Mission Impossible: Ghost Particle

Earlier this month, another “multi-messenger” announcement was made of the discovery of a new astronomical outburst by different instruments that study different parts of the universe. The first major multi-messenger astronomy discovery was announced last year after the collision of two neutron stars was observed in the nearby galaxy NGC 4993. The neutron star collision was observed first with the LIGO and Virgo gravitational wave detectors, coincident with a gamma ray burst detected by the Fermi space telescope, pinpointed with an optical telescope in South America, and followed up with different kinds of detectors.

IceCube Neutrino Observatory diagram
from IceCube Science Team

This new announcement is based on the detection of a very unusual neutrino or “ghost particle” at the IceCube Neutrino Observatory at the South Pole. This event is worth pointing out in SciDome because we have a horizon panorama that matches the horizon at the South Pole, and one or two other points that may help students understand how the sky works and what neutrinos are.

Neutrinos have been observed with detectors in both the northern and southern hemispheres of Earth, and they are created as a byproduct of various nuclear reactions. Neutrinos hardly interact with normal matter at all, and they tend to radiate outwards from their point of creation at the speed of light.

Neutrinos at rest were assumed to be massless until evidence to the otherwise shown by Art McDonald and Raymond Davis, Jr., led to them being awarded the Nobel Prize in Physics in 2015.

The interaction of neutrinos with normal matter is so weak that most neutrinos that encounter the Earth fly straight through it without hitting anything. In February 1987 when a nearby supernova popped off in the Large Magellanic Cloud, 25 neutrinos were detected at neutrino observatories in the northern hemisphere, where the Large Magellanic Cloud never rises above the horizon.

The new neutrino detection from IceCube at the South Pole was detailed enough to provide a vector back to its point of origin, somewhere within a 1.3-degree-wide circle on the sky.

The Spitz Fulldome Curriculum, included with every SciDome system, includes dozens of lessons prepared by noted astronomy educator Dr. David Bradstreet

The circle enclosed a radio source discovered in 1983, a galaxy 3.7 billion light years away with an active supermassive black hole at its core. This is one of the quasars like Dr. Bradstreet uses in his “Quasars Fulldome” show from the Fulldome Curriculum Vol. 3. Because this quasar’s jet is pointed at us, it is called a “blazar”; this term originated because the first of its type happened to be named “BL Lacertae”, and because blazars can appear brighter than normal quasars and their brightness can vary more quickly than normal quasars.

Like before, this neutrino detected from the South Pole had flown through the Earth to get to the detector. The blazar TXS 0506+056 is located at about 5 hours right ascension and +5° north of the celestial equator. Only objects south of the celestial equator are above the horizon as seen from the South Pole.

TXS 0506+056 is conveniently located in the Shield of Orion, part of the most easily recognized equatorial constellation on the sky. The blazar is labeled “MG 0509 +0541” in SciDome and is one of the quasars in Dr. Bradstreet’s “Galactocentric Distributions” minilesson.

In the part of the Fulldome Curriculum “Seasons” class that visits the South Pole, the audience may have a hard time recognizing Orion because it is upside down and its northern half, including TXS 0506+056 is below the horizon. The horizon needs to be switched off and then tilted up to bring the rest of the constellation into view to simulate a “neutrino filter”.

The prefix TXS stands for ‘Texas’, where UT-Austin astronomers set up a radio telescope array outside of Marfa for several years in the 1980s – now removed. MG stands for ‘MIT-Green Bank Observatory’.

The mass of neutrinos and other particles is calculated in electron volts, but because they are so small, only particles that have a large amount of kinetic energy are comparable to things that we can comprehend. 1 trillion electron volts (1 TeV using the prefix tera-) is comparable to the kinetic energy of a mosquito in flight. The most powerful cosmic ray ever detected had a mass of 300 quintillion electron volts, comparable to a pitched baseball.

The single neutrino detected by IceCube from TXS 0506+056 had a mass of 290 TeV. After crossing 3.7 billion light years in space, this is by far the most distant neutrino emission ever detected: the only other objects in the sky that have produced detected neutrinos have been the Sun (8 light-minutes away) and Supernova 1987A (168,000 light-years.)

(In 2012, the IceCube Collaboration detected three other high-energy neutrinos, which they named Bert, Ernie and Big Bird, but where Bert and Ernie came from is not known, and Big Bird was probably generated by the blazar PKS B1424-418 with a certainty of 95%. That’s only two sigma, which does not hold water with particle physicists who have much stricter statistical significance limits. TXS 0506+56 was much more narrowly confined.)

Because matter and energy are relative, an electron volt is equivalent to the energy exchanged by the charge of a single electron moving across an electric potential difference of one volt. The only way a neutrino can be detected is on the rare occasion when it enters a neutrino detector (like a large underground tank of heavy water or tetrachloroethylene or linear alkylbenzene or another chemical) and collides with an atomic nucleus or an electron inside the detector, emitting light that can be detected with photomultiplier tubes. IceCube is unusual because its detectors have been drilled into the Antarctic ice pack and are not suspended in water or another fluid.

Upcoming Fulldome Curriculum Lesson: Titius Bode Rule

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!

Messier Mischief

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.


  • http://messier.seds.org/m-q&a.html#why_M42-45
  • 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)

Exploring Roemer’s Method for Determining the Speed of Light

In the 17th century the speed of light was unknown, and scientists questioned whether it had a finite value. Descartes argued that if the speed of light was finite, when we looked out into space with telescopes we’d be looking into the past. That idea was so off-putting, he concluded the speed of light must be infinite.

We now know it’s not infinite. If it were, the universe couldn’t exist. Remember Einstein’s famous E=mc²: if the speed of light c was infinite, the amount of energy contained in any amount of matter would be infinite! Good luck with that…

Ole Roemer, a Danish astronomer in the 17th century, stumbled upon the speed of light during timing observations of the emergence of Jupiter’s closest Galilean moon, Io, from behind the planet’s limb. He noticed the moon’s appearances didn’t match his predicted times, and by studying them through the year realized it was ahead or behind the predicted time, depending upon how far away Jupiter was from Earth! He correctly reasoned that this variation was not due to some strange inconsistency with Io’s orbit but rather that he was observing what is now called the light-time effect.

Starry Night simulates the light time effect, so we can reproduce Roemer’s 1676 measurements of Io’s emergence from Jupiter’s limb to directly show the light time effect, and even measure the speed of light.

Figure 1: Io emerging from Jupiter’s eastern limb

Figure 1 shows Io emerging from Jupiter’s eastern limb. This view was measured by Roemer in Copenhagen on November 9, 1676. Using Starry Night’s ability to transport us anywhere in space, we can specify a direct route to Jupiter but hold the time constant.

In other words, if we could transport instantly to 0.20 AU from Jupiter (an arbitrarily distance for a nice view of the scene), what would we see? As we travel to Jupiter, we’ll see Io appear to move further and further eastward from the limb even though time has stopped and we’re traveling on a direct line to Jupiter, as shown in Figure 2.

Figure 2: Io appears farther from Jupiter as we reduce our distance

If the speed of light were infinite, when we transported to Jupiter Io would be emerging from the limb, the same view as from Copenhagen. Because the light time effect is built into Starry Night, we see Io has actually emerged significantly past the limb. In other words, on Earth we saw Io just emerging from Jupiter’s limb, but in the neighborhood of Jupiter it has already long since passed from behind the limb!

The difference occurs because of the light time effect.

We can measure the speed of light directly from these observations. We know the distance we covered in our journey from Earth (5.326 AU = 7.968 x 108 km). We can now step back time and return Io back to its emerging position from Jupiter’s limb as seen from this nearby location to Jupiter. If we place Io back on Jupiter’s eastern limb by reversing time in Starry Night, it takes 44m 20s to do so, or 2660 seconds. To estimate the speed of light, we simply take the distance we traveled and divide it by the time, as follows:

Thus we obtain a value for the speed of light only 0.08% different from the actual value of 299,792 km/s!

Figure 3: Line of sight from Earth to Jupiter’s limb

Steve Sanders (Eastern University Observatory Administrator) and I have created a simulation which clearly illustrates this phenomenon, as seen in the figures below. This simulation will be included in the release of Volume 3 of the Fulldome Curriculum and you can preview it on Youtube.

Figure 3 shows the line of sight from Earth to Io as it has emerged past Jupiter’s limb, the event that Roemer was measuring. We depict the event close to opposition with Jupiter (Earth’s closest approach to the planet) and the distance between the bodies is approximately 3.95 AU = 3.67 x 108 million miles.

The same event is shown in Figure 4 when Earth and Jupiter are nearing conjunction (Jupiter nearing a syzygy with the Earth and Sun in between). Note that the distance separating the planets is now 5.75 AU = 5.34 x 108 million miles.

Figure 4: Earth and Jupiter nearing conjunction

Roemer measured the emergence of Io as being about 15 minutes later than when this emergence occurred close to opposition and attributed the lateness (correctly) to the extra distance that the light had to travel across the Earth’s orbit.

If you assume that this tardiness is entirely due to the extra time required for light to travel the extra distance, you can estimate the speed of light as follows:


The value of the astronomical unit at that time was very crudely known, so Roemer’s value for the speed of light was not nearly this accurate, but nonetheless he demonstrated that the speed of light was finite, and its value was of this order.

We encourage SciDome operators to use the Roemer Speed of Light minilesson in Volume 1 of the Fulldome Curriculum, along with our new simulation. The discovery of the finite speed of light forever changed our view of the universe, turning our distance-shrinking telescopes into literal time machines as we explore back into our cosmic past.

Recreating Jupiter’s Galilean Moons in SciDome

Figure 1: Page from the original printing of Sidereus Nunicius showing Galileo’s sketches of the Medicean Moons

In many of our astronomy classes, we discuss the importance of Galileo’s first telescopic observations in eventually overthrowing the Ptolemaic geocentric system. His first observations were relayed to the public in his short book Sidereus Nuncius, which is Latin for The Starry Messenger (or arguably, The Starry Message). In it he relates his observations of the Moon, the myriad of new stars he observed (with sketches of the Pleiades and Praesepe regions), and the Moons of Jupiter.

He originally called these the Medicean Stars, a call out to his potential benefactors, the four Medici brothers (the book itself was dedicated to one of them who had been a former pupil). Seeking for funds for your science… things really haven’t changed very much in 400 years…

With Starry Night, SciDome can easily reproduce the date and situations of Galileo’s observations. Others have done this in the past, and I refer you to the excellent article by Enrico Bernieri called “Learning from Galileo’s Errors” published in the Journal of the British Astronomical Association, 122, 3 (2012) which goes through his observations in detail and discusses the errors which Galileo made.

Another excellent article is by Michael Mendillo in the Proceedings of the IAU Symposium No. 269 (2010) called “The Appearance of the Medicean Moons in 17th Century Charts and Books – How Long Did It Take?” which gives rich background on some of the aftermath of Galileo’s revelations.

I also highly recommend the Wikipedia article on Sidereus Nuncius as an excellent starting point in building your background information on Galileo’s first telescopic observations. In addition, Ernie Wright has graphically reproduced Galileo’s observations and placed them online in an excellent web presentation.

With the incredible talent of Steve Sanders (Eastern University Observatory Administrator), I have created a minilesson for Volume 3 of the Fulldome Curriculum which reproduces all of Galileo’s published observations of the Medicean moons.

Figure 2: SciDome presentation of Galileo’s first Jupiter observations from January 7, 1610 from Padua, Italy.

Using Padua, Italy as our observation location and the approximate times given for each observation in Sidereus Nuncius, we begin with the close-up view of Jupiter on the dome as seen on January 7, 1610 at approximately 6 PM local time. Next we place a slide of the view as drawn by Galileo in Sidereus Nuncius below the view to show just how accurate Galileo was in his sketches. The labels of the Galilean moons are then displayed.

Note that although all four moons presented themselves, Io and Europa were too close together to be resolved by Galileo’s homemade 20X telescope which suffered also from chromatic and spherical aberration. This is an important fact to remember, because essentially all of the “errors” which we will find in comparing his sketches to the actual viewing circumstances were because of his lack of resolution.

We proceed by advancing time in Starry Night so that the audience can watch the dance of the moons around Jupiter and stop at the next observations of Jupiter as recorded by Galileo, on January 8, 1610. Then his sketch of this configuration is displayed, and again we note the accuracy of his rough sketches.

The minilesson continues in this fashion, showing the moons moving from date to date and then presenting 21 successive sketches by Galileo as presented in Sidereus Nuncius. Galileo concluded after four nights of observations that these tiny “stars” were indeed most likely satellites of Jupiter, which was of momentous importance because it was the first time that moons had been discovered around another body.

It also indicated that a planet could move and moons “stay up with it” despite its motion, an Aristotelian argument once offered to discount that the Earth could be moving because, if it did, how could the Moon know enough to keep up with it? Obviously Jupiter had at least four moons and they had no problem staying with it!

I have found that going through many of these configurations with my students greatly enhances their appreciation of Galileo and the great discoveries that he made despite the limitations of his equipment. Presenting this minilesson engages students in the realization that Galileo was both an excellent and honest observer as well as a genius. His observations helped to lead to the downfall of the geocentric universe and the eventual acceptance of the heliocentric model

Tides Revisited and Explained

A historical lesson in Volume 2 of the Fulldome Curriculum is the astronomical aspect of the Boston Tea Party. As we learn, Colonists, furious at the tea tax, tossed chests of tea into Boston Harbor on the night of December 16, 1773. Eyewitnesses noted that the chests became stuck in the mud adjacent to the ship and piled up in such a way that the Colonists feared the chests wouldn’t float out to sea and might be partially recoverable. The low tide that night (between 6-9 PM local time), which occurred (coincidentally) simultaneously with the raid, was especially low that night.

Although our lesson concentrates on discovering the Moon’s phase that night, a key element is why both high and low tides were so extreme. It turns out that the Moon was close to New Moon phase and perigee that night, making the tides about as extreme as they ever get. So I’d like to concentrate on explaining why tides occur and why the Moon is the major cause of tides and not the Sun.

tides1The ancients knew that the Moon caused the tides because the tides roughly coincided with the position of the Moon in the sky. The interval between successive high and low tides is ~13 hours, and the high and low tides occurring the next day were approximately one hour later, mimicking the position of the Moon which moved about 13 degrees to the east each day.

The ancients also noted that the greatest tides occurred during New and Full Moons (spring tides) and the least extreme tides occurred at 1st and 3rd quarter (neap tides). But how the Moon caused the tides had to wait until Isaac Newton. I often ask students: “What causes tides on the Earth?” Their answer is always: “The Moon’s gravity pulling on the water of the Earth.” I then ask them, “Then why doesn’t the Sun cause the tides, since its gravitational pull on the Earth is 180 times stronger than the Moon’s (which is why we orbit the Sun and not the Moon!)?”

tides2The answer is that it’s the Moon’s differential gravitational force on the Earth that causes the tides. The Earth is close enough to the Moon that the Moon pulls considerably harder on the Earth’s near side compared to its far side. The percentage difference between the Moon’s gravitational pull on the Earth’s near side compared to the far side is 6.9%. The Sun, which is so far away from the Earth that it sees the Earth as essentially a point mass, pulls differently on each side of the Earth by a percentage difference of only 0.017%! Ok, most people (students) will buy this, but do NOT understand why the water bulges on both sides of the Earth.

Figure 1 illustrates the strength and direction of the Moon’s gravitational pull on the Earth at New Moon, i.e., the Sun and Moon are in the same direction. This was essentially the phase of the Moon during the Tea Party, i.e., a day or so past New Moon (thin waxing Crescent).

tides3Determining the differential force experienced by the Earth is equivalent to asking, “What does the Earth actually ‘feel’ due to the Moon’s uneven tugging on it?

We can calculate that by subtracting out the force vector that the Earth experiences at its center from all the other vectors. This is, by definition, the meaning of differential gravitational force.

To illustrate this, Figure 2 shows the inverse center vector’s tail (drawn in orange) placed at the head of each force vector. We will add this inverse vector to all five vectors and illustrate their resultants by white vectors in Figure 3.

For clarity, let’s just look at the resultant differential force vectors in Figure 4.

tides4As already noted, there is no vector at the center of the Earth because we added its exact inverse so that it canceled out. (That was the point – asking what does the Earth “feel” is a center of Earth force transformation.  Sounds cool anyway…) The remaining vectors make sense if you think about each one of them.

The resultant vector on the right occurs because the Moon pulls hardest on the near side, so subtracting the weaker central force resulted in a vector pointing to the right. The resultant vector on the far side to the left will also make sense because the Moon pulls least on that side, so subtracting the larger central force vector resulted in a force pointing to the left! The resultants on the top and bottom occur because of the slightly different directions that the Moon’s force pulls on those points compared to the direct line at the Earth’s center.

If we continued this exercise at 15-degree intervals (instead of 90-degree intervals) around the surface of the Earth, we would have the resultant vectors shown in Figure 5. The locus of all the vector heads has also been drawn in and this egg shape represents the gravitational equipotential of all the tidal forces, i.e., it’s this shape that the water will attempt to emulate.

tides5Ok, now what? Well, let’s label Boston in the diagram and talk about it – see Figure 6.

Remember that the Moon and Sun are off in the direction towards the right in all the figures. What approximate time is it in Boston in Figure 6? With the Sun highest in the sky, it would be noon. (I hesitate to say “directly over your head,” but you know what I mean.) What tide would the folks in Boston be experiencing at this moment?

The highest bulge is in the direction of the Sun and Moon, so they must be experiencing high tide. Now let’s advance 6 hours to sunset, i.e., let’s turn the Earth counterclockwise by 90 degrees, as depicted in Figure 7. (Pretend that the Moon hasn’t moved in those six hours, so that the tidal bulge is still in the same direction.)

This is essentially the situation during the Boston Tea Party! The Sun had set and the thin crescent Moon was setting. Boston was experiencing low tide at this time (as shown in Figure 7) and it was an especially extreme low tide because the Moon was (coincidentally) close to perigee, so its tidal effects were maximized. So, when would Boston experience its next high tide?

tides6Approximately 6 hours later, near midnight, when Boston was on the opposite side of the Earth relative to the Sun and Moon. Figure 7 implies that the high tide it experiences on the far side is not as high as the one on the near side, and this is exactly the case with the tides! The one facing the Moon is somewhat higher (by a foot or so) than the one on the far side! Most people don’t know this, since diagrams in books always draw the tidal bulge in equal amounts on both sides of the Earth, but (as you can see in our accurately drawn diagrams) they are wrong!

How do you implement this knowledge in the planetarium? If you understand the above analysis, you can understand that indeed the tides will be in synchronization with the position of the Moon relative to your location. So, if you have New Moon, then high tides at your location are going to occur (approximately) at noon and midnight as in our Boston Tea Party example. This is because New Moon is highest and lowest (near your nadir) in your sky near noon and midnight, respectively.

tides7Actually the tides lag by about an hour because the water is trying to keep up with the Moon and lags behind its position. Let’s not get too technical! We haven’t even worried about the irregular landforms of the continents and how they complicate the actual tide heights, like at the Bay of Fundy!

What about the tides at Full Moon? Full Moon will behave similarly to New Moon, i.e., high tides will occur when Full Moon is (approximately) highest and lowest in the sky, i.e., midnight and noon.

What about 1st quarter? Again, the principle is exactly the same! When 1st quarter is highest and lowest in the sky, you should be experiencing high tides. 1st quarter is highest at approximately sunset and lowest (near your nadir) at sunrise. Likewise, 3rd quarter is highest and lowest at sunrise and sunset (respectively).

Confused? It’s ok. What you need to do is understand that the tidal bulge (high tide) is always trying to point to the Moon. So high tide will follow the Moon and the Earth “rotates” within the tidal bulging water so to speak. If you carefully work through the explanation and figures above, you should be able to comprehend when to expect high and low tides! If you can convey this to your audiences, they will have re-discovered what the ancients knew and why knowing the position of the Moon in the sky was important to them!