Vollmond, High Tides and Lunacy

When teaching astronomy to non-science majors, I try to make connections with the student’s field of study or personal interests.  Sometimes this is not difficult.  For example, I can discuss NASA budgets and cost estimating with business majors.  For art majors, the deep red sunsets that followed the Krakatoa eruption of 1883 found their way into many paintings of the era.  The most notable example of this was The Scream painted by Edvar Munch in 1893.

The Scream by Edvard Munch. National Gallery, Olso, Norway. Aerosols injected into the atmosphere by powerful volcanic eruptions can cause very deep red skies at sunset.

A while back, I talked with someone whose career was in the performing arts, specifically dance.  I was stumped at the time to think of a possible tie in between astronomy and dance.  The closest analogy I could come up with was the classic case of a figure skater demonstrating the concept of angular momentum during a spin such as below.

Angular momentum is conserved, that is, it is not created or destroyed (it can be converted to heat via friction).  Angular momentum (L) is defined as:

L = mrv

m = mass, r = radius, v = velocity

As angular momentum is conserved, the value L is constant.  In the case of the figure skater in the video, she reduces r by drawing in her arms and legs closer to herself.  As the skater’s radius decreases, velocity must increase.  Hence, the rate of spin increases as radius decreases.  You can try this at home even if you do not  know how to skate.  Just find a swivel chair and have a friend spin you around with your arms extended, then draw in your arms close to your body.  You’ll feel your spin velocity accelerate.  Not as much as the skater, but enough to notice.

The conservation of angular momentum has several applications in astronomy, in particular, pulsars.  Pulsars are the remnants of stars that went supernova.  As the outer layers of the star are dispersed in the aftermath of a supernova, its inner core compresses forming the pulsar.  In a pulsar, the gravitational force is so great that electrons merge with protons to form neutrons.  Consequently, pulsars are a sub-class of what are known as neutron stars.  As the radius of a pulsar is reduced, its spin rate greatly accelerates.

We can measure the spin rates of pulsars as they emit radio waves in the same fashion a lighthouse emits a light beam.  The most famous pulsar is located in the Crab Nebula, which is a remnant of a supernova observed by Chinese astronomers in 1054.  This pulsar spins at a rate of 30 times per second.  To put that in perspective, the skater in the video above is spinning 5 times per second.

The pulsar in the Crab Nebula emits high energy x-rays. Red is lowest energy and blue highest energy x-rays. Credit: NASA/CXC/SAO

Is there any sort of analogy in the world of dance?  Ballet dancers use the same method as figure skaters to increase their spin.  However, as there is more friction from a wood floor than there is from ice, the effect is not as pronounced.  Looking around I found a different approach when it came to this and found a connection, albeit allegorical, to the dance performance Vollmond.

Translated from German, Vollmond means Full Moon.  Choreographed by Pina Bausch, the performance centers on two themes addressed in my class.  One is scientific, how the full Moon increases tides, the other not so scientific, how a full Moon affects human behavior.

During a full (and new) Moon, the difference between high and low tides are at their greatest.  During these two phases, the Earth, Moon, and Sun are aligned with each other.  At this time, the effect of the Sun and Moon’s gravity is greatest on the oceans as can be seen below.

Full Moon Tides
Credit: Wikipedia

The gravity from the Sun amplifies the lunar tides.  During a full Moon, high and low tides occur twice a day.  Tides during the full and new phases are referred to as spring tides.  This has nothing to do with the season of Spring.  In a way, it is during this time when the tides spring to life.  When the Moon and Sun are at a right angle relative to Earth, the Sun’s gravity partially offsets the Moon’s gravity and modulates the tides so low and high tidal differences are not as great as the spring tide.  These are referred to as neap tides.  Local conditions can also amplify the tides.  The most dramatic example of this is the Bay of Fundy where high and low tide can differ by 56 feet.

Spring tides at the Bay of Fundy Credit: Samuel Wantman/Wiki Commons.

So, if you live by the ocean, you’ll associate high tides with a full (and new) Moon.  How about the Great Lakes?  Not so much.  The lakes greatest tide is only 5 cm, not enough to be noticed with the naked eye.  The earth you stand on also feels the tidal pull from the Moon.  Like the lakes, it is not noticeable at 25 cm.  As the landmarks rise up and down with the ground, your eye cannot detect ground tides.  We can say, quite confidentially, that the full Moon affects tidal motions.  Can we say the same regarding human behavior?

The words lunar and lunatic have their roots in the Latin word luna.  In ancient Rome, Luna was the goddess of the Moon.  Lunatic means to be moon struck.  We are all familiar with the phrase, “It must be a full Moon.”  Meaning that the full Moon provides an explanation for an increase in bizarre/criminal behavior.  Does the empirical evidence support this?  The short answer is no.  Studies have indicated no change in criminal behavior during a full Moon, or even a scientific model to explain why that would happen.  This highlights the key difference between science and mythology.

Statue of the Roman Goddess Luna. Credit: Wiki Commons

Whenever a student writes the phrase, “I believe” in a science paper, I advise them to take pause and ask yourself why do you believe that?  Science is not about beliefs, but about investigation of the nature and causes of phenomena we observe around us.  If you want to assert something as being true in science, you need a model to explain why it happens, empirical evidence it actually does happen, and independent verification of the original results.  Sometimes you might have a model you think is reasonable, but the empirical evidence does not back it up.  One such case is in economics, where demand and supply curves indicate a minimum wage set above the market rate creates unemployment.  The evidence does not support that meaning a newer, more sophisticated model is required to explain what is happening.

The purpose of this exercise was to find ways to connect a student’s personal interest to a scientific topic.  If that can be accomplished, the chances of building the student’s interest and motivation in the class increases.  In this case, we can use two situations to discern between what passes for science and what does not.  For the teacher, it provides the opportunity to explore areas that were previously unknown.  I would have never learned of the Vollmond dance performance without attempting to match my specialty with the student’s.  It’s a good experience to reach out of your comfort zone to find common ground with your students.  Often, in the classroom, who is the teacher and who is the learner can be a fluid situation.  You have to permit yourself enter your current student’s world of interests.  I have found that as a teacher, that prevents my lessons from going stale over the years.

*Image on top of post is the full Moon, or Vollmond in German.  Credit:  Katsiaryna Naliuka/Wiki Commons.

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