09 December 1997: Angela Patrick [Crown School]
She made craters like those on the moon and Mars by launching various projectiles into a pan filled with flour, corn meal, and grits [mercifully, the uncooked variety] covered with Jello™  to give the layer a color. The projectiles dug out a hole, and caused elevations of material along the sides, and very much resembled the lunar/Martian variety. A NASA package suggested using dry sand, but since that was unavailable she improvised using more readily available materials.  The object is to throw objects at various speeds and mass to see how craters are created.  Adapted from casual observation to detailed analysis of rays, and measurement of results, etc.

27 October 1998: Earnest Garrison [Chicago Vocational HS]
He talked about astronomical units He had us line up in the hall, each with a sign for a planet (or the asteroid belt) Note: If the sun is a building, the closest planet would have to be several blocks away.

Porter Johnson commented that at the Westerbork Radio Antenna Array [http://www.nfra.nl/wsrt/WSRTintro/index.html and http://www.astron.nl/p/observing.htm] in The Netherlands there is a 4 kilometer path through the woods showing the solar system to scale. The sun is a 1 meter ball, whereas Pluto is visible only with a lens. According to Bode's Law [ http://astrosun2.astro.cornell.edu/academics/courses/astro201/bodes_law.htm] the average distance of planets from the sun doubles from one to the next. The orbits of planets are roughly circular, except for the closest [Mercury] and most distant [Pluto], and the planets have a common orbit plane [the ecliptic], at least approximately. According to Bill Shanks, there is a layout of the solar system to scale along a bike path near Peoria.

27 October 1998: Carol Zimmerman [Lane Tech HS]
added several limericks as mnemonics for identifying the planetary order.

   My      Very    Educated   Mother  Just   Served   Us  Nine    Pizza-pies
   Mary's  Violet  Eyes       Made    John   Stay     Up  Nights  Planning

Name                     Distance to Sun                Radius
                         [Earth = 1.0]               [Earth = 1.0]             
Mercury                       .39                        .38
Venus                         .72                        .95 
Earth                        1.0                        1.0 
Mars                         1.5                         .53 
Jupiter                      5.2                       11. 
Saturn                       9.5                        9.4 
Uranus                      19.                         4. 
Neptune                     30.                         3.8 
Pluto                       39                           .31 
*Planet X
[X=10 or "unknown"]        100. ?                         ??

*The effects of the known planets do not explain the motion of the planet Neptune. Some astronomers expect a tenth planet far beyond the others.

10 November 1998: Earl Zwicker [IIT Professor Emeritus and SMILE guru]
He brought in copies of the Chicago Tribune article of 11-9-98 about Search for Extraterrestrial Intelligence. The web site is http://setiathome.ssl.berkeley.edu

10 November 1998: John Bozovsky [Bowen HS]
With the earth represented by a beach ball 40 cm in diameter, how far away would the sun be? He showed a video tape he made. He walked and drove and drove until he went from Bowen HS to (familiar landmarks??) 95th and Cottage Grove.

Distance to the sun  =   2.87 miles at perihelion [Jan 6]
                     =   2.97 miles at  aphelion [6 months later]

          X [cm]               93,000,000 mi
      _____          =    __________________

         40 cm                      8,000 mi

John went on to indicate that his geology class is studying earthquakes, and has discovered that they occur very frequently somewhere on earth. Porter Johnson commented that there is a slight increase in number and intensity of earthquakes around May (thermal expansion of the earth is the suspected culprit!) but that earthquakes can happen at any time. The recent [7.0 Richter Scale: see http://www.matter.org.uk/schools/Content/Seismology/richterscale.html] eruption of the San Andreas Fault had its epicenter at Santa Cruz, which is precisely where a team of earthquake geologists had gathered to investigate the seismic anomalies.

He slyly commented that, in an earthquake you can tell which direction it is coming from by listening to where the auto alarms are going off ... just as we had a glitch in the electric power in the building. [In LALA earthquake land it might have been the big one -PJ.]

07 September 1999:  Roy Coleman [Morgan Park HS]
An observation from a Time Traveller book:

Jump back 6 months. You will be out in space because the earth has moved since then. You need to specify displacement and time change to land on earth. Paradox: What would happen if you went back in time and killed your mom? How could you be here without ever being born? Paradox].

PJ comment: Not if you reject the simple linear nature of time, and allow a more sophisticated connection between the past and the alternative futures. See the science fiction classic, TIMESCAPE by physicist Gregory Benford [Spectra 1996; ISBN: 0553297090].  See http://www.thesustainablevillage.com/awrbooks/html/BooksinHTML/timescape.html.  Here is a brief synopsis of the book [http://www.cloggie.org/esseff/millennial-32.html]:

In 1998: Using tachyons, Cambridge scientists try to warn 1962, about imminent ecological disasters. Toxic clouds, microbial blooms, and failing agriculture all conspire as the scientists desperately try their last resort experiment. But how will the past interpret the signals given that they are even received? Can scientists in 1962 act to affect the crumbling world of 1998? What are the effects of tampering with time? 

In 1962: Gordon Berstein, an assistant professor at UC La Jolla (now UCSD), is having trouble with his nuclear resonance experiment. Noise. But when he looks at the signal carefully, he sees there is a message -- fragments encoded in Morse code. How should he interpret this? Is it a real signal, an alien transmission, or an intercepted Russian communiqué? When no one will acknowledge what he has found, he must follow his own convictions to make his controversial discovery known. 

Timescape is a masterpiece of the modernist style, concentrating as much on how science is done as on the innovative idea. The characters are three-dimensional conveying well the gloom of 1998, and the inquisitive excitement of 1962. 

29 February 2000: Zoris Soderberg (Webster School)
showed us how to play "Astronomy," which she does with her students. We made a grid of 9 boxes (like tic tac toe), Zoris would call out a word, and we each would write that word (noun) in one of our boxes randomly. Example:

Then Zoris would call out a definition of one of the words, and we would make an X in the square that answers the definition. The first person to get 3 in a row calls out "Astronomy" - but then must give the correct definitions for the words in those three boxes on his sheet - and so win the prize. One might have

--- the words could be any that come up in a given area of study. A fun way to test for learning! Great, Zoris!

14 March 2000: Glenda Ellis (Williams School)
(handouts - Adler Planetarium) showed us an acronym for the order of the planets:

She challenged us to invent our own acronym, and to write a short rhyme that names the planets in order. Glenda also gave us a Solar System Scramble (drawings of the planets in their orbits and the spelling of their names scrambled), and a Star Map and Star Finder cut out. A fun way to learn some things about those "stars" in the sky!

12 September 2000 Bill Shanks showed a copy of the text for an Astronomy course he is taking

Michael A Seeks
Horizons [6th Edition]
Brooks/Cole Thomson Learning
511 Forest lodge Rd
Pacific Grove, CA 93950

ISBN 0-534-57258-0

They're studying about Astronomical Influences on Earth's Climate, among other topics. Bill told us about a researcher, Milankovitch, who wrote and made predictions in the 1920's about relatively small changes in earth's orbit, such as its shape, precession, and nutation. which would couple together with a periodicity of about 10,000 (?) years, making changes in how solar energy reaches earth, and triggering ice ages. For interesting web-based references see the websites

• http://deschutes.gso.uri.edu/~rutherfo/milankovitch.html: Milankovitch Cycles in Paleoclimate
• http://www.ncdc.noaa.gov/paleo/milankovitch.html Do Milankovitch Cycles Really Exist?

12 September 2000 Porter Johnson told us that variations in energy from the sun (sun spot activity variations and other processes) probably were more important. He pointed out the apparent connection between the disappearance of sunspots (Galileo) and a little ice age  For details see http://www.windows.ucar.edu/tour/link=/earth/climate/cli_sun.html&edu=high.

05 September 2000 Fred Schaal (Lane Tech HS)
told us to look due East about one hour before sunrise, and observe the sky. Watch the planets in the pre-dawn sky! They form a triangle: Saturn, Jupiter, and ?? (Do you know?) The beauty and pleasure of astronomy. Thanks, Fred!

05 December 2000 Janet M. Sheard (West School, Glencoe)
gave us a three page copy of Planets of Our Solar System, which she printed out for us from the site of the Homepage that she created this past summer in the SMART program http://www.iit.edu/~smart/. This lesson, which she originated for her students, is interactive, and to be appreciated it must be accessed live on our website: http://www.iit.edu/~smart/sheajan1/lesson1.htm She reviewed some of the features with us. It invites the website visitor (student) to participate in a "...magical journey of our solar system." There are six different Missions to attempt, which are of increasing challenge. For example, Mission II tells you to "...create a Power Point™ presentation about the solar system. Your next goal will be to develop a slide show for each planet. Each slide will have:

• two or three interesting facts about each planet.
• an image of each planet.
• one slide at the beginning with your name, date, grade and room number.
• and then the planets are listed along with the sun.

• Solar System Trading Cards Game
• Fun Things
• Multidisciplinary Activities on the Solar System
• Solar System Tutor
• Treasure Hunt Questions
• Solar System Quiz
• Space Trivia

Speaking of unvisited planets, Porter Johnson mentioned the recent 6 hour presentation of the classic science fiction novel Dune by Frank Herbert.  Details can be found on the Science Fiction Channel website http://www.scifi.com/dune/.

Her next project will be The Human Body Website.

23 January 2001 Fred Schaal (Lane Tech HS)
announced having difficulty seeing the partial eclipse of the sun on Christmas Day---whereas others had some success with a "pinhole box camera".  Fred then posed the question:  Can you tell the difference in a penny and a dime from its sound as it bounces on the table?  Adopting the "experimental approach", we found out the following things:

• Pre-1982 pennies, made of solid copper, hit the floor with less of a "thud" than the modern "clad" variety.
• Pre-1962 dimes, made of silver, make a more ringing sound than the modern "alloyed" variety.
• A modern dime definitely makes more of a high-pitched, ringing sound than a modern penny.
• The same is true of "old pennies" in comparison with "old dimes", as was mentioned in passing in the PBS series entitled Jazz, by Kenneth Burns, which is currently being shown: http://www.pbs.org/jazz. For Jazzy Classroom Lessons for K-12 Cats, see the site http://www.pbs.org/jazz/classroom.

Fred also brought in some Mexican coins that "bounce with a ring".

14 March 2001 Porter Johnson (IIT BCPS Department) Handout:  Day and Night
used a globe and a small bed light and showed how the length of day, zenith angle of the local noon, and the direction of the rising and setting sun depends on the latitude, as well as the time of year.  The handout, which contains technical details for calculating these quantities [neglecting atmospheric refraction, the finite size of the solar disk, and the eccentricity of the earth's orbit around the sun] is located on his website at URL http://www.iit.edu/~johnsonpo/daylight.html. He made the following qualitative observations: 

• The axis of rotation of the earth is tilted at an angle of about 23^o to the direction of its orbital angular momentum around the sun. This axis points roughly in the direction of the star Polaris in the Little Dipper / Ursa Minor constellation. 
• At the Winter solstice [21-22 December] the earth's axis is tilted away from the sun.  The sun appears lower in the sky and  it is Winter in the Northern Hemisphere, whereas it is and Summer in the Southern Hemisphere.
• The earth rotates counterclockwise [as seen from the North Pole].  A period of about 23 hours and 56 minutes [sidereal day] is required for one rotation, [or about 366 1/4 rotations occur in one year].  The tracking motor on a telescope must be designed so that it will make a full rotation in a sidereal day, rather than in the more familiar solar day.
• At the poles there are 6 months of continuous darkness, followed by 6 months of continuous sunlight.  The transitions occur at the Vernal Equinox [21-22 March] and the Autumnal Equinox [21-22 September].
• At any point above the Arctic circle or below the Antarctic circle [latitude about 67^o] there are 24 hour periods continuous sunlight [summer] and of continuous [darkness].  The sun lies very close to the horizon and its horizontal projection lies in every direction at some point of the day. 
• Everywhere on the equator there are precisely 12 hours of daylight, and the sun rises exactly in the East and sets exactly in the West---at any time of the year.
• On the Vernal and the Autumnal Equinox there are precisely 12 hours of daylight and the sun rises precisely in the East and sets in the West, at all latitudes North and South.
• Between the Autumnal and Vernal Equinox [fall and winter] the sun rises South of East in the Northern Hemisphere, whereas for spring and summer it rises North of East in the Northern Hemisphere.  The times are reversed in the Southern Hemisphere.

06 November 2001: Erma Lee (Williams School) Solar System
Erma said that this lesson had been done with 6th and 7th graders.  She began with a poster of the solar system, showing the locations of the sun and the planets.  Each group of two people was given a string and some beads, and they made a necklace with the beads and string, indicating the proper order for the sun and planets, using pre-printed labels to place between each bead "planet".  The planets were ordered in increasing distance from the sun.

She also presented a puzzle called Search for the Solar System, like the following one, which contains the names of all nine planets in the solar system:

She also showed the following image showing the relative sizes of the planets:

Some excellent space photos may be found on the websites: http://www.jpl.nasa.gov/galileo  and http://oposite.stsci.edu/pubinfo/Pictures.html.  Very interesting, Erma!

06 November 2001: Richard Goberville (Joliet Central, Physics) Garage Sale Planetary Model
Richard showed scale models of the sun and planets that he had purchased at a recent garage sale.  We took the models for the first four planets, calculated the scaled distances, and laid out the scaled distances in the hall.  Here are representative numbers:

It was impressive to see how great the distances were compared to the sizes of the (model) planets.  Thanks, Rich.

04 December 2001: Fred Farnell (Lane Tech HS) Why is the flag on the Moon Wrinkled in the standard "moon landing" photo?
The standard image of the astronauts putting a flag on the moon shows the flag wrinkled and waving.  Why?  The "moon landing hoax" people have used this point, among others, to forward their case.  For a discussion of the scientific basis for this and other moon hoax effects, see the website http://www.badastronomy.com/bad/tv/foxapollo.html.  The NASA website [http://www.jsc.nasa.gov/history/flag/flag.htm] contains specific discussion of how the astronauts managed to put a flag on the moon. Good Question, Fred!

02 April 2002: Bill Blunk (Joliet Central HS Physics) -- Comets
Bill first mentioned that the Comet Ikeya-Zhang (magnitude 3.5) is visible in the Northwest sky after sunset.  For additional information check the Sky and Telescope website, and in particular http://pqasb.pqarchiver.com/skyandtelescope/results.html?start=0&id=1.

07 October 2003: Porter Johnson  called attention to the new website Space Wander Round Trip http://www.spacewander.com/USA/english.html, which contains time-sequenced shots of space launches and landings.  It is excellent, in spite of its unfortunate use of the British units.

18 November 2003: Ed Scanlon [Morgan Park HS]      KEPLER'S THIRD LAW
Ed then led us through an activity to illustrate KEPLER'S THIRD LAW, which relates the orbital revolution time ("years") of the planets to their distances from the sun. He passed out homemade devices consisting of a medium sized rubber stopper tied to high-test fish line (100 pound), the line passed through a six inch length of glass tubing (taped on the outside for safety and to provide a firmer grip) with a washer on the other end to keep the line from sliding out of the tube. Ed then asked us to work in groups, one person wrapping the "washer" end of the line around the rod, holding firmly and swinging the stopper horizontally. we measured the revolution time as a function of the radius of the circle, varied by adjusting the string which was marked at 10 cm intervals. We all observed that the longer the string (larger the orbit) the slower revolutions (longer year) in accordance with the behavior of the planets in our solar system. We tried (not very successfully) to get the quantitative relations predicted by Kepler's third law -- perhaps some refinements to the experiment might produce better results.

18 November 2003: Rudy Keil [retired teacher] called attention to an excellent set of photographs of the Northern Lights, taken recently in Iceland, on the website http://www.iww.is/art/shs/pages/thumbs.html.

02 December 2003: John Scavo called attention to a website containing a Powerpoint® slide show of images from the Hubble Telescope, at the website http://www.ioncmaste.ca/homepage/resources/web_resources/CSA_Astro/hubble/hubble_presentation.html. It takes a while to download, even on a fast server, but it is well worth watching.  Check it out!

24 February 2004: Arlyn Van Ek [Illiana Christian HS, Physics]           The Gravity Probe B Mission
Arlyn set up his laptop computer and played a DVD he had obtained about the joint NASA - Stanford University project called Gravity Probe B,  which is scheduled to be launched soon on a polar orbit about the earth. We saw beautiful graphical images describing this exciting project. In addition,  he passed around an article appearing in the November 1 2003 issue of Science News:  http://www.sciencenews.org/articles/20031101/bob9.asp.  Here is an excerpt from that article (p 280):

"A satellite designed to test one of the more twisted predictions of Albert Einstein's general theory of relativity is finally at its launch site after 40 years of preparation. The probe will look for evidence of a gravitational effect known as frame dragging. Just as a dipper drags honey along as it twirls in a honey jar, any spinning body in space, including Earth, ought to drag some space-time along with it. That was Einstein's prediction, anyway. The effect has never been convincingly observed. ... To create gyroscopes sensitive enough to register such minute rotations, the GP-B team has crafted niobium-coated, solid quartz spheres the size of ping-pong balls.  Nowhere do these silvery orbs deviate by more than 40 atoms from perfect sphericity. In each gyroscope, one of these balls will spin at 10,000 revolutions per minute while floating weightless within a chamber."

In Einstein's theory of General Relativity, gravity is not merely a "force" of usual variety (i.e., electric, magnetic, etc). Rather, it is treated as a distortion of the fabric of space and time (metric tensor), resulting in an intrinsically curved space-time, as described by Riemann geometry, rather than Euclidean geometry. The theoretical situation is briefly summarized on the ST Andrews [UK] Mathematics History websites, on webpages Non-Euclidean Geometry [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html#67],  as well as General Relativity:  http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/General_relativity.html#23 --- from which the following has been excerpted:

" ... In 1907, two years after proposing the special theory of relativity, Einstein was preparing a review of special relativity when he suddenly wondered how Newtonian gravitation would have to be modified to fit in with special relativity. At this point there occurred to Einstein, described by him as the happiest thought of my life, namely that an observer who is falling from the roof of a house experiences no gravitational field. He proposed the Equivalence Principle as a consequence: ... 'we shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame.' ..."

Unfortunately, Einstein's theory has been notoriously difficult to test in full detail, because its effects are extremely small in the "weak" gravitational field of the earth.

A real mind-opener, Arlyn!

23 March 2004: Porter Johnson called attention to a presentation made at the most recent Chicago Section AAPT meeting by Laura Nickerson [IMSA, Physics teacher] concerning Venus in Transit.  That is, the planet Venus will pass directly between the Earth and the Sun on 08 June 2004, and will appear as a dark spot on the solar disk on that date.  Since the orbital plane of Venus is tilted at an angle of 3.39° to the orbital plane of Earth, such conjunctions are vary rare.  They occur either on J = 08 June or D = 08 December, on which the orbital plane of Venus is in line with the Earth and Sun.  These conjunctions have occurred (or will occur) on these dates:  D:1631, D:1639, J: 1761, J: 1769, D:1874, D:1882, J:2004, J:2012. No person alive today has ever witnessed this conjunction before!  The 1631 conjunction was predicted by Johannes Kepler (who died in 1630), whereas the 1639 conjunction was the first one seen.  For details see the Venus Transit website http://www.venus-transit.de/,  In particular, see the page Konjunktion und Transit (D):  http://www.venus-transit.de/VenusConjunction/index.html.

06 April 2004: John Scavo called attention to the fact that the Gravity Probe B, described by Arlyn van Ek in the 24 February 2004 SMILE meeting [mp022404.html], is scheduled for launching on 17 April 2004.

04 May 2004: Walter McDonald  [CPS Substitute:  Radiology Technician at Veterans Administration]           Is a 2nd Earth out there?
Walter passed around a recent article by Pamela Simpson (AP) that recently appeared in the Chicago Sun Times, which involved the discovery of a solar system on star HU 70642, a star similar to our sun, which lies about 94 light years from earth, and around which a planet lies in an orbit similar in shape and distance to the planet Jupiter in our own solar system.  The article appears on the Red Nova News website at http://www.redorbit.com/news/scifi-gaming/11557/is_a_2nd_earth_out_there__jupiterlike_planet_found/index.html. See also the article Celestial Soulmate? Jupiter-like Plane Found in System Similar to Ours by Tariq  Malik:  http://www.space.com/scienceastronomy/jupiterlike_planet_030703.html.  According to Alan Penny of Rutherford Appleton Laboratory

"This is the first one that is really like our own solar system of the 110 that we've found.  We think it's a substantial step on the way to finding another earth.

Comment by PJ:  Planets in nearby stars, while quite undetectable through direct observation, can be identified through detection of time-dependent Doppler shift of light coming from that star.  For the case in which there is only one major planet, the star and major planet rotate about their center of mass, with a period determined through Newtonian gravitation in terms of the distance between the star and the planet.  The magnitude of the Doppler shift of light from the star is proportional to the the orbital velocity of the star about that center of mass.  In practice, only planets the size of Jupiter or larger can be found, and they must be fairly close to the star, since otherwise the Doppler shift would be too small for detection with current techniques. For HU70642, the planet is twice the mass of Jupiter, and lies at a distance of 3.5 Astronomical Units.  The Jupiter-like planet  would sweep the solar system of unwanted debris and stabilize the orbits of the inner planets -- perhaps one like our own planet Earth.

Very interesting Walter!

08 March 2005: Earl Zwicker called attention to the article Quiet at the End on the American Physical Society webpage:  http://focus.aps.org/story/v15/st8. This article, which refers to a paper recently published in Physical Review Letters, contains the following statement:

"They say in space no one can hear you scream, but if you are falling into a black hole, you can't even hear yourself.  According to the so-called asymptotic silence hypothesis, spacetime becomes so contorted that signals can't travel any significant distance -- not even from your mouth to your ear. ..." 

In addition, Earl mentioned the article Motoring Oil Drops, which also appeared on the American Physical Society webpage:   http://focus.aps.org/story/v15/st7.

29 March 2005 Roy Coleman mentioned the article by Chicago Tribune Science Editor Ronald Kotulak concerning the Miracle Year (1905) and its commemoration in this World Year of Physics.

Roy also mentioned that NASA is providing a limited number of CDs that describe Microgravity Experiments for Students.  He will attempt to get several of them for our group. See the NASA website http://exploration.grc.nasa.gov/DIME.html.

18 October 2005: Fred Schaal (Lane Tech HS, mathematics)        Illusion
Fred asked why the full moon seems to hanging so low in the sky.  For additional information see the NASA web page Summer Moon Illusion:  http://science.nasa.gov/headlines/y2005/20jun_moonillusion.htm. Thanks, Fred.

21 March 2006: Fred Farnell (Lane Tech HS,physics)                       Kepler's Law Website
Fred found The Planetary Orbital Simulation website, from The University of Nebraska, Lincoln:  http://astro.unl.edu/naap/pos/animations/kepler.swf. It  presents a nice simulation/explanation of various aspects of Kepler's Laws and simulations of the orbits of the planets. Fred had put together a nice exercise based on the simulator:

• Introduction
  In this activity you will investigate the relationship between the orbital period of a planet as it moves around the Sun and the length of the semimajor axis of its orbit. We will use a computer simulation for this activity. In the simulation, you will measure the relative amount of time it takes planets in our solar system to complete one orbit around the Sun. You will also be given the length of the semimajor axis of the orbit for each planet.
• Procedure
  
  1. On the planetary orbital simulation website, click on the 1st Law tab and choose the following options:
     Show semimajor axis.
     Show center.
  2. Click on the 3rd Law tab and choose the following options:
     Show solar system orbits.
     Show labels of solar system orbits.
  3. Set animation rate to 0.025 yr/sec.
  4. Choose Mercury from the planet menu and click on OK.
  5. Click on the start animation button and observe Mercury moving along the orbit.
  6. Record the length of the semimajor axis, in AU, from information given on the screen.
  7. Use a stopwatch to measure the time it takes Mercury to complete one simulated orbit. record this time, in seconds, and the simulated orbital period.
  8. After the data for Mercury have been recorded, repeat the procedure for Venus, Earth, and Mars.
  9. Also collect data for Jupiter, but change the animation rate to 0.10 yr/sec before running the animation for Jupiter. Record the length of the semimajor axis and the time to complete one simulated orbit. When recording the simulated orbital period, multiply the measured time in seconds by 4 to adjust for the change in the animation time.
• Data
  Determine the semimajor axis length (R) and simulated orbital period (T) for the planets Mercury, Venus, Earth, Mars, and Jupiter.
• Analysis
  Determine these ratios involving the Orbital Period (T) and semimajor axis (R) for the planets Mercury, Venus, Earth, Mars, and Jupiter.
  • T/ R
  • T² / R
  • T² / R²
  • T² / R³
• Conclusion
  Discuss how the orbital period of a planet is related to the length of the semimajor axis of the orbit. Be specific and give examples from your data that support your conclusion.

The first example was Mercury, and the simulation clearly showed the details of the elliptical orbit. We displayed vectors for its velocity and acceleration, which changed continuously as the planet traversed the orbit; the correlation of this property with the change in velocity of the planet as it gets further away and closer to the sun could be clearly simulated by adjusting the orbital parameters. Kepler's Second Law (equal areas in equal times) could also be simulated in a very useful way.

Porter Johnson pointed out that the planet Pluto moves about the sun with a period that is precisely 3/2 that of the planet Neptune. Furthermore, there are several objects that move with this same period. For details see the website The Plutinos:  http://www2.ess.ucla.edu/%7Ejewitt/kb/plutino.html.  In addition, the planet Mercury rotates with a period of 2/3 of its orbital period about the sun:  http://cseligman.com/text/planets/mercuryrot.htm.
This is a very nice teaching tool! Thanks, Fred.