics of a chaotic dynamical system. On million year time scales the four outer
planets show quasiperiodic behavior. The orbits of the inner planets are also chaotic and this chaos
combined with imperfect knowledge of initial conditions and planetary masses implies that it may
never be possible to accurately calculate the location of the Earth in its orbit 100 million years in the
in the future or in the past.
The small bodies in our Solar System-asteroids, comets, and interplanetary dust particles contain a
mix of stable and chaotic populations with a wide range of orbital instability timescales, a
characteristic that makes the Solar System as a whole a continuously changing and dynamic system
Despite the observed chaos it is likely that the Solar System is astronomically stable in the sense
that the 8 or 9 largest known planets will probably remain bound to the Sun in low eccentricity, low
inclination orbits. From a mathematical point of view even in the absence of solar evolution and
external perturbations, the Solar System is unlikely to remain stable forever.
At the end of the 19th century Henri Poincare realized that in the Solar System, chaos and order,
stability and instability were closely connected with a phenomenon called resonance. Chaos in the
Solar System is associated with gravitational resonances. Resonance pervades the Solar System as
strong and weak resonances thread the entire phase space of the Solar System. A resonance may
happen when there is a simple numerical relationship between two periods lead to repeated
configurations.
The most fundamental period for an object in the Solar System is its orbital period. This is the time
its takes to complete one orbit and depends only on its distance from the central object. The
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simplest case of a gravitational resonance occurs when the orbital periods of two planets are in the
ratio of two small integers, e.g. 1:2, 3:5, etc.
The most likely reason that resonance is so common in satellite systems is due to the effects of
tides. As a satellite raises a tide on a planet, there is an exchange of angular momentum between
the bodies, resulting in a change in the orbit of the satellite and in the spin of the planet.
Consequently the orbits of the natural satellites today may bear little resemblance to their original
ones. As a satellite develops, its orbital period changes and it may encounter a resonance with
another satellite. In certain circumstances, the satellites become locked in a resonance and continue
to develop tidally, so maintaining the resonant configuration.
Another form of resonance in the Solar System is spin orbit resonance, where the period of spin (the
time it takes the orbit to rotate once about its axis) has a simple numerical relationship with its
orbital period. Most natural satellites are in synchronous spin states although this was not their
original state: they have developed into such configurations because of tidal effects. Although
chaos means that some orbits are unpredictable, it does not necessarily mean that planets will
collide- chaotic motion can still be bounded.
The long term dynamics of the planetary system is the dynamics of gravitational resonances.
Gravitational resonances may effect very large orbital changes or only modest orbital changes (in
some cases, even provide protection from large perturbations), depending sensitively on initial
conditions.
Numerical simulations all indicate that the orbits of the planets themselves develop chaotically.
However the presence of chaos implies that there is a finite limit to how accurately the positions of
the planets can be predicted over long times. In 1989, Jacques Laskar published the results of his
numerical integration of the Solar System over 200 million years. Laskar’s work showed that the
Earth’s orbit (as well as the orbits of all the inner planets) is chaotic and that an error as small as 15
meters in measuring the position of the Earth today would make it impossible to predict where the
Earth would be in its orbit in just over 100 million years time.
We can take comfort from the fact that his work does not imply that orbital catastrophe awaits our
planet, only that its future path is unpredictable. It seems likely that the Solar System is chaotic but
nevertheless confined, although we have yet to prove it. In a qualitative sense the planetary orbits
are stable- because the planets remain near their present orbits-over the lifetime of the Sun
Changes in the orbit of the Earth, which can have potentially large effects on its surface climate
system through solar insolation variation, have been found by numerical simulations to be small.
On billion-year time scales, the classic question for climatologists is the so-called “faint young Sun
problem”: How did Earth’s climate remain warm despite a solar luminosity decrease of 20-30
percent compared to today? [33] (The conventional hypothesis is that a greater green house effect
was previously in existence). Increases in volcanogenic CO2 and biogenic CH4 can contribute to
long term climate stability due to the greenhouse effect. Several times in Earth’s history this
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stability appeared to have broken down leading to periods of global or near-global glaciation. The
question of how Earth’s biota managed to survive these climate catastrophes is thus posed? [33]
(The standard answer is that several episodes of mass extinctions appear in the geologic record, thus
at present it is an anomaly as to why life would survive all of these catastrophes).
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Is the Solar System Stable? [46]
Carl Murray
You might be surprised to learn that the Earth's orbit round the Sun, like those of other planets,is
chaotic. What does this mean for the future of the Solar System?
A resonance may happen when there is a simple
numerical relationship between two periods leads to
repeated configurations. Consider the case of an
asteroid and Jupiter orbiting the Sun. For simplicity, we
will be take Jupiter's orbit to be circular and assume that
all objects orbit in the same plane.An asteroid at the 2:1
Jovian resonance will have orbital period of six
years,which is half Jupiter' s period of 12 years. To see
how the resonance can be stable or unstable,consider
two possible initial configurations with the asteroid and
Jupiter aligned with the Sun on the same side of their
orbits (conjunction). The asteroid's orbit will
be considerably affected by Jupiter if conjunctions occur
when the asteroid is at its furthermost point from the Sun
(aphelion) is where the two orbits are closest.
In the stable case,conjunctions occur at the asteroid's
closest point to the Sun (perihelion). The asteroid
reaches the danger point of aphelion after three and nine
years,but in each case Jupiter is a different point in its
orbit. Every 12 years, the initial configuration repeats
itself and so the asteroid always avoids conjunctions at
aphelion and is in a stable resonant orbit. In the unstable
case, conjunctions always occur at the asteroid's
aphelion, leading to a repeated, unstable configuration
that cannot continue (see Figure a). There is a simple
analogy with the motion of a pendulum (see Figure b).
It is stable when you start the bob in the vertically down position. Any small shifts of the bob will cause
oscillations about the stable point. However, if you start the bob in the vertically up position, it can remain
balanced there only for a short time before it becomes unstable. In fact, the equations of motion of an
asteroid in resonance with Jupiter are very similar to those of a simple pendulum. To introduce chaos into the
pendulum system we need only to oscillate the point of suspension in a regular fashion. The equivalent
action in the Sun- Jupiter-asteroid system would be to make the eccentricity of Jupiter' s orbit nonzero.
FURTHER READING
ANITA M. KILLAIN, Playing dice with the Solar System, Sky and Telescope, Vol. 72, l987, p. 24l.
The New Scientist Guide to Chaos File Info: Created Updated 14/7/2002 Page Address: http://members.fortunecity.com/templarser/solarsys.html
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