Phases of the Moon - University of Massachusetts Amherst

16 Pages·2006·2.33 MB·English

Presents

Momix: Lunar Sea

Thursday, November 16, 2006
10am Concert Hall

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ABOUT THE COMPANY

Known internationally for presenting work of exceptional inventiveness and physical beauty, MOMIX is a
company of dancer-illusionists under the direction of Moses Pendleton. For 25 years, MOMIX has been
celebrated for its ability to conjure up a world of surrealistic images using props, light, shadow, humor and the
human body.

In addition to stage performances world-wide, the company has frequently worked on special projects, in film and
in television. MOMIX has made five Italian RAI television features broadcast to 55 countries (including the
USSR and China) and has performed on Antenne II in France. MOMIX was also featured in PBS’s “Dance in
America” series. The company participated in the “Homage a Picasso” in Paris and was selected to represent the
United States at the European Cultural Center at Delphi. MOMIX dancers Cynthia Quinn and Karl Baumann
played the role of “Bluey” in the film “FX II,” under the direction of Moses Pendleton. The company is featured
on a Decca Records laser disc, appearing with Charles Dutoit and the Montreal Symphony in the Rhombus Media
film of Mussorgsky’s “Pictures at an Exhibition”, winner of an International Emmy for Best Performing Arts
Special. In 1992, Mr. Pendleton created “Bat Habits,” developed with the support of the Scottsdale Cultural
Council/Scottsdale Center for the Arts, Scottsdale Arizona and the University of Washington to celebrate the
opening of the San Francisco Giants’ new spring training park in Scottsdale, Arizona. This work was the
forerunner of “Baseball” which was created by Mr. Pendleton in 1994. MOMIX is featured in one of the first
IMAX films in 3-D, “IMAGINE,” which premiered at the Taejon Expo 93 and was subsequently released at
IMAX theaters world-wide. In 2004, “White Widow”, co-choreographed by Moses Pendleton and Cynthia Quinn,
was featured in Robert Altman’s movie, “The Company.” MOMIX has performed throughout the United States,
Canada, Spain, Greece, Italy, France, Germany, Russia, Denmark, Spain, England, Austria, Ireland, Holland,
Argentina, Mexico, Brazil, Chile, Japan, Taiwan, Singapore, Australia and New Zealand. The company is based
in Washington, Connecticut.

MOSES PENDLETON (Artistic Director) has been one of America's most innovative and widely performed
choreographers and directors for over 30 years. One of the founding members of the ground-breaking Pilobolus
Dance Theater in 1971, he formed his own company, MOMIX, in the early 80’s and has been its Artistic Director
since 1984. Mr. Pendleton has also worked extensively in film, TV, and opera and as a choreographer for ballet
companies and special events.
Mr. Pendleton was born and raised on a dairy farm in Northern Vermont. His earliest experiences as a showman
came exhibiting his family's dairy cows at the Caledonian County Fair. He received his B.A. in English Literature
from Dartmouth College in 1971 and immediately began touring with Pilobolus, which had grown out of dance
classes with Alison Chase at Dartmouth. The group shot to fame in the 1970’s, performing on Broadway under
the sponsorship of Pierre Cardin, touring internationally, and appearing in PBS's "Dance in America" and "Great
Performances" series.
By the end of the decade, Mr. Pendleton had begun to work outside of Pilobolus, performing in and serving as
principal choreographer for the Paris Opera's "Integrale Erik Satie" in 1979 and choreographing the Closing
Ceremonies of the Winter Olympics at Lake Placid in 1980. In 1981 he created MOMIX, which rapidly
established an international reputation for highly inventive and often illusionistic choreography. The troupe has
been touring steadily and is currently performing several programs internationally. The company has made
numerous special programs for Italian and French television and received the Gold Medal of the Verona Festival
in 1994.
His film and television work includes the feature film "FXII," with Cynthia Quinn, "Moses Pendleton Presents
Moses Pendleton" for ABC ARTS cable, winner of a Cine Golden Eagle award, and "Pictures at an Exhibition,"
with Charles Dutoit and the Montreal Symphony, which received an International Emmy for Best Performing
Arts Special in 1991. Mr. Pendleton has made music videos with Prince, Julian Lennon, and Cathy Dennis,
among others.
MOMIX Influenced by the Moon

In “With Earthly Tricks, Momix Conjures Up a Moon Dance,” by Kathryn Shattuck in the New York
Times (Thursday, May 26, 2005), she writes: “In Lunar Sea, his latest work, Moses Pendleton sends the
dancers to the moon to frolic weightlessly in a petri-dish fantasy brewing new life. But the celestial
effects, it turns out, are earthbound. ‘I like to call it by the subtitle, ‘No Visible Means of Support,’’ Mr.
Pendleton said after one performance. ‘I was basically trying to devise a ballet as if you were witnessing
it on the Moon with one-sixth of the Earth’s gravity by using various tricks and techniques to elevate the
body. The reality is that much of it is very difficult physical pas de deux partnering work.’”

The heavily cratered surface of Earth's moon (image courtesy of NASA)
Phases of the Moon
The Moon orbits Earth at an average distance of 382,400 kilometers. The lunar month is the 29.53 days
it takes to go from one new moon to the next. During the lunar month, the Moon goes through all its
phases. You can see the phases drawn in the image below. Just like the Earth, half of the Moon is lit by
the Sun while the other half is in darkness. The phases we see result from the angle the Moon makes
with the Sun as viewed from Earth. The diagram below on the right is one you typically see in books.
Don't let it confuse you. The images of the Moon show what you see the Moon look like from Earth
when it is at given points in its orbit. It does not show which side of the Moon is lit by the Sun. The side
lit by the Sun is always the side that is pointed toward the Sun, as seen in the diagram below on the left.

We only see the Moon because sunlight reflects back to us from its surface. During the course of a
month, the Moon circles once around the Earth. If we could magically look down on our solar system,
we would see that the half of the Moon facing the Sun is always lit. But the lit side does not always face
the Earth! As the Moon circles the Earth, the amount of the lit side we see changes. These changes are
known as the phases of the Moon and it repeats in a certain way over and over.
At new moon, the Moon is lined up between the Earth and the Sun. We see the side of the Moon that is
not being lit by the Sun (in other words, we see no Moon at all, because the brightness of the Sun
outshines the dim Moon!) When the Moon is exactly lined up with the Sun (as viewed from Earth), we
experience an eclipse.
As the Moon moves eastward away from the Sun in the sky, we see a bit more of the sunlit side of the
Moon each night. A few days after new moon, we see a thin crescent in the western evening sky. The
crescent Moon waxes, or appears to grow fatter, each night. When half of the Moon's disc is illuminated,
we call it the first quarter moon. This name comes from the fact that the Moon is now one-quarter of the
way through the lunar month. From Earth, we are now looking at the sunlit side of the Moon from off to
the side.
The Moon continues to wax. Once more than half of the disc is illuminated, it has a shape we call
gibbous. The gibbous moon appears to grow fatter each night until we see the full sunlit face of the
Moon. We call this phase the full moon. It rises almost exactly as the Sun sets and sets just as the Sun
rises the next day. The Moon has now completed one half of the lunar month.
During the second half of the lunar month, the Moon grows thinner each night. We call this waning. Its
shape is still gibbous at this point, but grows a little thinner each night. As it reaches the three-quarter
point in its month, the Moon once again shows us one side of its disc illuminated and the other side in
darkness. However, the side that we saw dark at the first quarter phase is now the lit side. As it
completes its journey and approaches new moon again, the Moon is a waning crescent.
Try This!

You can demonstrate the phases of the Moon for yourself by using a lamp and a baseball. Place the lamp
with its shade removed in one end of a darkened room. Sit in the other end of the room and hold the
baseball up in front of you so that it is between your face and the lamp. Now move the ball around your
head at arm's length. Do this slowly and move your arm from right to left. As the baseball orbits your
head, you will see it go through the same phases as the Moon.

Another description of why the moon has phases:

In the diagram above, you can see the Moon always has a lit side (facing the Sun) and a dark side
(facing away from the Sun). From the Earth, we can only see the part of the Sun that is facing toward us
at any time (which is often called the near side of the Moon) and we cannot see the part of the Moon
facing away from Earth ( called the far side of the Moon). The phase of the Moon, or the shape of the lit
part of it, that we see at any time is then determined by the combination of these two factors - which part
of the Moon is lit by the Sun and visible to Earth at the same time!
More About the Moon

Called Luna by the Romans, Selene and Artemis by the Greeks, and many other names in other
mythologies.
The Moon, of course, has been known since prehistoric times. It is the second brightest object in the sky
after the Sun. As the Moon orbits around the Earth once per month, the angle between the Earth, the
Moon and the Sun changes; we see this as the cycle of the Moon's phases. The time between successive
new moons is 29.5 days (709 hours), slightly different from the Moon's orbital period (measured against
the stars) since the Earth moves a significant distance in its orbit around the Sun in that time.
The Moon was first visited by the Soviet spacecraft Luna 2 in 1959. It is the only extraterrestrial body to
have been visited by humans. The first landing was on July 20, 1969; the last was in December 1972.
The Moon is also the only body from which samples have been returned to Earth. In the summer of
1994, the Moon was very extensively mapped by the little spacecraft Clementine and again in 1999 by
Lunar Prospector.
The gravitational forces between the Earth and the Moon cause some interesting effects. The most
obvious is the tides. The Moon's gravitational attraction is stronger on the side of the Earth nearest to the
Moon and weaker on the opposite side. Since the Earth, and particularly the oceans, is not perfectly rigid
it is stretched out along the line toward the Moon. From our perspective on the Earth's surface we see
two small bulges, one in the direction of the Moon and one directly opposite. The effect is much
stronger in the ocean water than in the solid crust so the water bulges are higher. And because the Earth
rotates much faster than the Moon moves in its orbit, the bulges move around the Earth about once a day
giving two high tides per day. (This is a greatly simplified model; actual tides, especially near the coasts,
are much more complicated.)
But the Earth is not completely fluid, either. The Earth's rotation carries the Earth's bulges slightly ahead
of the point directly beneath the Moon. This means that the force between the Earth and the Moon is not
exactly along the line between their centers producing a torque on the Earth and an accelerating force
on the Moon. This causes a net transfer of rotational energy from the Earth to the Moon, slowing down
the Earth's rotation by about 1.5 milliseconds/century and raising the Moon into a higher orbit by about
3.8 centimeters per year. (The opposite effect happens to satellites with unusual orbits such as Phobos
and Triton).
The asymmetric nature of this gravitational interaction is also responsible for the fact that the Moon
rotates synchronously, i.e. it is locked in phase with its orbit so that the same side is always facing
toward the Earth. Just as the Earth's rotation is now being slowed by the Moon's influence so in the
distant past the Moon's rotation was slowed by the action of the Earth, but in that case the effect was
much stronger. When the Moon's rotation rate was slowed to match its orbital period (such that the
bulge always faced toward the Earth) there was no longer an off-center torque on the Moon and a stable
situation was achieved. The same thing has happened to most of the other satellites in the solar system.
Eventually, the Earth's rotation will be slowed to match the Moon's period, too, as is the case with Pluto
and Charon.
Actually, the Moon appears to wobble a bit (due to its slightly non-circular orbit) so that a few degrees
of the far side can be seen from time to time, but the majority of the far side (left) was completely
unknown until the Soviet spacecraft Luna 3 photographed it in 1959. (Note: there is no "dark side" of
the Moon; all parts of the Moon get sunlight half the time (except for a few deep craters near the poles).
Fast Facts: The Moon
Age About the same age as Earth: 4.5 billion years
Location Solar system
Avg. distance from Earth 384,400 km (238,900 miles)
Diameter 3476 km (2160 miles)
Orbital period around Earth 27 Earth days
Mass 7.35 x 1022 kg
Distinguishing features The Moon has no atmosphere or magnetic field. Most rocks on the
surface of the Moon seem to be between 4.5 and 3 billion years old,
older than those usually found on Earth. Thus the Moon provides
evidence about the early history of our solar system.

Links
Phases of the Moon and Try This! can be found at the following website:
http://starchild.gsfc.nasa.gov/docs/StarChild/shadow/questions/question3.html
More About the Moon: http://www.ex.ac.uk/Mirrors/nineplanets/luna.html
Fast Facts and Photo of the Moon can be found at:
http://amazing-space.stsci.edu/resources/fastfacts/moon.php.p=Astronomy+basics@,eds,astronomy-
basics.php&a=,eds
What is the Diameter of the Moon Activity can be found at:
http://school.discovery.com/lessonplans/programs/lightofthemoon/
No Visible Means of Support gravity activity can be found at:
http://school.discovery.com/lessonplans/programs/invisibleforce/

Additional Links

Tides and Currents Education: http://tidesandcurrents.noaa.gov/education.html

Tide Lesson Plans (grades 9-12 but can be adapted to younger grades):
http://www.nos.noaa.gov/education/kits/tides/supp_tides_lessons.html
What are Tides: http://www.nos.noaa.gov/education/kits/tides/tides01_intro.html

Weightlessness Lesson Plans (grades 5-8): http://www.challenger.org/lessons/78.pdf

The Earth and its Moon: http://www.ex.ac.uk/Mirrors/nineplanets/earth.html

Earth and Moon Viewer (very cool site for viewing the earth from the moon, or the moon from the earth,
and other interesting sites to observe): http://www.fourmilab.ch/earthview/vplanet.html

Interesting Moon Facts: http://lunar.gsfc.nasa.gov/moon/moonfacts.html
World Book: http://www.nasa.gov/worldbook/moon_worldbook.html
Universal Gravitation http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l3a.html
Teacher Tom Henderson provides us with an interactive physics textbook that helps students to
understand gravity with text and animations.

Amusement Park Physics - Roller Coaster http://www.learner.org/exhibits/parkphysics/coaster.html
Put your knowledge of gravitational potential energy to work and design and test drive your very own
roller coaster at this hands-on and "physics is phun" web site.

No Visible Means of Support: Gravity Activity
Because the moon has less mass than Earth, the force due to gravity at the lunar surface is only about 1/6
of that on Earth. Thus, a person standing on the moon would feel as if his or her weight had decreased
by 5/6. And if that person dropped a rock, the rock would fall to the surface much more slowly than the
same rock would fall to Earth.

Students will understand the following:

Objectives:
1. Without air resistance, all objects would fall with the same acceleration, regardless of mass.
2. Gravity is the force that causes objects to fall.
3. Air resistance, a type of friction, works against gravity to decrease the acceleration of a falling
object.

Materials:
An encyclopedia or a computer with Internet access should be available to students. The following
materials should be provided for each group:
• A variety of object pairs, such as balls of different sizes and weights, or a book and a sheet of
cardboard the same length and width as the book
• Objects, such as a feather or a sheet of paper, that encounter more air resistance when dropped
than the other objects

Procedures:
1. Ask your students if they predict that a heavier or larger object, if dropped from a height, will fall
to Earth faster than a lighter or smaller object. Tell them that Galileo Galilei (1564-1642)
performed a famous experiment that they are going to replicate in order to confirm or refute their
predictions.
2. Have students use the Internet or an encyclopedia to find out about Galileo’s experiment in
which he dropped objects from the Leaning Tower of Pisa in Italy.
3. Divide the class into groups, giving each group a variety of objects to experiment with (see
Materials).
4. Instruct groups to meet in order to design their own experiments. Remind them that a good
experiment should have a control and introduce only one variable at a time. Each group’s
experimental design should include a chart on which to record the results of each test performed.
5. Have students experiment with the object pairs, dropping them, one at a time, while standing on
a chair or desk. Other students in the group should observe closely to see whether one object
reached the floor before another or both objects reached the floor at the same time. Students
should carefully record their results on their charts. (Students should find that balls of different
sizes and weights fall at the same rate of speed, as do a book and a sheet of cardboard the same
length and width as the book.)
6. When students try dropping a feather or a sheet of paper from the same height from which they
dropped the other objects, they will discover that the feather and the paper fall more slowly.
Suggest that they bunch the sheet of paper up into a ball and drop it from the same height. They
will find that the ball of paper reaches the floor in less time than the sheet of paper.
7. Have students meet in their groups to discuss possible reasons for these results. They should
conclude that air resistance, a type of friction, is slowing down the feather and the sheet of paper.
8. Ask students what they think would happen if they performed the same experiment in a vacuum
tube, which has no air in it. (The feather would fall at the same rate of speed as a ball or a brick.)
9. Each student should write a report explaining the results of the experiments and drawing
conclusions regarding the effects of both gravity and air resistance on the acceleration of falling
objects. Encourage students to accompany their paragraphs with labeled drawings and diagrams.

Adaptations for Older Students:
Have students research and explain Newton’s three laws of motion. They should identify the law that
builds on Galileo’s experiments with gravity.

Discussion Questions:
1. Describe how the human body has adapted to the force of gravity on Earth over time. How might
it have evolved if gravity had not been present?
2. Compare and contrast the force of gravity on Earth with the force of gravity on one of the other
planets in our solar system. Which planet has a stronger gravitational force? What would be the
effects on astronauts’ bodies when visiting this planet for an extended period of time?
3. Describe the physical features on the Earth’s surface that were influenced by gravity during their
formation or that are influenced by it now. How would these features look if Earth’s gravitational
force were significantly weaker or stronger?
4. Discuss Newton’s Laws of Motion. Which law or laws involve the force of gravity? Give
examples of each law of motion that occurs in your everyday life.
5. A roller coaster is usually designed to give its riders the sense of defying the laws of gravity.
Sometimes the back car is moving slightly faster than the others, thanks to the acceleration due
to gravity, and at other times the first car is going slightly faster. With that in mind, which seat in
a roller coaster is the scariest? How might a roller coaster designer make a roller coaster that
gives the greatest sensation to the passengers?
6. Describe the gravity experiments conducted by Galileo, Newton, and Cavendish. How were
these experiments similar? How did these scientists build on each other’s research and
observations to make their discoveries?
Evaluations:
You can evaluate your students on their reports using the following three-point rubric:
• Three points: results accurately reported; illustrations or diagrams clearly labeled; conclusions
explained logically in well-written, well-organized paragraphs

• Two points: results adequately reported; illustrations or diagrams included; paragraphs lacking
in organization

• One point: reporting of results sketchy or inaccurate; no illustrations or diagrams; conclusions
lacking in logic; paragraphs poorly organized
You can ask your students to contribute to the assessment rubric by determining which results should be
reported and which conclusions explained.

Extensions:
Swinging Pendulums
One of Galileo’s key experiments involved observing pendulums. Using a variety of different lengths
and weights, he carefully noted each pendulum’s period (the amount of time it takes for a pendulum to
make one complete swing). Galileo’s observations allowed him to determine that the period of a
pendulum’s swing is affected by its length but not its weight—an observation that may run counter to
what students intuitively expect. To begin this activity, lead a class discussion about the fact that
scientists cannot rely on intuition alone, but must perform experiments to test their hypotheses. Ask your
students to replicate Galileo’s pendulum experiments using varying lengths of string with different
numbers of washers attached to the ends. Students should measure each pendulum’s length, weight, and
period, making sure that they keep the amplitude, or angle to which the pendulum is raised, consistent.
When their observations are complete, gather their data into a chart for easy reference.

Defying Gravity in Your Own Home
Considering recent developments in space programs around the world, it may not be long before humans
are able to live for a long time in outer space—not just astronauts, but families. Have your students
imagine that their own homes are going to be transported to an orbit around Earth; then ask them to
design a room that could exist in a microgravity environment in outer space. The students’ descriptions
should be detailed—how, for example, will they prevent food from floating up off kitchen plates? How
will they stay in bed while sleeping? You can start by brainstorming a list of common activities that are
performed in each room of a standard house; then make sure that students take all of those needs into
consideration. If time permits, students can build a model of their newly designed room. You can even
divide students into groups and have each group work together to design a model outer-space house.

Suggested Readings:

Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher
Richard Feynman. Addison-Wesley Publishing Company, 1995.
This witty discussion of gravity, written without equations and technical jargon, is an ideal introduction
to the concept written by one of the most admired and accessible scientists of our time.

The Character of Physical Law
Richard Feynman. MIT Press, 1994.
Fascinating writing by a truly great scientist—gravitation is Richard Feynman’s principal law in this