I’m excited to announce that Volume 3 of the Spitz Fulldome Curriculum is being released to all SciDome users, and will of course be automatically incorporated into all future SciDome installations. We thought that this would be an opportune time to give a very brief overview of what’s contained in this volume. There are several revisions to previous minilessons as well as several all new offerings:
This minilesson gives 26 examples (in order of date) of Galileo’s first observations of the four major moons of Jupiter during the winter of 1610. The actual configuration of each night is beautifully displayed on the dome by Starry Night and then Galileo’s sketch is presented directly underneath it so that your audience can compare the sketch to reality. You will be astonished at Galileo’s accuracy, as well as the restrictions of his poor optics and resolution that confined his work. My students enjoy these comparisons even more than I do!
North Celestial Pole (NCP) Altitude
My students always scratch their heads when presented with the idea that the North Celestial Pole is always the same number of degrees above your horizon as your latitude. This series of overlaying diagrams attempts to clearly lay out exactly why this is the case.
Steve Sanders, Observatory Administrator at Eastern University and my right hand man, came up with this idea to beautifully illustrate the various planetary axis tilts side by side as well as their rotation periods. This animation is so impactful that the folks at ViewSpace used it in one of their presentations last year!
This is one of my all time favorite mind-blowing demonstrations! In a series of overlaying fulldome illustrations (again created by Steve Sanders), the second cosmological principle of the universe looking the same everywhere is demonstrated by using the appearance of quasars as seen from any galaxy, starting from the Milky Way. Your audience will be left awestruck when they discover that the Milky Way is a quasar as seen by a distant galaxy which to us looks like a quasar!
Roemer’s Method Revised
One of my favorite minilessons from Volume 1, we’ve revised this presentation with a new animation by Steve Sanders which very clearly shows the concept behind the light time effect and how Roemer was the first to demonstrate that the speed of light was finite and approximate its value. You can not only show this effect to your audience but make an incredibly precise and straightforward measurement from it of the speed of light!
Solar System Scale Revised
I still use this minilesson in nearly every one of my presentations and for all ages. We have greatly improved the graphics used in this minilesson and I know you will like the results!
Stellar Sizes Revised
Like Solar System Scale, I use this minilesson frequently in most of my presentations, and we’ve revised it by adding a final graphic at the end which shows VY Canis Majoris in its entirety on the dome in one final scale shift.
Synodic Periods of Mercury, Venus, Mars and Jupiter
These are my favorite new additions in Volume 3! Each is a separate minilesson and carefully steps the audience through how Copernicus disentangled synodic periods of the planets into their sidereal periods around the Sun! Although very few people have ever been taught this concept, it’s very straightforward and illuminating when you see it on the dome. Test one out for yourself and you’ll be hooked!
We often mention this infamous “Law” in our astronomy classes, so I wanted to present it in a historical fashion to demonstrate what effect it had on astronomer’s thinking when the Solar System was being explored and new planets being discovered. It’s the perfect example of a mathematical oddity that may or may not be scientifically meaningful. I think you will find it a fascinating subject as presented on the dome in this minilesson!
This little minilesson playfully depicts the fact that the region of the sky known as “The Sea” by the ancients has water-related constellations residing in it for a specific reason, namely that the Sun traversed this part of the sky during the rainy season in the Mediterranean. You will also be able to show your audience in a natural way that the position of the winter solstice used to be in Capricorn around 1000 BC, and hence that latitude parallel is called the Tropic of Capricorn.
Perhaps the greatest contribution to the official contents of Volume 3 is the availability of three unique fulldome interactive programs: Epicycles, Newton’s Mountain, and Tides. These three programs allow you to clearly demonstrate subjects which I have found extremely challenging for my students:
- Epicycles shows many of the intricacies and systematics of the simplified Ptolemaic geocentric system and will alert your audiences to the vagaries of “saving the model at any cost.”
- Newton’s Mountain is a 21st century interactive version of Newton’s attempt to explain exactly what an orbit is allowing you to show your audience in real time different orbits as a cannonball literally falls around the Earth.
- Tides shows exactly why the Moon causes the water to bulge on either side of the Earth via differential gravitational forces as well as demonstrating that the bulge is not the same on both sides!
These three programs require purchase because of the many years of work which went into their development and implementation. They are now available for online purchase and immediate download:
Purchase Astrophyics Apps
I hope that you and your audiences thoroughly enjoy this latest addition to the Fulldome Curriculum, and that they will be helpful as you continue to strive to educate people in the subjects that we all love.
Three long-awaited fulldome astrophysics apps created by Dr. David H. Bradstreet are now available for purchase and immediate download for installation on SciDome systems. Tides, Newton’s Mountain and Epicycles are selling for $200 individually or $500 for all three.
Purchase Astrophyics Apps
These programs teach the difficult concepts of tides, orbital motion, and epicycles in unique ways on your dome. All three programs are completely controllable via an intuitive interface on your Preflight computer. In addition, Tides is controllable via SciTouch for a seamless teaching experience for your audience.
The respective At A Glance teaching guides are all available for free download if you’d like to preview what you can do with these unique Fulldome interactive programs:
Volume 3 of the Fulldome Curriculum includes a lesson based on the Titius-Bode “Rule.” In this new teaching module we present the orbits predicted by the Titius-Bode relation in a historical timeline compared to the actual planetary orbits to show students why this apparent rule was important in 18th and 19th century astronomy.
The Titius-Bode “Rule” purports to describe an apparent mathematical correspondence in the sizes of the orbits of the classic planets in our Solar System. Although the idea of some kind of relationship had been hypothesized before Johann Daniel Titius and Johann Elert Bode, their publications in 1766 and 1772, respectively, brought this relation into the limelight of astronomical thought, and hence it is named after them.
The idea is that there is a mathematical relationship between each of the orbits of the classic planets. Usually it is presented in the following form:
… where m = -∞, 0, 1, 2, 3,… and d is the semi major axis of the planet in astronomical units.
Historically, this relationship was believed to be revealing something intrinsic about the positioning of the planets in the Solar System, that there might have been some type of resonance phenomenon within the formation of the planets within the solar nebula. The reason for this belief came out of the astronomical discoveries which were made subsequent to its popularization in the 18th century. To see this in its historical context, let’s set up a table the way it would have been constructed in the late 1700’s:
Interesting results, but the huge gap between Mars and Jupiter posed a real problem!
SciDome view showing Uranus’ orbit
compared to the Titius-Bode prediction
Shortly after the Titius-Bode “Law” became publicized, William Herschel in 1781 discovered a new planet, Uranus! This was a paradigm changing discovery, but what was just as incredible was that its semi major axis was calculated to be 19.2 AU, nearly doubling the size of the Solar System! Just as remarkable, the next predicted semi major axis from the Titius-Bode “Law” was 19.6 AU, only 2.1% different from the measured size!
This discovery started astronomers thinking that perhaps there was more to the Titius-Bode “Law” than they once thought, that perhaps it wasn’t coincidence but was revealing a yet undiscovered physical relationship within the Solar System. Twenty years later, on the first night of the new century, 1801, Father Giuseppe Piazzi discovered a new “planet,” later named Ceres.
What was truly remarkable about this new planet was that it’s semi major axes was eventually calculated with a new mathematical method by Carl Friedrich Gauss to be 2.8 AU, nearly exactly what the Titius-Bode “Law” had predicted for a planetary body residing in the gap between Mars and Jupiter! Of course soon thereafter many more bodies were discovered to reside within the gap, and by the 1850’s these objects were renamed asteroids.
However, the belief in the Titius-Bode “Law” was gaining new proponents, since it seemed to have predicted positions in which Solar System objects were subsequently discovered! The next predicted orbit would lie at 38.8 AU, and the search was on for yet another planet! Sure enough, Neptune was discovered with the aid of Newtonian physics in 1846, but its semi major axis was 30.1 AU, not the 38.8 AU expected from the Titius-Bode relationship.
SciDome display showing the large discrepancy between Neptune’s orbit (30.1 AU) and the predicted Titius-Bode orbit of 38.8 AU
This large discrepancy led to the virtual abandonment of the Titius-Bode relationship as a physical law. However, it’s interesting to note that when Pluto was discovered in 1930 its semi major axis was determined to be 39.5 AU, very close to the previously expected distance. Of course Pluto has now been relegated to dwarf planet status because of the myriad of new objects which have been discovered in the Kuiper Belt.
The next expected semi major axis from the Titius-Bode relationship is 77.2 AU. And isn’t it interesting that Sedna’s perihelion distance is 76.1 AU, although its semi major axis is a whopping 506.8 AU!
The moral of the story seems to be that although the Titius-Bode relationship has never been convincingly proven to come from physical laws, it is noteworthy historically but also serves to perhaps warn us about jumping to conclusions even though the initial evidence may seem inviting. The Titius-Bode relationship is today such a controversial topic that Icarus, the main professional journal for presenting papers on Solar System dynamics, refuses to publish any articles on the subject!
What’s Up with the Pleiades Being M45?
Hubble image of the Pleiades (M45)
During a recent planetarium conference session, an interesting question came up about why the Pleiades is listed as M45 in Messier’s catalog. Few people know the reason for it.
Charles Messier is best known for his list of some of the best deep sky objects in the sky, and most everyone knows that he ostensibly put this list together to alert other sky watchers so that they wouldn’t mistake any of these objects for comets. Of course discovering comets was the big thing in those days because the comet was then named after the discoverer!
This reasoning begs the question as to why the Pleiades, the bright and nearby Seven Sisters open cluster (which has been well known since antiquity), was designated as M45! No one is going to mistake this for a comet, and everyone knew of its existence! What gives?
In reality, there’s more to this mystery than just M45. Messier accidentally discovered M41 (an open cluster SW of Sirius) in 1765 – so at that time his list contained 41 objects. He decided to publish the list in 1771, but that list had 45 objects.
Note the last 4 are well-known objects, objects that had been detected by the naked eye for many centuries:
Hubble image of the Orion Nebula (M42 and M43)
None of these objects could possibly be mistaken for a comet! Although no one knows for certain, it seems that Messier wanted to have a longer list with a more “rounded” number of objects in it than 41, hence the addition of four well-known objects for this first publication by measuring their positions himself.
My suspicion (and that of some others as well, see references) is that he wanted to have more objects in it than a well-known list published by Lacaille in 1755 which had 42 objects in it. While this is only speculation, it certainly makes sense from an egotistical point of view. After all, why else did people want to discover comets so badly?
M42 through M45 are all up in the late winter-early spring sky so markers could be placed on all four of them at once to emphasize this. This could make an interesting little side note planetarium lesson for your audiences.
Spitz is developing a Fulldome Curriculum Mini-lesson based on this idea in the future, but I thought I’d relay this interesting hypothesis beforehand in case you want to steal it for your own use.
- Messier’s Nebulae and Star Clusters, Kenneth Glyn Jones (1968; 1991), p. 352
- The Messier Album, John H. Mallas and Evered Kreimer (1978), pp. 1-16 (historical introduction written by Owen Gingerich, originally published in Sky and Telescope, August 1953 and October 1960)
Our ancestors were highly intelligent people who devised ingenious methods to model what they perceived to be reality in the skies. Unfortunately, they came at many of these observations with deep-rooted prejudices and a priori (preconceived) beliefs which shackled their creativity.
Figure 1: Close up of the Ptolemaic system out to the Sun’s sphere
The prevalent, far-reaching belief was that the Earth was immovable and at the center of the universe. Of course we know this is preposterous (even to the point that there is no such thing as a center to the universe), it is still a useful exercise to challenge students to prove, without leaving the Earth or using satellites, that the Earth does indeed rotate and that it revolves about the Sun.
Another a priori assumption was that celestial bodies never stopped moving, as opposed to “earthly” objects which eventually came to a halt. So, when the planets periodically went back and forth in the sky, this was unacceptable and Apollonius of Perga came up with a “solution” that allowed the wanderers to be always moving without stopping by coupling two motions at once. The planets were not simply attached to a mystical sphere (“deferent”) but they were actually attached to a mini-sphere (“epicycle”) which rotated on the larger one.
Figure 2: Mercury’s retrograde path in the Ptolemaic system
In this way planets could move around the sky but intersperse that generally easterly motion with apparent backwards motion (retrograde) when the transparent epicycle carried the planet backwards. The ancients latched on to it and it was greatly preferred to having deferents slow down, stop, go backwards, stop, then resume their original direction.
My colleague David Steelman and I created a program called Epicycles for SciDome that illustrates the main characteristics of the Ptolemaic Geocentric Model. It helps students discover the systemics of the model which can only be explained as “it just has to be that way”. Whenever that is the reasoning, it signals a problem with the theory/model. This will become obvious as we go through this paper.
Let’s first take a close look at the bodies closest to the Earth in the geocentric model, as shown in Figure 1.
The Moon moves the fastest in the sky (and even changes shape!) so it was assumed to be closest to Earth. Placement of Mercury and Venus closer to the Earth than the Sun was problematic. The theory was based upon the idea that those that appeared to move the slowest must be farthest away from Earth. The problem is that the epicycle containing Mercury, the epicycle containing Venus, and the Sun all orbited around the Earth in one year! So their order was reluctantly agreed upon because Mercury moved fastest on it epicycle, Venus next fastest, and of course the Sun had no epicycle (because it never retrograded).
Figure 3: Venus and Mercury’s retrograde paths in the Ptolemaic system
The epicycle sizes are based on arbitrarily assumed distances from Earth. The angles had to match the size of the retrograde loops seen in the sky so, looking at Figure 1, Mercury’s epicycle is tiny compared to Venus’ because Mercury’s retrograde loop is about 52 degrees in extent whereas Venus’ is about 92 degrees! The fact that Venus is farther away than Mercury from the Earth in this model requires it to be considerably larger than one might expect, but these are to scale to create the properly sized retrograde patterns.
As time is progressed a trace can be turned on which shows the retrograding patterns of the planets. Figure 2 shows a close up of Mercury and Figure 3 that of Venus.
When I ask students if they see anything peculiar as time progresses, eventually someone notices that the centers of the epicycles of Mercury and Venus are exactly and always lined up with the line connecting the Earth and Sun (the Earth-Sun Line). What explanation would the ancients have given for this? “It just has to be this way for this model to work.” Red flag number 1 that there’s something wrong with this theory.
Figure 4: The planets beyond the Sun’s sphere
Of course we know that in the Copernican heliocentric model we don’t need epicycles to cause Mercury and Venus to wobble back and forth around the Sun because they are simply closer to the Sun than Earth and they orbit the Sun. In fact, Copernicus was the first to completely untangle the motions of Mercury and Venus from the Sun’s motion.
This confusion is one rarely-discussed reason why the Copernican heliocentric model was so appealing. It unambiguously separated the motions of Mercury and Venus and even established, for the first time, their orbital periods around the Sun (88 days and 225 days, respectively).
Now observe the planets beyond the Sun, as shown in Figure 4. As we advance time another strange systematic displays itself, although this one is a lot more challenging to pick out. The Earth-Sun Line is always parallel to the planet’s epicycle radius! You can easily see this in Figure 4 now that you know to look for it.
Again, the ancients noted this “coincidence” but could never explain it other than “it has to be this way for the model to work.” Another red flag has raised itself in the flawed Ptolemaic model! The basic reason for this “coincidence” is because the retrograde motion of each planet is a function of its position relative to the Earth in its own orbit. Since we’re locking down the Earth and moving the Sun, it’s the orientation of the Earth-Sun Line that is the determining factor as to when planets exhibit their retrograde motions.
Figure 5 – The retrograde paths of the planets beyond the Sun’s sphere
When the planets leave breadcrumbs (see Figure 5) their retrograding paths become obvious. Again, the model has been carefully defined to accurately recreate the width of the retrograde loops as well as their frequency.
This is a fun and thought provoking lesson for my students because it demonstrates how intelligent and clever the ancients were in mimicking celestial motions, but it also shows how preconceived notions can weigh one down and severely complicate the model. It also clearly points out that when certain “features” of a model have no other explanation than “it has to be that way for the model to work” that the model is most likely flawed or incorrect at its core. But having the Earth move was a huge paradigm shift, and it took over 1500 years to overthrow it!